Finite Group Databasebeta

← C2×#72216677 #72217510

Subgroups — C2×#72216677 #72217510

Order 4096.

At least 6191 conjugacy classes of subgroups; only the 2347 normal subgroups are shown.

The subgroup lattice has 940 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#72216581C212yesmaximal, complemented
2C2×#72216518C212yesmaximal, complemented
3C2×#72216494C212yesmaximal, complemented
4#72216677C2116yesmaximal, direct product factor
5#72216581C22116yescomplemented
6C2×#72216543C212yesmaximal, complemented
7#72216543C22116yescomplemented
8#72216518C22116yescomplemented
9#72216494C22116yescomplemented
10C2×#72213016C211yesmaximal, characteristic, complemented
11C2×#6373967C2211yescharacteristic
12C2×#72214246C211yesmaximal, characteristic, complemented
13C2×#495527C2212yes—
14C2×#72214964C211yesmaximal, characteristic, complemented
15C2×#481264C2212yes—
16C2×#494044C2212yes—
17#72214964C2218yescomplemented
18C2×#72214315C211yesmaximal, characteristic, complemented
19C2×#126884C2212yes—
20C2×#495476C2212yes—
21#72214315C2218yescomplemented
22#72214246C2218yescomplemented
23C2×#126882C2212yes—
24C2×#72213530C211yesmaximal, characteristic
25C2×#7623096C2212yes—
26#72213530C418yescomplemented
27#72213530C2218yes—
28C2×#481279C2212yes—
29C2×#143151C414yescomplemented
30C2×#143148C414yescomplemented
31C2×#72213022C211yesmaximal, characteristic, complemented
32C2×#493177C2212yes—
33#72213022C2218yescomplemented
34#72213016C2218yescomplemented
35C2×#183351C2211yescharacteristic
36C2×#72211630C211yesmaximal, characteristic, complemented
37C2×#358697C2212yes—
38C22×C4×#442C2212yes—
39#72211630C2218yescomplemented
40C2×#206367C2211yescharacteristic
41C2×#206367C2211yescharacteristic
42C2×#109018C2211yescharacteristic
43C2×#109018C2211yescharacteristic
44C2×#126586C2212yes—
45C2×#126586C2211yescharacteristic
46C2×#126586C2211yescharacteristic
47C2×#358973C2211yescharacteristic
48C22×#23798C2211yescharacteristic
49C2×#353159C2211yescharacteristic
50C2×#60673C2311yescharacteristic
51C23×#442D414yes—
52C23×C4×D8C2312yes—
53#7623096C2×C418yescomplemented
54#7623096C2318yes—
55C2×#33670C2×C414yescomplemented
56C2×#33669C2×C414yescomplemented
57C2×#33418C2312yes—
58C2×#33418C2312yes—
59C2×#23798C2×C414yes—
60C2×#23798C2×C414yes—
61C2×#23798C2314yes—
62#6373967D414yescomplemented
63#6373967C2314yes—
64C2×#21734D412yescomplemented
65C2×#21706D412yescomplemented
66C2×#20826C2311yescharacteristic
67C2×C4×#442D418yes—
68C2×C4×#442C2318yes—
69C22×#1776D414yes—
70C22×C4×#106C2312yes—
71C22×#1744D411yescharacteristic
72C22×#1744D411yescharacteristic
73C22×#1744C2311yescharacteristic
74C22×#1744C2311yescharacteristic
75C22×C4×#97D411yescharacteristic
76C22×C4×#97C2311yescharacteristic
77C2×#17793C2311yescharacteristic
78C2×#17793C2311yescharacteristic
79C2×C44D411yescharacteristic
80#495527C2318yes—
81#495476C2318yes—
82#494044C2318yes—
83#493177D418yescomplemented
84#493177C2318yes—
85C2×#12594D414yescomplemented
86C2×C4×#347D414yescomplemented
87#481279C2×C418yescomplemented
88#481279C2318yes—
89C2×#11663C2×C418yescomplemented
90#481264C2318yes—
91#358973C2314yes—
92#358697C2318yes—
93#353159D414yes—
94#353159C2314yes—
95#206367C2×C414yescomplemented
96#206367C2314yes—
97#206367C2314yes—
98C2×#9853C2×C412yescomplemented
99C2×#9852C2×C412yescomplemented
100#183351C2314yes—
101#143151C2×C4132yescomplemented
102#143148C2×C4132yescomplemented
103#126884C2318yes—
104#126882C2318yes—
105#126586C2×C414yescomplemented
106#126586C2318yes—
107#126586C2314yes—
108#126586C2314yes—
109C2×#7143C2×C414yescomplemented
110#109018C2314yes—
111#109018C2314yes—
112C24×D8C2×D412yes—
113#60673C22×C412yes—
114#60673C2×D412yes—
115#60673#4112yes—
116#60673C2412yes—
117C2×#3170C22×C411yescharacteristic
118C2×#3170#4111yescharacteristic
119C2×#3169C22×C411yescharacteristic
120C2×#3169#4111yescharacteristic
