Finite Group Databasebeta

← #72285659

Subgroups — #72285659

Order 2048.

At least 6091 conjugacy classes of subgroups; only the 1476 normal subgroups are shown.

The subgroup lattice has 608 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480245C211yesmaximal, characteristic, complemented
2#72285622C211yesmaximal, characteristic, complemented
3#72285391C218yesmaximal, complemented
4#72285266C214yesmaximal, complemented
5#72284815C212yesmaximal, complemented
6#72284781C212yesmaximal, complemented
7#72284501C214yesmaximal, complemented
8#72284275C218yesmaximal, complemented
9C22×#23986C211yesmaximal, characteristic
10C22×#3491C2211yescharacteristic
11C22×#2280C2211yescharacteristic
12C2×#23986C412yes—
13C2×#23986C412yes—
14C2×#23986C414yes—
15C2×#23986C414yes—
16C2×#23986C2212yes—
17C2×#23986C2212yes—
18C2×#23986C2214yes—
19C2×#23986C2214yes—
20C22×#2030C411yescharacteristic
21C22×#2029C411yescharacteristic
22C22×#2022C411yescharacteristic
23C22×#2021C411yescharacteristic
24#6386515C2214yescomplemented
25#6386514C2214yescomplemented
26#6374745C2212yescomplemented
27#6370928C2212yes—
28C22×#1820C2211yescharacteristic
29#6370175C2212yescomplemented
30C2×#17357C2212yes—
31#480245C2214yescomplemented
32#480245C2214yescomplemented
33C2×#11501C2212yescomplemented
34C2×#11501C2212yescomplemented
35#185309C2218yescomplemented
36#185303C2218yescomplemented
37#185297C2218yescomplemented
38#139646C22132yescomplemented
39#139627C22116yescomplemented
40#139626C22116yescomplemented
41#127221C2218yescomplemented
42#127219C2218yescomplemented
43#127189C2218yescomplemented
44C26×C4D411yescharacteristic
45C2×#3491C2×C412yes—
46C2×#3491C2×C414yes—
47C2×#3491C2312yes—
48C2×#3491C2314yes—
49C22×#543C2×C411yescharacteristic
50C22×#534C2×C411yescharacteristic
51C23×#117D411yescharacteristic
52C23×#117C2311yescharacteristic
53C2×#2920D412yescomplemented
54C2×#2920D412yescomplemented
55C2×#2280C2×C411yescharacteristic
56C2×#2280C2×C411yescharacteristic
57C2×#2280C2×C412yes—
58C2×#2280C2×C412yes—
59C2×#2280D412yes—
60C2×#2280D412yes—
61C2×#2280D411yescharacteristic
62C2×#2280D411yescharacteristic
63C2×#2280D412yes—
64C2×#2280D412yes—
65C2×#2280D411yescharacteristic
66C2×#2280D411yescharacteristic
67C2×#2280C2312yes—
68C2×#2280C2312yes—
69C2×#2280C2311yescharacteristic
70C2×#2280C2311yescharacteristic
71C22×#381C2×C411yescharacteristic
72C22×#381D411yescharacteristic
73C22×#379C2×C411yescharacteristic
74C22×#379D411yescharacteristic
75#23986C2×C418yes—
76#23986C2×C414yes—
77#23986C2×C414yes—
78#23986C2×C418yes—
79#23986C2×C418yes—
80#23986C2×C418yes—
81#23986C2×C418yes—
82#23986C2314yes—
83#23986C2314yes—
84#23986C2318yes—
85C2×#2030C2×C412yes—
86C2×#2030C2×C412yes—
87C2×#2030C2×C414yes—
88C2×#2030C2×C414yes—
89C2×#2029C2×C412yes—
90C2×#2029C2×C412yes—
91C2×#2029C2×C414yes—
92C2×#2029C2×C414yes—
93C2×#2022C2×C412yes—
94C2×#2022C2×C412yes—
95C2×#2022C2×C414yes—
96C2×#2022C2×C414yes—
97C2×#2021C2×C412yes—
98C2×#2021C2×C412yes—
99C2×#2021C2×C414yes—
100C2×#2021C2×C414yes—
