Finite Group Databasebeta

← C2×#72317357 #72317618

Subgroups — C2×#72317357 #72317618

Order 2048.

At least 8735 conjugacy classes of subgroups; only the 2544 normal subgroups are shown.

The subgroup lattice has 695 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#146478C211yesmaximal, characteristic, complemented
2C2×#146463C211yesmaximal, characteristic, complemented
3C2×#359556C211yesmaximal, characteristic, complemented
4C2×#10574299C211yesmaximal, characteristic, complemented
5C2×#146655C214yesmaximal, complemented
6C2×#494606C214yesmaximal, complemented
7C2×#359551C211yesmaximal, characteristic, complemented
8#72317357C2116yesmaximal, direct product factor
9C2×#493402C211yesmaximal, characteristic, complemented
10C2×#6437463C211yesmaximal, characteristic
11C2×#62811C2211yescharacteristic
12C2×#62811C2211yescharacteristic
13C2×#60387C2212yes—
14#10574299C2218yescomplemented
15C2×#60235C2214yes—
16C2×#60064C2211yescharacteristic
17C23×#408C2211yescharacteristic
18C2×#33369C2214yes—
19#6437463C418yes—
20#6437463C2218yes—
21C2×#23898C414yes—
22C2×#23897C414yes—
23C2×#21012C2212yes—
24C2×#20612C2212yescomplemented
25C22×#1791C2212yescomplemented
26C2×#20591C2211yescharacteristic
27C2×#20591C2211yescharacteristic
28C2×#20591C2211yescharacteristic
29#494606C22132yescomplemented
30#493402C2218yescomplemented
31C2×#12579C2214yescomplemented
32C22×#1392C2214yescomplemented
33#359556C2218yescomplemented
34#359551C2218yescomplemented
35C2×#10756C2212yescomplemented
36C2×#10747C2212yescomplemented
37#146655C22132yescomplemented
38#146478C2218yescomplemented
39#146463C2218yescomplemented
40C22×#585D411yescharacteristic
41C22×#585C2311yescharacteristic
42C24×#41C2311yescharacteristic
43C22×#568D411yescharacteristic
44C22×#568D411yescharacteristic
45C24×M16D411yescharacteristic
46C25×C8D411yescharacteristic
47#62811C2×C414yes—
48#62811C2×C414yes—
49#62811D414yes—
50#62811D414yes—
51#62811C2314yes—
52#62811C2314yes—
53C2×#3487C2×C412yes—
54C2×#3486D412yes—
55C2×#3485C2×C412yes—
56C2×#3485D412yes—
57C2×#3484C2×C412yes—
58C2×#3484C2×C412yes—
59C2×#3449C2312yes—
60C22×#525D412yes—
61C2×#3428D411yescharacteristic
62C2×#3428C2311yescharacteristic
63#60387C2×C418yes—
64#60387C2318yes—
65C2×#3019C2×C418yes—
66#60235D4116yescomplemented
67#60235C23116yes—
68C2×#2980D418yescomplemented
69C2×#2979D418yescomplemented
70C22×#413C2312yes—
71C22×#413C2312yes—
72C22×#413C2312yes—
73#60064D414yes—
74#60064C2314yes—
75C2×#2879C2312yes—
76C22×#408D412yes—
77C22×#408D414yes—
78C22×#408C2314yes—
79C22×#408C2312yes—
80C22×#407D412yes—
81#33369C23116yes—
82#23898C2×C4132yes—
83#23897C2×C4132yes—
84#21012C2×C418yes—
85#21012C2318yes—
86C2×#1911C2×C418yes—
87#20612C2318yescomplemented
88C2×#1791C2318yescomplemented
89#20591C2×C414yes—
90#20591C2314yes—
91#20591C2314yes—