121C2×#3160C2×D411yescharacteristic
122C2×#3147C2×D411yescharacteristic
123C22×#442C2×D4116yes—
124C22×C4×D8C22×C414yes—
125C22×C4×D8C22×C414yes—
126C22×C4×D8C2×D414yes—
127C22×C4×D8#4114yes—
128C22×C4×D8#4114yes—
129C22×C4×D8C2414yes—
130C23×#107C2×D412yes—
131C23×#106C2×D414yes—
132C23×#97C2×D414yes—
133C23×C4×C8C2×D411yescharacteristic
134C23×C4×C8C2×D411yescharacteristic
135C23×C4×C8C2×D411yescharacteristic
136C23×C4×C8C2411yescharacteristic
137C22×C43C2×D411yescharacteristic
138C22×C43C2×D411yescharacteristic
139C22×C43C2×D411yescharacteristic
140#33670C22×C4116yescomplemented
141#33669C22×C4116yescomplemented
142#33418C22×C414yes—
143#33418C2×D414yes—
144#33418C2×D414yes—
145#33418#4114yes—
146#33418C2414yes—
147#33418C2414yes—
148C2×#2163C22×C414yes—
149C2×#2163#4114yes—
150C2×C4×M32C2×D414yes—
151C2×C4×M32C2×D414yes—
152#23798C22×C4116yes—
153#21734C2×D418yescomplemented
154#21706C2×D418yescomplemented
155#20826C2×D412yes—
156#20826C2412yes—
157C2×#1848C2×D412yes—
158C2×#1776C2×D4116yes—
159C2×C4×#106C2×D414yes—
160C2×C4×#106C2414yes—
161C2×#1744C22×C412yes—
162C2×#1744C22×C412yes—
163C2×#1744C2×D412yes—
164C2×#1744C2×D414yes—
165C2×#1744C2×D414yes—
166C2×#1744C2×D412yes—
167C2×#1744#4112yes—
168C2×#1744#4112yes—
169C2×#1744C2412yes—
170C2×#1744C2412yes—
171C2×C4×#97C2×D414yes—
172C2×C4×#97C2×D412yes—
173C2×C4×#97C2×D412yes—
174C2×C4×#97C2×D412yes—
175C2×C4×#97C2×D412yes—
176C2×C4×#97C2×D414yes—
177C2×C4×#97C2×D414yes—
178C2×C4×#97C2×D412yes—
179C2×C4×#97#4112yes—
180C2×C4×#97#4112yes—
181C2×C4×#97C2412yes—
182#17793C22×C412yes—
183#17793#4112yes—
184#17793C2412yes—
185#17793C2412yes—
186C2×#1567#4112yes—
187C2×#1566C22×C412yes—
188C44C2×D414yes—
189#12594C2×D4116yescomplemented
190C4×#347C2×D4116yescomplemented
191#11663C22×C4132yescomplemented
192#9853C22×C418yescomplemented
193#9852C22×C418yescomplemented
194#7143C22×C4116yescomplemented
195C23×D8C4×D414yes—
196C23×D8C4×D414yes—
197C23×D8C22×D414yes—
198C24×C8#12012yes—
199C24×C8C22×D412yes—
200C23×C42#12012yes—
201C23×C42AGL(1,ℤ/8)12yes—
202C23×C42AGL(1,ℤ/8)12yes—
203C23×C42C22×D411yescharacteristic
204#3170C4×D412yescomplemented
205#3170C4×D412yescomplemented
206#3170C23×C412yes—
207#3170C2×#4112yes—
208#3169C4×D412yescomplemented
209#3169C4×D412yescomplemented
210#3169C23×C412yes—
211#3169C2×#4112yes—
212#3160C4×D412yescomplemented
213#3160C22×D412yes—
214C2×#500C4×D411yescharacteristic, complemented
215C2×#500C4×D411yescharacteristic, complemented
216#3147C4×D412yescomplemented
217#3147C22×D412yes—
218C2×#494C4×D411yescharacteristic, complemented
219C2×#493C4×D411yescharacteristic, complemented
220C2×C4×D8C4×D418yes—
221C2×C4×D8C4×D418yes—
222C2×C4×D8C23×C418yes—
223C2×C4×D8C2×#4118yes—
224C22×#107C4×D414yes—
225C22×#107C4×D414yes—
226C22×#107C22×D414yes—
227C22×#106C22×D418yes—
228C22×#97#12018yes—
229C22×#97#12014yes—
230C22×#97#12014yes—
231C22×#97#12018yes—
232C22×#97#12114yes—
233C22×#97#12118yes—
234C22×#97#12114yes—
235C22×#97C22×D418yes—
236C22×C4×C8C4×D412yes—
237C22×C4×C8C4×D412yes—
238C22×C4×C8#12012yes—
239C22×C4×C8#12112yes—
240C22×C4×C8#12112yes—
241C22×C4×C8#12712yes—
242C22×C4×C8#12711yescharacteristic
243C22×C4×C8#12711yescharacteristic
244C22×C4×C8AGL(1,ℤ/8)12yes—
245C22×C4×C8AGL(1,ℤ/8)12yes—
246C22×C4×C8AGL(1,ℤ/8)12yes—
247C22×C4×C8AGL(1,ℤ/8)12yes—
248C22×C4×C8AGL(1,ℤ/8)12yes—
249C22×C4×C8AGL(1,ℤ/8)12yes—
250C22×C4×C8C23×C411yescharacteristic
251C22×C4×C8C23×C411yescharacteristic
252C22×C4×C8C22×D412yes—
253C22×C4×C8C22×D412yes—
254C22×C4×C8C22×D412yes—
255C22×C4×C8C22×D411yescharacteristic
256C22×C4×C8C22×D411yescharacteristic
257C22×C4×C8C22×D411yescharacteristic
258C22×C4×C8C22×D412yes—
259C22×C4×C8C22×D412yes—
260C22×C4×C8C22×D412yes—
261C22×C4×C8C2×#4112yes—
262C22×C4×C8C2×#4112yes—
263C22×C4×C8C2×#4111yescharacteristic
264C22×C4×C8C2×#4111yescharacteristic