101#21910C2318yescomplemented
102#20717D414yescomplemented
103#20717D414yescomplemented
104#20717C2314yes—
105#20717C2314yes—
106C2×#1820C2×C414yes—
107C2×#1820C2×C412yes—
108C2×#1820C2312yes—
109C2×#1820C2314yes—
110#20529C2314yescomplemented
111#20528C2314yescomplemented
112#20377D414yescomplemented
113#20377C2314yes—
114C22×#342C2×C411yescharacteristic
115C22×#342C2×C411yescharacteristic
116#17357C2314yes—
117#17357C2314yes—
118C2×#1464C2314yes—
119#11501C2314yescomplemented
120#11501C2314yescomplemented
121#11501C2318yescomplemented
122#8348C23132yescomplemented
123#7214C23132yescomplemented
124C27C22⋊C411yescharacteristic
125C25×C4C22⋊C411yescharacteristic
126C25×C4C22⋊C411yescharacteristic
127C25×C4C22⋊C411yescharacteristic
128C25×C4C22⋊C412yes—
129C25×C4C22⋊C412yes—
130C25×C4C2×D411yescharacteristic
131C25×C4C2×D411yescharacteristic
132C25×C4C2×D412yes—
133C25×C4C2×D411yescharacteristic
134C25×C4C2×D412yes—
135#3491C22×C414yes—
136#3491C22×C418yes—
137#3491C2414yes—
138C2×#543C22×C412yes—
139C2×#543C22×C414yes—
140C2×#534C22×C412yes—
141C2×#534C22×C414yes—
142C22×#117C22⋊C411yescharacteristic
143C22×#117C22⋊C411yescharacteristic
144C22×#117C22⋊C412yes—
145C22×#117C22⋊C412yes—
146C22×#117C22×C411yescharacteristic
147C22×#117C22×C412yes—
148C22×#117C2×D411yescharacteristic
149C22×#117C2×D411yescharacteristic
150C22×#117C2×D412yes—
151C22×#117C2×D412yes—
152C22×#117C2×D411yescharacteristic
153C22×#117C2×D412yes—
154C22×#117C2×D411yescharacteristic
155C22×#117C2×D412yes—
156C22×#117C2×D412yes—
157C22×#117C2×D412yes—
158C22×#117C2×D412yes—
159C22×#117#4112yes—
160C22×#117#4112yes—
161C22×#117#4112yes—
162C22×#117C2411yescharacteristic
163C22×#117C2412yes—
164C23×C4⋊C4#4112yes—
165C23×C22⋊C4C22⋊C411yescharacteristic
166C23×C22⋊C4C22⋊C411yescharacteristic
167C23×C22⋊C4C22×C411yescharacteristic
168C23×C22⋊C4C2×D411yescharacteristic
169C23×C42C2×D412yes—
170C2×#432C2×D414yescomplemented
171C2×#432C2×D414yescomplemented
172C2×#431C2×D414yescomplemented
173C2×#431C2×D414yescomplemented
174C2×C4×M16C2×D414yescomplemented
175C2×C4×M16C2×D414yescomplemented
176#2280C22⋊C412yes—
177#2280C22⋊C412yes—
178#2280C22⋊C412yes—
179#2280C22⋊C412yes—
180#2280C22⋊C412yes—
181#2280C22⋊C412yes—
182#2280C22⋊C412yes—
183#2280C22⋊C412yes—
184#2280C22⋊C412yes—
185#2280C22⋊C412yes—
186#2280C22⋊C412yes—
187#2280C22⋊C412yes—
188#2280C22×C411yescharacteristic
189#2280C22×C411yescharacteristic
190#2280C22×C412yes—
191#2280C22×C412yes—
192#2280C22×C412yes—
193#2280C22×C412yes—
194#2280C22×C412yes—
195#2280C2×D412yes—
196#2280C2×D412yes—
197#2280C2×D412yes—
198#2280C2×D412yes—
199#2280C2×D411yescharacteristic
200#2280C2×D411yescharacteristic
201#2280C2×D412yes—
202#2280C2×D411yescharacteristic
203#2280C2×D411yescharacteristic
204#2280C2×D412yes—
205#2280C2×D412yes—
206#2280C2×D412yes—
207#2280C2×D412yes—
208#2280C2×D412yes—
209#2280C2411yescharacteristic
210#2280C2411yescharacteristic
211#2280C2412yes—
212C2×#381C22⋊C411yescharacteristic
213C2×#381C22⋊C412yes—