92#20591C2314yes—
93C2×#1785C2×C412yes—
94C2×#1783C2×C412yes—
95#12579C23116yescomplemented
96C2×#1392C23116yescomplemented
97#10756C2318yescomplemented
98#10747C2318yescomplemented
99C2×#585C22⋊C414yes—
100C2×#585C22×C412yes—
101C2×#585C2×D414yes—
102C2×#585C2412yes—
103C22×2−1+4C22⋊C412yes—
104C22×H(5,𝔽2)C22⋊C412yes—
105C22×H(5,𝔽2)C22×C412yes—
106C23×#41C22×C411yescharacteristic
107C23×#41C22×C412yes—
108C23×#41C2×D412yes—
109C23×#41C2×D411yescharacteristic
110C23×#41C2×D412yes—
111C23×#41C2×D411yescharacteristic
112C23×#41C2×D412yes—
113C23×#41C2×D411yescharacteristic
114C23×#41C2×D411yescharacteristic
115C23×#41C2×D412yes—
116C23×#41C2×D412yes—
117C23×#41#4111yescharacteristic
118C23×#41#4111yescharacteristic
119C23×#41#4112yes—
120C23×#41#4112yes—
121C23×#41C2412yes—
122C23×#41C2411yescharacteristic
123C24×Q8C2×D411yescharacteristic
124C24×D4C22×C411yescharacteristic
125C24×D4#4111yescharacteristic
126C24×D4#4111yescharacteristic
127C25×C4C2×D411yescharacteristic
128C25×C4C2×D411yescharacteristic
129C25×C4C2×D411yescharacteristic
130C2×#568C2×D414yes—
131C2×#568C2×D414yes—
132C23×M16C2×D414yes—
133C23×M16C2×D412yes—
134C23×M16C2×D412yes—
135C23×M16C2×D412yes—
136C24×C8C2×D414yes—
137C24×C8C2×D412yes—
138#3487C22⋊C418yes—
139#3487C22×C418yes—
140#3486C22⋊C418yes—
141#3486C2×D418yes—
142#3485C22⋊C418yes—
143#3485C22×C418yes—
144#3485C2×D418yes—
145#3484C22⋊C418yes—
146#3484C22×C418yes—
147#3484C22×C418yes—
148#3449C22×C414yes—
149#3449C2×D414yes—
150#3449C2×D418yes—
151#3449C2×D414yes—
152#3449#4118yes—
153#3449C2414yes—
154C2×#536C2×D414yes—
155C2×#536#4114yes—
156C2×#535C22×C414yes—
157C2×#535#4114yes—
158C2×#532C2×D418yes—
159C2×#525C22⋊C414yes—
160C2×#525C22⋊C414yes—
161C2×#525C22⋊C418yes—
162C2×#525C2×D418yes—
163#3428C22⋊C414yes—
164#3428C22×C412yes—
165#3428C2×D414yes—
166#3428C2412yes—
167C2×#519C22⋊C412yes—
168C2×#518C22⋊C412yes—
169C2×#518C22×C412yes—
170C22×#117C2×D412yes—
171#3019C22×C4132yes—
172#2980C2×D4132yescomplemented
173#2979C2×D4132yescomplemented
174C2×#413C22×C414yes—
175C2×#413C2414yes—
176C2×#413C2414yes—
177C2×#413C2414yes—
178C22×#100C22×C414yes—
179#2879C2×D418yes—
180#2879C2×D414yes—
181#2879C2414yes—
182C2×#408C2×D418yes—
183C2×#408C2×D414yes—
184C2×#408C2×D414yes—
185C2×#408C2×D418yes—
186C2×#408C2×D418yes—
187C2×#408C2×D414yes—
188C2×#408C2414yes—
189C2×#407C2×D418yes—
190#1911C22×C4132yes—
191#1785C22×C418yes—
192#1783C22×C418yes—
193C26C4×D411yescharacteristic
194C26C4×D411yescharacteristic
195C26#12311yescharacteristic
196C2×2−1+4C2×C22⋊C418yes—
197C2×H(5,𝔽2)C2×C22⋊C418yes—
198C2×H(5,𝔽2)C23×C414yes—
199C22×#41C2×C22⋊C414yes—
200C22×#41C2×C22⋊C414yes—
201C22×#41C2×C22⋊C412yes—
202C22×#41C2×C22⋊C412yes—
203C22×#41C2×C22⋊C412yes—
204C22×#41C4×D412yes—
205C22×#41C4×D412yes—
206C22×#41C4×D412yes—