265C22×C4×C8C2×#4111yescharacteristic
266C22×C4×C8C2×#4111yescharacteristic
267C22×C4×C8C2×#4111yescharacteristic
268C22×C4×C8C2×#4111yescharacteristic
269C22×C4×C8C2×#4112yes—
270C22×C4×C8C2×#4112yes—
271C22×C4×C8C2×#4111yescharacteristic
272C22×C4×C8C2×#4111yescharacteristic
273C22×C4×C8C2511yescharacteristic
274C2×C43C4×D412yes—
275C2×C43C4×D412yes—
276C2×C43#12012yes—
277C2×C43#12112yes—
278C2×C43#12112yes—
279C2×C43#12712yes—
280C2×C43#12712yes—
281C2×C43AGL(1,ℤ/8)12yes—
282C2×C43AGL(1,ℤ/8)12yes—
283C2×C43AGL(1,ℤ/8)12yes—
284C2×C43AGL(1,ℤ/8)12yes—
285C2×C43C22×D412yes—
286C2×C43C22×D412yes—
287C2×C43C22×D412yes—
288#2163C4×D418yescomplemented
289#2163C4×D418yescomplemented
290#2163C23×C418yes—
291#2163C2×#4118yes—
292C4×M32C4×D418yescomplemented
293C4×M32C22×D418yes—
294C4×M32C22×D418yes—
295C2×#346C4×D418yescomplemented
296#1848C22×D414yes—
297#1744C4×D414yes—
298#1744C4×D414yes—
299#1744C23×C414yes—
300#1744C2×#4114yes—
301C4×#97#12014yes—
302C4×#97#12014yes—
303C4×#97#12018yes—
304C4×#97#12114yes—
305C4×#97#12114yes—
306C4×#97#12114yes—
307C4×#97#12114yes—
308C4×#97#12118yes—
309C4×#97#12714yes—
310C4×#97#12714yes—
311C4×#97C22×D414yes—
312C4×#97C22×D414yes—
313C4×#97C22×D414yes—
314C4×#97C2×#4114yes—
315#1567C2×#4114yes—
316#1566C23×C414yes—
317C24×C4C2×#12011yescharacteristic
318C24×C4C2×AGL(1,ℤ/8)11yescharacteristic
319C24×C4C2×AGL(1,ℤ/8)11yescharacteristic
320C22×D8C2×C4×D418yes—
321C23×C8#39212yes—
322C23×C8#39212yes—
323C23×C8#39214yes—
324C23×C8C2×C4×D412yes—
325C23×C8C2×C4×D412yes—
326C23×C8C2×#12012yes—
327C23×C8C2×#12014yes—
328C23×C8C2×#12012yes—
329C23×C8C2×#12012yes—
330C23×C8C2×#12112yes—
331C23×C8C2×#12112yes—
332C23×C8#52512yes—
333C23×C8#52512yes—
334C23×C8#52512yes—
335C23×C8#52512yes—
336C23×C8#53212yes—
337C23×C8#53212yes—
338C23×C8C23×D412yes—
339C22×C42#39214yes—
340C22×C42#39214yes—
341C22×C42#44214yes—
342C22×C42#44214yes—
343C22×C42C2×C4×D411yescharacteristic
344C22×C42C2×C4×D411yescharacteristic
345C22×C42C2×#12014yes—
346C22×C42C2×#12011yescharacteristic
347C22×C42C2×#12111yescharacteristic
348C22×C42C2×#12111yescharacteristic
349C22×C42#52511yescharacteristic
350C22×C42#52511yescharacteristic
351C22×C42#52511yescharacteristic
352C22×C42#52511yescharacteristic
353C22×C42C2×#12711yescharacteristic
354C22×C42C2×#12711yescharacteristic
355C22×C42#53211yescharacteristic
356C22×C42#53211yescharacteristic
357C22×C42C2×AGL(1,ℤ/8)14yes—
358C22×C42C2×AGL(1,ℤ/8)14yes—
359C22×C42C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C42C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C42C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C42C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C42C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C42C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C42C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C42C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C42C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C42C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C42#57511yescharacteristic
370C22×C42#57511yescharacteristic
371C22×C42#57511yescharacteristic
372C22×C42#57511yescharacteristic
373C22×C42C23×D411yescharacteristic
374#500C2×C4×D412yescomplemented
375#500C2×C4×D412yescomplemented
376#494C2×C4×D412yescomplemented
377#493C2×C4×D412yescomplemented
378C2×#107C2×C4×D418yes—
379C2×#97#39218yes—
380C2×#97#39218yes—
381C2×#97#39218yes—
382C2×#97#39218yes—
383C2×#97C2×#12018yes—
384C2×#97C2×#12018yes—
385C2×#97C2×#12118yes—
386C2×#97C2×#12118yes—
387C2×C4×C8#39212yes—
388C2×C4×C8#39212yes—
389C2×C4×C8#39214yes—
390C2×C4×C8#44214yes—
391C2×C4×C8#44214yes—
392C2×C4×C8#44214yes—
393C2×C4×C8#44214yes—
394C2×C4×C8C2×C4×D414yes—
395C2×C4×C8C2×C4×D411yescharacteristic
396C2×C4×C8C2×C4×D411yescharacteristic
397C2×C4×C8C2×C4×D412yes—
398C2×C4×C8C2×C4×D412yes—
399C2×C4×C8C2×C4×D412yes—
400C2×C4×C8C2×C4×D412yes—
401C2×C4×C8C2×C4×D411yescharacteristic
402C2×C4×C8C2×C4×D411yescharacteristic
403C2×C4×C8C2×C4×D411yescharacteristic
404C2×C4×C8C2×C4×D411yescharacteristic
405C2×C4×C8C2×C4×D412yes—
406C2×C4×C8C2×C4×D412yes—
407C2×C4×C8C4×#4111yescharacteristic
408C2×C4×C8C4×#4111yescharacteristic
409C2×C4×C8C4×#4111yescharacteristic
410C2×C4×C8C4×#4111yescharacteristic
411C2×C4×C8C2×#12012yes—
412C2×C4×C8C2×#12012yes—
413C2×C4×C8C2×#12114yes—
414C2×C4×C8C2×#12112yes—
415C2×C4×C8C2×#12112yes—
416C2×C4×C8C2×#12111yescharacteristic
417C2×C4×C8C2×#12111yescharacteristic
418C2×C4×C8#52512yes—
419C2×C4×C8#52512yes—
420C2×C4×C8#52512yes—
421C2×C4×C8#52512yes—
422C2×C4×C8#52512yes—
423C2×C4×C8#52512yes—
424C2×C4×C8#52512yes—
425C2×C4×C8#52512yes—
426C2×C4×C8#52512yes—
427C2×C4×C8#52512yes—
428C2×C4×C8#52512yes—
429C2×C4×C8#52512yes—
430C2×C4×C8#52512yes—
431C2×C4×C8#52512yes—
432C2×C4×C8#52512yes—
433C2×C4×C8#52512yes—
434C2×C4×C8#52512yes—
435C2×C4×C8#52511yescharacteristic
436C2×C4×C8#52511yescharacteristic
437C2×C4×C8#52912yes—
438C2×C4×C8#52912yes—
439C2×C4×C8#52912yes—
440C2×C4×C8#52912yes—
441C2×C4×C8#52911yescharacteristic
442C2×C4×C8#52911yescharacteristic
443C2×C4×C8#52911yescharacteristic
444C2×C4×C8#52911yescharacteristic
445C2×C4×C8C2×#12712yes—
446C2×C4×C8C2×#12712yes—
447C2×C4×C8C2×#12712yes—
448C2×C4×C8#53212yes—
449C2×C4×C8#53212yes—
450C2×C4×C8#53212yes—
451C2×C4×C8#53212yes—
452C2×C4×C8#53212yes—
453C2×C4×C8#53211yescharacteristic
454C2×C4×C8#53211yescharacteristic
455C2×C4×C8#53211yescharacteristic
456C2×C4×C8#53211yescharacteristic
457C2×C4×C8#53212yes—
458C2×C4×C8#53212yes—
459C2×C4×C8C2×AGL(1,ℤ/8)14yes—
460C2×C4×C8C2×AGL(1,ℤ/8)14yes—
461C2×C4×C8C2×AGL(1,ℤ/8)14yes—
462C2×C4×C8C24×C411yescharacteristic
463C2×C4×C8C23×D411yescharacteristic
464C2×C4×C8C23×D412yes—
465C2×C4×C8C22×#4111yescharacteristic
466C2×C4×C8C22×#4112yes—
467C2×C4×C8C22×#4111yescharacteristic
468C2×C4×C8C22×#4111yescharacteristic
469C2×C4×C8C22×#4112yes—
470C2×C4×C8C22×#4111yescharacteristic
471C43#39214yes—
472C43#39214yes—
473C43#44214yes—
474C43#44214yes—
475C43C2×C4×D414yes—
476C43C2×#12114yes—
477C43C2×#12714yes—
478C43C2×AGL(1,ℤ/8)14yes—
479#346C2×C4×D4116yescomplemented
480C25#300311yescharacteristic
481C23×C4C4×#12011yescharacteristic
482C23×C4C4×#12011yescharacteristic
483C23×C4C2×#39211yescharacteristic
484C23×C4C2×#39211yescharacteristic
485C23×C4#238811yescharacteristic
486C23×C4#238811yescharacteristic
487C23×C4C2×#44211yescharacteristic
488C23×C4C2×#44211yescharacteristic
489C23×C4C4×AGL(1,ℤ/8)11yescharacteristic
490C23×C4C4×AGL(1,ℤ/8)11yescharacteristic
491C23×C4#300311yescharacteristic
492C23×C4#300311yescharacteristic
493C23×C4#300311yescharacteristic
494C23×C4#300311yescharacteristic
495C23×C4#300311yescharacteristic
496C23×C4#300611yescharacteristic
497C23×C4#300611yescharacteristic
498C23×C4#300611yescharacteristic
499C23×C4#300611yescharacteristic
500C23×C4#303811yescharacteristic
501C23×C4#303811yescharacteristic
502C23×C4#303811yescharacteristic
503C23×C4#303811yescharacteristic
504C23×C4#310911yescharacteristic
505C23×C4#310911yescharacteristic
506C23×C4#310911yescharacteristic
507C23×C4#310911yescharacteristic
508C23×C4#311411yescharacteristic
509C23×C4#311411yescharacteristic
510C23×C4#311511yescharacteristic
511C23×C4#311511yescharacteristic
512C23×C4#315111yescharacteristic
513C23×C4#315111yescharacteristic
514C23×C4#315111yescharacteristic
515C23×C4#315111yescharacteristic
516C23×C4#318011yescharacteristic
517C23×C4#318011yescharacteristic
518C23×C4#318411yescharacteristic
519C23×C4#318411yescharacteristic
520C23×C4C22×#12011yescharacteristic
521C23×C4C22×AGL(1,ℤ/8)11yescharacteristic
522C23×C4C22×AGL(1,ℤ/8)11yescharacteristic
523C22×C8C4×#12012yes—
524C22×C8C4×#12012yes—
525C22×C8C4×#12012yes—
526C22×C8C4×#12012yes—