207C22×#41C4×D412yes—
208C22×#41C4×D412yes—
209C22×#41C4×D412yes—
210C22×#41#12014yes—
211C22×#41#12014yes—
212C22×#41#12012yes—
213C22×#41#12012yes—
214C22×#41#12012yes—
215C22×#41#12112yes—
216C22×#41#12112yes—
217C22×#41#12112yes—
218C22×#41#12112yes—
219C22×#41#12112yes—
220C22×#41#12112yes—
221C22×#41#12314yes—
222C22×#41#12312yes—
223C22×#41#12312yes—
224C22×#41#12312yes—
225C22×#41C23×C412yes—
226C22×#41C23×C411yescharacteristic
227C22×#41C22×D414yes—
228C22×#41C22×D412yes—
229C22×#41C22×D411yescharacteristic
230C22×#41C22×D414yes—
231C22×#41C22×D414yes—
232C22×#41C22×D412yes—
233C22×#41C22×D411yescharacteristic
234C22×#41C22×D412yes—
235C22×#41C22×D412yes—
236C22×#41C22×D411yescharacteristic
237C22×#41C22×D411yescharacteristic
238C22×#41C2×#4112yes—
239C22×#41C2×#4112yes—
240C22×#41C2×#4111yescharacteristic
241C22×#41C2×#4111yescharacteristic
242C22×#41C2×#4114yes—
243C22×#41C2×#4114yes—
244C22×#41C2511yescharacteristic
245C23×Q8C2×C22⋊C411yescharacteristic
246C23×Q8C2×C22⋊C412yes—
247C23×Q8#12111yescharacteristic
248C23×Q8#12111yescharacteristic
249C23×Q8#12112yes—
250C23×Q8#12112yes—
251C23×Q8#12312yes—
252C23×Q8C22×D412yes—
253C23×Q8C22×D411yescharacteristic
254C23×D4C2×C22⋊C411yescharacteristic
255C23×D4C2×C22⋊C412yes—
256C23×D4C4×D411yescharacteristic
257C23×D4C4×D411yescharacteristic
258C23×D4C4×D411yescharacteristic
259C23×D4C4×D411yescharacteristic
260C23×D4C4×D412yes—
261C23×D4C4×D412yes—
262C23×D4C4×D412yes—
263C23×D4C4×D412yes—
264C23×D4#12111yescharacteristic
265C23×D4#12111yescharacteristic
266C23×D4#12112yes—
267C23×D4#12112yes—
268C23×D4#12312yes—
269C23×D4#12311yescharacteristic
270C23×D4#12311yescharacteristic
271C23×D4#12312yes—
272C23×D4#12312yes—
273C23×D4C23×C412yes—
274C23×D4C23×C411yescharacteristic
275C23×D4C2×#4112yes—
276C23×D4C2×#4112yes—
277C23×D4C2×#4111yescharacteristic
278C23×D4C2×#4111yescharacteristic
279C24×C4C2×C22⋊C411yescharacteristic
280C24×C4C2×C22⋊C411yescharacteristic
281C24×C4C2×C22⋊C412yes—
282C24×C4C4×D411yescharacteristic
283C24×C4C4×D412yes—
284C24×C4C4×D411yescharacteristic
285C24×C4C4×D412yes—
286C24×C4#12011yescharacteristic
287C24×C4#12011yescharacteristic
288C24×C4#12011yescharacteristic
289C24×C4#12012yes—
290C24×C4#12011yescharacteristic
291C24×C4#12012yes—
292C24×C4#12012yes—
293C24×C4#12111yescharacteristic
294C24×C4#12111yescharacteristic
295C24×C4#12112yes—
296C24×C4#12111yescharacteristic
297C24×C4#12111yescharacteristic
298C24×C4#12112yes—
299C24×C4#12311yescharacteristic
300C24×C4#12312yes—
301C24×C4C22×D412yes—
302C24×C4C22×D411yescharacteristic
303C24×C4C22×D411yescharacteristic
304C24×C4C22×D411yescharacteristic
305C24×C4C22×D412yes—
306C24×C4C22×D412yes—
307C22×M16#12014yes—
308C22×M16#12014yes—
309C22×M16#12014yes—
310C22×M16#12014yes—
311C22×M16#12014yes—