527C22×C8C4×#12012yes—
528C22×C8C4×#12012yes—
529C22×C8C4×#12112yes—
530C22×C8C4×#12112yes—
531C22×C8C4×#12112yes—
532C22×C8C4×#12112yes—
533C22×C8C2×#39214yes—
534C22×C8C2×#39214yes—
535C22×C8C2×#39212yes—
536C22×C8C2×#39212yes—
537C22×C8#238812yes—
538C22×C8#238812yes—
539C22×C8#238812yes—
540C22×C8#238812yes—
541C22×C8#238812yes—
542C22×C8#238812yes—
543C22×C8#239212yes—
544C22×C8#239212yes—
545C22×C8#239212yes—
546C22×C8#239212yes—
547C22×C8C22×C4×D412yes—
548C22×C8C22×#12012yes—
549C22×C8C22×#12112yes—
550C22×C8C2×#52512yes—
551C22×C8C2×#52512yes—
552C22×C8C2×#53212yes—
553C2×C42#2010116yes—
554C2×C42C4×#12011yescharacteristic
555C2×C42C4×#12011yescharacteristic
556C2×C42C4×#12111yescharacteristic
557C2×C42C4×#12111yescharacteristic
558C2×C42C4×#12111yescharacteristic
559C2×C42C4×#12111yescharacteristic
560C2×C42C4×#12711yescharacteristic
561C2×C42C4×#12711yescharacteristic
562C2×C42C4×#12711yescharacteristic
563C2×C42C4×#12711yescharacteristic
564C2×C42C2×#39218yes—
565C2×C42C2×#39211yescharacteristic
566C2×C42C2×#39211yescharacteristic
567C2×C42#238811yescharacteristic
568C2×C42#238811yescharacteristic
569C2×C42#239211yescharacteristic
570C2×C42#239211yescharacteristic
571C2×C42#239211yescharacteristic
572C2×C42#239211yescharacteristic
573C2×C42#239711yescharacteristic
574C2×C42#239711yescharacteristic
575C2×C42#239711yescharacteristic
576C2×C42#239711yescharacteristic
577C2×C42C2×#44218yes—
578C2×C42C2×#44211yescharacteristic
579C2×C42C2×#44211yescharacteristic
580C2×C42C2×#44211yescharacteristic
581C2×C42C2×#44211yescharacteristic
582C2×C42C2×#44211yescharacteristic
583C2×C42C2×#44211yescharacteristic
584C2×C42C4×AGL(1,ℤ/8)11yescharacteristic
585C2×C42C4×AGL(1,ℤ/8)11yescharacteristic
586C2×C42C4×AGL(1,ℤ/8)11yescharacteristic
587C2×C42C4×AGL(1,ℤ/8)11yescharacteristic
588C2×C42C4×AGL(1,ℤ/8)11yescharacteristic
589C2×C42C4×AGL(1,ℤ/8)11yescharacteristic
590C2×C42#300311yescharacteristic
591C2×C42#300311yescharacteristic
592C2×C42#300611yescharacteristic
593C2×C42#300611yescharacteristic
594C2×C42#300611yescharacteristic
595C2×C42#300611yescharacteristic
596C2×C42#303611yescharacteristic
597C2×C42#303611yescharacteristic
598C2×C42#303611yescharacteristic
599C2×C42#303611yescharacteristic
600C2×C42#303611yescharacteristic
601C2×C42#303611yescharacteristic
602C2×C42#303611yescharacteristic
603C2×C42#303611yescharacteristic
604C2×C42#303811yescharacteristic
605C2×C42#303811yescharacteristic
606C2×C42#303811yescharacteristic
607C2×C42#303811yescharacteristic
608C2×C42#310911yescharacteristic
609C2×C42#310911yescharacteristic
610C2×C42#310911yescharacteristic
611C2×C42#310911yescharacteristic
612C2×C42#310911yescharacteristic
613C2×C42#310911yescharacteristic
614C2×C42#310911yescharacteristic
615C2×C42#310911yescharacteristic
616C2×C42#310911yescharacteristic
617C2×C42#310911yescharacteristic
618C2×C42#310911yescharacteristic
619C2×C42#310911yescharacteristic
620C2×C42#311411yescharacteristic
621C2×C42#311411yescharacteristic
622C2×C42#311411yescharacteristic
623C2×C42#311411yescharacteristic
624C2×C42#311411yescharacteristic
625C2×C42#311411yescharacteristic
626C2×C42#311511yescharacteristic
627C2×C42#311511yescharacteristic
628C2×C42#311511yescharacteristic
629C2×C42#311511yescharacteristic
630C2×C42#311511yescharacteristic
631C2×C42#311511yescharacteristic
632C2×C42#315111yescharacteristic
633C2×C42#315111yescharacteristic
634C2×C42#315111yescharacteristic
635C2×C42#315111yescharacteristic
636C2×C42#315111yescharacteristic
637C2×C42#315111yescharacteristic
638C2×C42#315111yescharacteristic
639C2×C42#315111yescharacteristic
640C2×C42#315311yescharacteristic
641C2×C42#315311yescharacteristic
642C2×C42#315311yescharacteristic
643C2×C42#315311yescharacteristic
644C2×C42#318011yescharacteristic
645C2×C42#318011yescharacteristic
646C2×C42#318011yescharacteristic
647C2×C42#318011yescharacteristic
648C2×C42#318011yescharacteristic
649C2×C42#318011yescharacteristic
650C2×C42#318411yescharacteristic
651C2×C42#318411yescharacteristic
652C2×C42#318411yescharacteristic
653C2×C42#318411yescharacteristic
654C2×C42#318411yescharacteristic
655C2×C42#318411yescharacteristic
656C2×C42C22×C4×D411yescharacteristic
657C2×C42C22×#12111yescharacteristic
658C2×C42C2×#52511yescharacteristic
659C2×C42C2×#52511yescharacteristic
660C2×C42C22×#12711yescharacteristic
661C2×C42C2×#53211yescharacteristic
662C2×C42C22×AGL(1,ℤ/8)11yescharacteristic
663C2×C42C22×AGL(1,ℤ/8)11yescharacteristic
664C2×C42C22×AGL(1,ℤ/8)11yescharacteristic
665C2×C42C22×AGL(1,ℤ/8)11yescharacteristic
666C2×C42C2×#57511yescharacteristic
667C2×C42C2×#57511yescharacteristic
668C4×C8C4×#12012yes—
669C4×C8C4×#12012yes—
670C4×C8C4×#12012yes—
671C4×C8C4×#12012yes—
672C4×C8C4×#12112yes—
673C4×C8C4×#12112yes—
674C4×C8C4×#12112yes—
675C4×C8C4×#12112yes—
676C4×C8C4×#12111yescharacteristic
677C4×C8C4×#12111yescharacteristic
678C4×C8C4×#12111yescharacteristic
679C4×C8C4×#12111yescharacteristic
680C4×C8C4×#12712yes—
681C4×C8C4×#12712yes—
682C4×C8#238812yes—
683C4×C8#238812yes—
684C4×C8#238812yes—
685C4×C8#238812yes—
686C4×C8#239212yes—
687C4×C8#239212yes—
688C4×C8#239212yes—
689C4×C8#239212yes—
690C4×C8#239212yes—
691C4×C8#239212yes—
692C4×C8#239712yes—
693C4×C8#239712yes—
694C4×C8C2×#44218yes—
695C4×C8C22×C4×D411yescharacteristic
696C4×C8C22×C4×D412yes—
697C4×C8C2×C4×#4111yescharacteristic
698C4×C8C2×#52512yes—
699C4×C8C2×#52512yes—
700C4×C8C2×#52512yes—
701C4×C8C2×#52912yes—
702C4×C8C2×#52911yescharacteristic
703C4×C8C2×#53211yescharacteristic
704C4×C8C2×#53212yes—
705C24#2145211yescharacteristic
706C24#2145211yescharacteristic
707C24#2343011yescharacteristic
708C24#2343011yescharacteristic
709C24#2357311yescharacteristic
710C24#2357311yescharacteristic
711C24C2×#300311yescharacteristic
712C22×C4C4×#39211yescharacteristic
713C22×C4C4×#39211yescharacteristic
714C22×C4C4×#39211yescharacteristic
715C22×C4C4×#39211yescharacteristic
716C22×C4#2145211yescharacteristic
717C22×C4#2145211yescharacteristic
718C22×C4#2145211yescharacteristic
719C22×C4#2145211yescharacteristic
720C22×C4#2145211yescharacteristic
721C22×C4#2145211yescharacteristic
722C22×C4#2145211yescharacteristic
723C22×C4#2145211yescharacteristic
724C22×C4#2145211yescharacteristic
725C22×C4#2145211yescharacteristic
726C22×C4#2150311yescharacteristic
727C22×C4#2150311yescharacteristic
728C22×C4#2150311yescharacteristic
729C22×C4#2150311yescharacteristic
730C22×C4#2150311yescharacteristic
731C22×C4#2150311yescharacteristic
732C22×C4#2150311yescharacteristic
733C22×C4#2150311yescharacteristic
734C22×C4#2169011yescharacteristic
735C22×C4#2169011yescharacteristic
736C22×C4#2169011yescharacteristic
737C22×C4#2169011yescharacteristic
738C22×C4#2170111yescharacteristic
739C22×C4#2170111yescharacteristic
740C22×C4#2170111yescharacteristic
741C22×C4#2170111yescharacteristic
742C22×C4C2×#201018yes—
743C22×C4#2342811yescharacteristic
744C22×C4#2342811yescharacteristic
745C22×C4#2342811yescharacteristic
746C22×C4#2342811yescharacteristic
747C22×C4#2343011yescharacteristic
748C22×C4#2343011yescharacteristic
749C22×C4#2343011yescharacteristic
750C22×C4#2343011yescharacteristic
751C22×C4#2343011yescharacteristic
752C22×C4#2343011yescharacteristic
753C22×C4#2357311yescharacteristic
754C22×C4#2357311yescharacteristic
755C22×C4#2357311yescharacteristic
756C22×C4#2357311yescharacteristic
757C22×C4#2357311yescharacteristic
758C22×C4#2357311yescharacteristic
759C22×C4#2357311yescharacteristic
760C22×C4#2357311yescharacteristic
761C22×C4#2357311yescharacteristic
762C22×C4#2357311yescharacteristic
763C22×C4#2368211yescharacteristic
764C22×C4#2368211yescharacteristic
765C22×C4#2368211yescharacteristic
766C22×C4#2368211yescharacteristic