312C22×M16C22×D414yes—
313C22×M16C22×D414yes—
314C22×M16C22×D414yes—
315C23×C8#12014yes—
316C23×C8#12012yes—
317C23×C8#12012yes—
318C23×C8#12014yes—
319C23×C8C22×D414yes—
320#536C2×C22⋊C418yes—
321#536C4×D418yes—
322#536#121116yes—
323#536#12118yes—
324#536#12318yes—
325#536C22×D418yes—
326#536C2×#4118yes—
327#535C2×C22⋊C418yes—
328#535C4×D4116yes—
329#535C4×D418yes—
330#535#12118yes—
331#535#12318yes—
332#535C23×C418yes—
333#535C2×#4118yes—
334#532C4×D4116yes—
335#532#120116yes—
336#532#121116yes—
337#532C22×D4116yes—
338C2×C4⋊Q8#12118yes—
339C2×#127C4×D418yes—
340C2×#124C4×D418yes—
341C2×#124#12118yes—
342#525C2×C22⋊C4116yes—
343#525C2×C22⋊C4116yes—
344#519C2×C22⋊C418yes—
345#518C2×C22⋊C418yes—
346#518C23×C414yes—
347C2×#117C2×C22⋊C414yes—
348C2×#117C2×C22⋊C414yes—
349C2×#117#12014yes—
350C2×#117#12314yes—
351C2×#117#12314yes—
352C2×#117C22×D414yes—
353C22×C42#12014yes—
354C2×#100C23×C418yes—
355#408#12018yes—
356#408#12018yes—
357#408#120116yes—
358#408C22×D418yes—
359#408C22×D418yes—
360#408C22×D4116yes—
361C25#38611yescharacteristic
362C25#38611yescharacteristic
363C25#38611yescharacteristic
364C25#38612yes—
365C25#38611yescharacteristic
366C25#38612yes—
367C25#38612yes—
368C25C2×C4×D412yes—
369C25C2×C4×D411yescharacteristic
370C25C2×C4×D411yescharacteristic
371C25C2×C4×D412yes—
372C25C2×#12311yescharacteristic
373C25C2×#12312yes—
374C2×#41#38618yes—
375C2×#41#38618yes—
376C2×#41C22×C22⋊C418yes—
377C2×#41C2×C4×D414yes—
378C2×#41C2×C4×D414yes—
379C2×#41C2×#12018yes—
380C2×#41C2×#12014yes—
381C2×#41C2×#12014yes—
382C2×#41C2×#12014yes—
383C2×#41C2×#12114yes—
384C2×#41C2×#12114yes—
385C2×#41C2×#12314yes—
386C2×#41#52514yes—
387C2×#41#52514yes—
388C2×#41#52514yes—
389C2×#41#52514yes—
390C2×#41#52514yes—
391C2×#41#52514yes—
392C2×#41C23×D414yes—
393C2×#41C22×#4114yes—
394C22×Q8#38614yes—
395C22×Q8#38614yes—
396C22×Q8#38612yes—
397C22×Q8#38612yes—
398C22×Q8#38612yes—
399C22×Q8C22×C22⋊C412yes—
400C22×Q8C22×C22⋊C411yescharacteristic
401C22×Q8C2×#12114yes—
402C22×Q8C2×#12114yes—
403C22×Q8C2×#12112yes—
404C22×Q8C2×#12112yes—
405C22×Q8C2×#12111yescharacteristic
406C22×Q8C2×#12111yescharacteristic
407C22×Q8C2×#12314yes—
408C22×Q8C23×D411yescharacteristic
409C22×D4#38612yes—
410C22×D4#38612yes—
411C22×D4#38612yes—
412C22×D4#38612yes—
413C22×D4#38612yes—
414C22×D4#38612yes—
415C22×D4#38612yes—
416C22×D4#38612yes—
417C22×D4#38612yes—
418C22×D4#38614yes—
419C22×D4#38614yes—
420C22×D4C22×C22⋊C412yes—
421C22×D4C22×C22⋊C411yescharacteristic
422C22×D4C2×C4×D412yes—
423C22×D4C2×C4×D412yes—
424C22×D4C2×C4×D412yes—
425C22×D4C2×C4×D412yes—
426C22×D4C2×C4×D414yes—
427C22×D4C2×C4×D414yes—
428C22×D4C2×C4×D411yescharacteristic
429C22×D4C2×C4×D411yescharacteristic
430C22×D4C2×C4×D411yescharacteristic
431C22×D4C2×C4×D411yescharacteristic
432C22×D4C2×#12112yes—