767C22×C4#2368211yescharacteristic
768C22×C4#2368211yescharacteristic
769C22×C4#2368211yescharacteristic
770C22×C4#2368211yescharacteristic
771C22×C4#2380211yescharacteristic
772C22×C4#2380211yescharacteristic
773C22×C4#2380211yescharacteristic
774C22×C4#2380211yescharacteristic
775C22×C4#2380611yescharacteristic
776C22×C4#2380611yescharacteristic
777C22×C4#2380611yescharacteristic
778C22×C4#2380611yescharacteristic
779C22×C4#3368818yes—
780C22×C4C2×C4×#12011yescharacteristic
781C22×C4C22×#39211yescharacteristic
782C22×C4C2×#238811yescharacteristic
783C22×C4C22×#44211yescharacteristic
784C22×C4C2×C4×AGL(1,ℤ/8)11yescharacteristic
785C22×C4C2×#300311yescharacteristic
786C22×C4C2×#300611yescharacteristic
787C22×C4C2×#300611yescharacteristic
788C22×C4C2×#303811yescharacteristic
789C22×C4C2×#303811yescharacteristic
790C22×C4C2×#311411yescharacteristic
791C22×C4C2×#311511yescharacteristic
792C22×C4C2×#310911yescharacteristic
793C22×C4C2×#310911yescharacteristic
794C22×C4C2×#315111yescharacteristic
795C22×C4C2×#315111yescharacteristic
796C22×C4C2×#318011yescharacteristic
797C22×C4C2×#318411yescharacteristic
798C2×C8C4×#39212yes—
799C2×C8C4×#39212yes—
800C2×C8C4×#39212yes—
801C2×C8C4×#39212yes—
802C2×C8C2×C4×#12012yes—
803C2×C8C2×C4×#12112yes—
804C2×C8C2×#238812yes—
805C2×C8C2×#239212yes—
806C42C4×#39211yescharacteristic
807C42C4×#39211yescharacteristic
808C42C4×#39211yescharacteristic
809C42C4×#39211yescharacteristic
810C42#2145211yescharacteristic
811C42#2145211yescharacteristic
812C42#2145211yescharacteristic
813C42#2145211yescharacteristic
814C42#2150311yescharacteristic
815C42#2150311yescharacteristic
816C42#2150311yescharacteristic
817C42#2150311yescharacteristic
818C42#2150311yescharacteristic
819C42#2150311yescharacteristic
820C42#2150311yescharacteristic
821C42#2150311yescharacteristic
822C42#2169011yescharacteristic
823C42#2169011yescharacteristic
824C42#2169011yescharacteristic
825C42#2169011yescharacteristic
826C42#2170111yescharacteristic
827C42#2170111yescharacteristic
828C42#2170111yescharacteristic
829C42#2170111yescharacteristic
830C42C2×#2010116yes—
831C42#2342811yescharacteristic
832C42#2342811yescharacteristic
833C42#2342811yescharacteristic
834C42#2342811yescharacteristic
835C42#2357311yescharacteristic
836C42#2357311yescharacteristic
837C42#2357311yescharacteristic
838C42#2357311yescharacteristic
839C42#2368211yescharacteristic
840C42#2368211yescharacteristic
841C42#2368211yescharacteristic
842C42#2368211yescharacteristic
843C42#2368211yescharacteristic
844C42#2368211yescharacteristic
845C42#2368211yescharacteristic
846C42#2368211yescharacteristic
847C42#2380211yescharacteristic
848C42#2380211yescharacteristic
849C42#2380211yescharacteristic
850C42#2380211yescharacteristic
851C42#2380611yescharacteristic
852C42#2380611yescharacteristic
853C42#2380611yescharacteristic
854C42#2380611yescharacteristic
855C42C2×C4×#12111yescharacteristic
856C42C2×C4×#12711yescharacteristic
857C42C2×#239211yescharacteristic
858C42C2×#239711yescharacteristic
859C42C22×#44211yescharacteristic
860C42C2×C4×AGL(1,ℤ/8)11yescharacteristic
861C42C2×#303611yescharacteristic
862C42C2×#303611yescharacteristic
863C42C2×#311411yescharacteristic
864C42C2×#311511yescharacteristic
865C42C2×#310911yescharacteristic
866C42C2×#310911yescharacteristic
867C42C2×#315111yescharacteristic
868C42C2×#315311yescharacteristic
869C42C2×#318011yescharacteristic
870C42C2×#318411yescharacteristic
871C23#23361014yes—
872C23#35904211yescharacteristic
873C23#35904211yescharacteristic
874C23#35904211yescharacteristic
875C23#35904211yescharacteristic
876C23#49573614yes—
877C23#49926314yes—
878C23C2×#2145211yescharacteristic
879C23C2×#2343011yescharacteristic
880C23C2×#2357311yescharacteristic
881C2×C4#23360814yes—
882C2×C4#23360814yes—
883C2×C4#23361014yes—
884C2×C4C4×#201014yes—
885C2×C4C4×#201014yes—