433C22×D4C2×#12112yes—
434C22×D4C2×#12111yescharacteristic
435C22×D4C2×#12111yescharacteristic
436C22×D4C2×#12314yes—
437C22×D4C2×#12312yes—
438C22×D4C2×#12312yes—
439C22×D4C2×#12311yescharacteristic
440C22×D4C2×#12311yescharacteristic
441C22×D4#52514yes—
442C22×D4#52514yes—
443C22×D4#52514yes—
444C22×D4#52514yes—
445C22×D4C24×C411yescharacteristic
446C22×D4C22×#4111yescharacteristic
447C22×D4C22×#4111yescharacteristic
448C23×C4#38611yescharacteristic
449C23×C4#38612yes—
450C23×C4#38611yescharacteristic
451C23×C4#38611yescharacteristic
452C23×C4#38612yes—
453C23×C4#38612yes—
454C23×C4#38612yes—
455C23×C4#38612yes—
456C23×C4#38612yes—
457C23×C4#38611yescharacteristic
458C23×C4#38612yes—
459C23×C4#38612yes—
460C23×C4#38612yes—
461C23×C4#38612yes—
462C23×C4#38612yes—
463C23×C4#38612yes—
464C23×C4#38612yes—
465C23×C4B(4,𝔽2)12yes—
466C23×C4B(4,𝔽2)12yes—
467C23×C4B(4,𝔽2)12yes—
468C23×C4B(4,𝔽2)12yes—
469C23×C4C22×C22⋊C411yescharacteristic
470C23×C4C22×C22⋊C411yescharacteristic
471C23×C4C22×C22⋊C412yes—
472C23×C4C22×C22⋊C412yes—
473C23×C4C2×C4×D412yes—
474C23×C4C2×C4×D411yescharacteristic
475C23×C4C2×C4×D411yescharacteristic
476C23×C4C2×C4×D412yes—
477C23×C4C2×#12012yes—
478C23×C4C2×#12012yes—
479C23×C4C2×#12012yes—
480C23×C4C2×#12012yes—
481C23×C4C2×#12012yes—
482C23×C4C2×#12012yes—
483C23×C4C2×#12012yes—
484C23×C4C2×#12011yescharacteristic
485C23×C4C2×#12011yescharacteristic
486C23×C4C2×#12011yescharacteristic
487C23×C4C2×#12012yes—
488C23×C4C2×#12012yes—
489C23×C4C2×#12012yes—
490C23×C4C2×#12011yescharacteristic
491C23×C4C2×#12112yes—
492C23×C4C2×#12112yes—
493C23×C4C2×#12111yescharacteristic
494C23×C4C2×#12111yescharacteristic
495C23×C4C2×#12111yescharacteristic
496C23×C4C2×#12111yescharacteristic
497C23×C4C2×#12112yes—
498C23×C4C2×#12112yes—
499C23×C4C2×#12311yescharacteristic
500C23×C4C2×#12312yes—
501C23×C4C2×#12312yes—
502C23×C4C2×#12312yes—
503C23×C4#52512yes—
504C23×C4#52512yes—
505C23×C4#52512yes—
506C23×C4#52512yes—
507C23×C4C23×D411yescharacteristic
508C23×C4C23×D411yescharacteristic
509C23×C4C23×D411yescharacteristic
510C2×M16C2×#12018yes—
511C2×M16C2×#12018yes—
512C22×C8C2×#12014yes—
513C22×C8C2×#12014yes—
514C22×C8C2×#12018yes—
515C4⋊Q8#386116yes—
516C4⋊Q8C2×#121116yes—
517#127#386116yes—
518#127C2×C4×D4116yes—
519#124#386116yes—
520#124#386116yes—
521#124C2×C4×D4116yes—
522#124C2×#121116yes—
523#117#38618yes—
524#117#38618yes—
525#117C22×C22⋊C418yes—
526#117C2×#12318yes—
527C2×C42#38618yes—
528C2×C42#38618yes—
529C2×C42C2×#12018yes—
530C24#188912yes—
531C24#188912yes—
532C24C2×#38612yes—
533C24C2×#38612yes—
534C24C2×#38612yes—
535C24C2×#38611yescharacteristic
536C24C2×#38611yescharacteristic
537C24C2×#38611yescharacteristic
538C24C2×#38612yes—
539C24C2×#38611yescharacteristic
540C24C4×#12012yes—
541C24C4×#12012yes—
542C24C4×#12012yes—
543C24C4×#12012yes—
544C24#284912yes—
545C24#284912yes—
546C24C22×C4×D411yescharacteristic
547C24C22×C4×D411yescharacteristic
548C24C22×#12311yescharacteristic
549C2×Q8C2×#38618yes—
550C2×Q8C2×#38614yes—
551C2×Q8#284714yes—
552C2×Q8#284714yes—
553C2×Q8C22×#12114yes—
554C2×D4C2×#38618yes—
555C2×D4C2×#38614yes—
556C2×D4C4×#12014yes—
557C2×D4C4×#12014yes—
558C2×D4C4×#12014yes—
559C2×D4C4×#12014yes—
560C2×D4#284714yes—
561C2×D4#284714yes—
562C2×D4#284914yes—
563C2×D4#284914yes—
564C2×D4C22×C4×D414yes—
565C2×D4C2×#52514yes—
566C2×D4C2×#52514yes—
567C22×C4#188912yes—
568C22×C4#188914yes—
569C22×C4#188914yes—
570C22×C4#188912yes—
571C22×C4C2×#38612yes—
572C22×C4C2×#38612yes—
573C22×C4C2×#38612yes—
574C22×C4C2×#38611yescharacteristic
575C22×C4C2×#38611yescharacteristic
576C22×C4C2×#38611yescharacteristic
577C22×C4C2×#38612yes—
578C22×C4C2×#38612yes—
579C22×C4C2×#38612yes—
580C22×C4C2×#38612yes—
581C22×C4C2×#38612yes—
582C22×C4C2×#38611yescharacteristic
583C22×C4C4×#12012yes—
584C22×C4C4×#12012yes—
585C22×C4C4×#12012yes—
586C22×C4C4×#12012yes—
587C22×C4#284612yes—
588C22×C4#284612yes—
589C22×C4#284612yes—
590C22×C4#284611yescharacteristic
591C22×C4#284611yescharacteristic
592C22×C4#284712yes—
593C22×C4#284712yes—
594C22×C4#284712yes—
595C22×C4#284712yes—
596C22×C4#284712yes—
597C22×C4#284712yes—
598C22×C4#284712yes—
599C22×C4#284712yes—
600C22×C4#284912yes—
601C22×C4#284912yes—
602C22×C4#284912yes—
603C22×C4#284912yes—
604C22×C4#284912yes—
605C22×C4#284911yescharacteristic
606C22×C4#284911yescharacteristic
607C22×C4C2×B(4,𝔽2)14yes—
608C22×C4C2×B(4,𝔽2)14yes—
609C22×C4C2×B(4,𝔽2)11yescharacteristic
610C22×C4C2×B(4,𝔽2)11yescharacteristic
611C22×C4C2×B(4,𝔽2)11yescharacteristic
612C22×C4C2×B(4,𝔽2)11yescharacteristic
613C22×C4#302611yescharacteristic
614C22×C4#302611yescharacteristic
615C22×C4#302611yescharacteristic
616C22×C4#302611yescharacteristic
617C22×C4C23×C22⋊C411yescharacteristic
618C22×C4C22×#12012yes—
619C22×C4C22×#12012yes—
620C22×C4C22×#12012yes—
621C22×C4C22×#12011yescharacteristic
622C22×C4C22×#12111yescharacteristic
623C22×C4C22×#12111yescharacteristic
624C22×C4C22×#12312yes—
625C22×C4C2×#52512yes—
626C22×C4C2×#52512yes—
627C42C2×#386116yes—
628C23#1469411yescharacteristic
629C23#1469412yes—
630C23#1469412yes—
631C23#1469412yes—
632C23#1469411yescharacteristic
633C23C2×#188911yescharacteristic
634C23C2×#188914yes—
635C23C2×#188911yescharacteristic
636C23#2096011yescharacteristic
637C23#2096011yescharacteristic
638C23C22×#38611yescharacteristic
639C23C2×C4×#12012yes—
640C23C2×C4×#12012yes—
641C23C2×#284912yes—
642C2×C4#1469412yes—
643C2×C4#1469412yes—
644C2×C4#1469412yes—
645C2×C4#1469411yescharacteristic
646C2×C4#1469411yescharacteristic
647C2×C4C2×#188914yes—
648C2×C4C2×#188911yescharacteristic
649C2×C4C2×#188911yescharacteristic