886C2×C4#35904211yescharacteristic
887C2×C4#35904211yescharacteristic
888C2×C4#35904211yescharacteristic
889C2×C4#35904211yescharacteristic
890C2×C4#35904211yescharacteristic
891C2×C4#35904211yescharacteristic
892C2×C4#35904211yescharacteristic
893C2×C4#35904211yescharacteristic
894C2×C4#35904211yescharacteristic
895C2×C4#35904211yescharacteristic
896C2×C4#35904211yescharacteristic
897C2×C4#35904211yescharacteristic
898C2×C4#49585014yes—
899C2×C4#49585014yes—
900C2×C4#49926314yes—
901C2×C4#49965614yes—
902C2×C4#49965614yes—
903C2×C4C2×C4×#39211yescharacteristic
904C2×C4C2×#2145211yescharacteristic
905C2×C4C2×#2150311yescharacteristic
906C2×C4C2×#2150311yescharacteristic
907C2×C4C2×#2169011yescharacteristic
908C2×C4C2×#2170111yescharacteristic
909C2×C4C22×#201014yes—
910C2×C4C2×#2342811yescharacteristic
911C2×C4C2×#2357311yescharacteristic
912C2×C4C2×#2368211yescharacteristic
913C2×C4C2×#2368211yescharacteristic
914C2×C4C2×#2380211yescharacteristic
915C2×C4C2×#2380611yescharacteristic
916C2×C4C2×#3368814yes—
917C22#7221165412yes—
918C22#7221165412yes—
919C22C2×#35904211yescharacteristic
920C22C2×#23361012yes—
921C22#7221664512yes—
922C22#7221664512yes—
923C22#7221664712yes—
924C22#7221664712yes—
925C22C2×#49573612yes—
926C22C2×#49926312yes—
927C4#7221165412yes—
928C4#7221165412yes—
929C4C2×C4×#201012yes—
930C4C2×#23360812yes—
931C4#7221664512yes—
932C4#7221664512yes—
933C4C2×#49585012yes—
934C4C2×#49965612yes—
935C2C2×#7221165411yescharacteristic
936C2#7221667714yesdirect product factor
937C2C2×#7221664511yescharacteristic
938C2C2×#7221664711yescharacteristic
subgroupG/H
centerC22×C4#23802
commutatorC2×C4×C8C24×C4
Frattini, cosocleC22×C4×C8C25
socleC23#359042
prime radicalC2×#72213530C2
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ C2×#353159 ◁ G
LECSG ▷ C22×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#72216581C2semidirect
2. C2×#72216518C2semidirect
3. C2×#72216494C2semidirect
4. #72216677C2direct (N × H)
5. #72216581C22semidirect
6. C2×#72216543C2semidirect
7. #72216543C22semidirect
8. #72216518C22semidirect
9. #72216494C22semidirect
10. C2×#72213016C2semidirect
12. C2×#72214246C2semidirect
14. C2×#72214964C2semidirect
17. #72214964C22semidirect
18. C2×#72214315C2semidirect
21. #72214315C22semidirect
22. #72214246C22semidirect
26. #72213530C4semidirect
29. C2×#143151C4semidirect
30. C2×#143148C4semidirect
31. C2×#72213022C2semidirect
33. #72213022C22semidirect
34. #72213016C22semidirect
36. C2×#72211630C2semidirect
39. #72211630C22semidirect
53. #7623096C2×C4semidirect
55. C2×#33670C2×C4semidirect
56. C2×#33669C2×C4semidirect
62. #6373967D4semidirect
64. C2×#21734D4semidirect
65. C2×#21706D4semidirect
83. #493177D4semidirect
85. C2×#12594D4semidirect
86. C2×C4×#347D4semidirect
87. #481279C2×C4semidirect
89. C2×#11663C2×C4semidirect
95. #206367C2×C4semidirect
98. C2×#9853C2×C4semidirect
99. C2×#9852C2×C4semidirect
101. #143151C2×C4semidirect
102. #143148C2×C4semidirect
105. #126586C2×C4semidirect
109. C2×#7143C2×C4semidirect
140. #33670C22×C4semidirect
141. #33669C22×C4semidirect
153. #21734C2×D4semidirect
154. #21706C2×D4semidirect
189. #12594C2×D4semidirect
190. C4×#347C2×D4semidirect
191. #11663C22×C4semidirect
192. #9853C22×C4semidirect
193. #9852C22×C4semidirect
194. #7143C22×C4semidirect
204. #3170C4×D4semidirect
205. #3170C4×D4semidirect
208. #3169C4×D4semidirect
209. #3169C4×D4semidirect
212. #3160C4×D4semidirect
214. C2×#500C4×D4semidirect
215. C2×#500C4×D4semidirect
216. #3147C4×D4semidirect
218. C2×#494C4×D4semidirect
219. C2×#493C4×D4semidirect
288. #2163C4×D4semidirect
289. #2163C4×D4semidirect
292. C4×M32C4×D4semidirect
295. C2×#346C4×D4semidirect
374. #500C2×C4×D4semidirect
375. #500C2×C4×D4semidirect
376. #494C2×C4×D4semidirect
377. #493C2×C4×D4semidirect
479. #346C2×C4×D4semidirect
936. C2#72216677direct (N × H)