650C2×C4#2096011yescharacteristic
651C2×C4#2096011yescharacteristic
652C2×C4#3289811yescharacteristic
653C2×C4#3289811yescharacteristic
654C2×C4#3289811yescharacteristic
655C2×C4#3289811yescharacteristic
656C2×C4#3289811yescharacteristic
657C2×C4#3289811yescharacteristic
658C2×C4#3289811yescharacteristic
659C2×C4#3289811yescharacteristic
660C2×C4#3302011yescharacteristic
661C2×C4#3302011yescharacteristic
662C2×C4#3302011yescharacteristic
663C2×C4#3302011yescharacteristic
664C2×C4#3302011yescharacteristic
665C2×C4#3302011yescharacteristic
666C2×C4#3302011yescharacteristic
667C2×C4#3302011yescharacteristic
668C2×C4C22×#38612yes—
669C2×C4C2×#284611yescharacteristic
670C2×C4C2×#284712yes—
671C2×C4C2×#284712yes—
672C2×C4C2×#284911yescharacteristic
673C2×C4C22×B(4,𝔽2)11yescharacteristic
674C2×C4C22×B(4,𝔽2)11yescharacteristic
675C2×C4C2×#302611yescharacteristic
676C2×C4C2×#302611yescharacteristic
677C22#39265811yescharacteristic
678C22#39265811yescharacteristic
679C22#39265811yescharacteristic
680C22#39265811yescharacteristic
681C22C2×#1469411yescharacteristic
682C22C22×#188911yescharacteristic
683C22C2×#2096011yescharacteristic
684C4#39265811yescharacteristic
685C4#39265811yescharacteristic
686C4#39265811yescharacteristic
687C4#39265811yescharacteristic
688C4C2×#3289811yescharacteristic
689C4C2×#3289811yescharacteristic
690C4C2×#3302011yescharacteristic
691C4C2×#3302011yescharacteristic
692C2C2×#39265811yescharacteristic
693C2#7231735712yesdirect product factor
subgroupG/H
centerC2×C4#32898
commutatorC22×D4C24×C4
Frattini, cosocleC22×#41C25
socleC22#392658
prime radicalC2×#6437463C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C24×#41 ◁ G
LECSG ▷ C22×#41 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#146478C2semidirect
2. C2×#146463C2semidirect
3. C2×#359556C2semidirect
4. C2×#10574299C2semidirect
5. C2×#146655C2semidirect
6. C2×#494606C2semidirect
7. C2×#359551C2semidirect
8. #72317357C2direct (N × H)
9. C2×#493402C2semidirect
14. #10574299C22semidirect
24. C2×#20612C22semidirect
25. C22×#1791C22semidirect
29. #494606C22semidirect
30. #493402C22semidirect
31. C2×#12579C22semidirect
32. C22×#1392C22semidirect
33. #359556C22semidirect
34. #359551C22semidirect
35. C2×#10756C22semidirect
36. C2×#10747C22semidirect
37. #146655C22semidirect
38. #146478C22semidirect
39. #146463C22semidirect
66. #60235D4semidirect
68. C2×#2980D4semidirect
69. C2×#2979D4semidirect
87. #20612C23semidirect
88. C2×#1791C23semidirect
95. #12579C23semidirect
96. C2×#1392C23semidirect
97. #10756C23semidirect
98. #10747C23semidirect
172. #2980C2×D4semidirect
173. #2979C2×D4semidirect
693. C2#72317357direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#1464782
C2×#1464632
C2×#3595562
C2×#105742992
C2×#1466552
C2×#4946062
C2×#3595512
#723173572
C2×#4934022
C2×#64374632