214C2×#381C22⋊C412yes—
215C2×#381C22⋊C411yescharacteristic
216C2×#381C22⋊C411yescharacteristic
217C2×#381C22⋊C412yes—
218C2×#381C22⋊C412yes—
219C2×#381C22⋊C411yescharacteristic
220C2×#381C22×C411yescharacteristic
221C2×#381C22×C412yes—
222C2×#381C22×C412yes—
223C2×#381C22×C411yescharacteristic
224C2×#381C2×D411yescharacteristic
225C2×#381C2×D411yescharacteristic
226C2×#381C2×D412yes—
227C2×#381C2×D412yes—
228C2×#379C22⋊C412yes—
229C2×#379C22⋊C411yescharacteristic
230C2×#379C22⋊C412yes—
231C2×#379C22⋊C411yescharacteristic
232C2×#379C22⋊C412yes—
233C2×#379C22⋊C411yescharacteristic
234C2×#379C22⋊C412yes—
235C2×#379C22⋊C411yescharacteristic
236C2×#379C22×C412yes—
237C2×#379C22×C411yescharacteristic
238C2×#379C22×C412yes—
239C2×#379C22×C411yescharacteristic
240C2×#379C2×D411yescharacteristic
241C2×#379C2×D411yescharacteristic
242C2×#379C2×D412yes—
243C2×#379C2×D412yes—
244#2030C22×C414yes—
245#2030C22×C414yes—
246#2030C22×C418yes—
247#2029C22×C414yes—
248#2029C22×C414yes—
249#2029C22×C418yes—
250#2022C22×C414yes—
251#2022C22×C414yes—
252#2022C22×C418yes—
253#2021C22×C414yes—
254#2021C22×C414yes—
255#2021C22×C418yes—
256#1820C22×C414yes—
257#1820C22×C418yes—
258#1820C2414yes—
259#1750C2×D418yescomplemented
260#1750C2×D418yescomplemented
261#1750C2×D418yescomplemented
262#1750C2418yes—
263C2×#342C22×C412yes—
264C2×#342C22×C414yes—
265C2×#342C22×C412yes—
266C2×#342C22×C414yes—
267#1464C2418yes—
268C26C2×C22⋊C411yescharacteristic
269C26C2×C22⋊C411yescharacteristic
270C26C2×C22⋊C412yes—
271C26C2×C22⋊C412yes—
272C26C2×C22⋊C411yescharacteristic
273C24×C4C2×C22⋊C411yescharacteristic
274C24×C4C2×C22⋊C411yescharacteristic
275C24×C4C2×C22⋊C411yescharacteristic
276C24×C4C2×C22⋊C411yescharacteristic
277C24×C4C2×C22⋊C412yes—
278C24×C4C2×C22⋊C412yes—
279C24×C4C2×C22⋊C412yes—
280C24×C4C2×C22⋊C411yescharacteristic
281C24×C4C2×C22⋊C412yes—
282C24×C4C2×C22⋊C412yes—
283C24×C4C2×C22⋊C412yes—
284C24×C4C2×C22⋊C412yes—
285C24×C4C2×C22⋊C412yes—
286C24×C4C4×D412yes—
287C24×C4#12011yescharacteristic
288C24×C4#12012yes—
289C24×C4#12011yescharacteristic
290C24×C4#12112yes—
291C24×C4#12311yescharacteristic
292C24×C4#12311yescharacteristic
293C24×C4#12312yes—
294C24×C4C22×D411yescharacteristic
295C24×C4C22×D411yescharacteristic
296C24×C4C22×D411yescharacteristic
297C24×C4C22×D412yes—
298C24×C4C22×D412yes—
299#543C23×C414yes—
300#534C23×C414yes—
301C2×#117C2×C22⋊C412yes—
302C2×#117C2×C22⋊C411yescharacteristic
303C2×#117C2×C22⋊C411yescharacteristic
304C2×#117C2×C22⋊C412yes—
305C2×#117C2×C22⋊C412yes—
306C2×#117C2×C22⋊C412yes—
307C2×#117C2×C22⋊C412yes—
308C2×#117C2×C22⋊C412yes—
309C2×#117C2×C22⋊C412yes—
310C2×#117C2×C22⋊C412yes—
311C2×#117C4×D412yes—
312C2×#117C4×D412yes—
313C2×#117C4×D412yes—
314C2×#117C4×D412yes—
315C2×#117C4×D412yes—
316C2×#117C4×D412yes—
317C2×#117#12011yescharacteristic
318C2×#117#12011yescharacteristic
319C2×#117#12012yes—
320C2×#117#12012yes—
321C2×#117#12112yes—
322C2×#117#12112yes—
323C2×#117#12112yes—
324C2×#117#12112yes—
325C2×#117#12112yes—
326C2×#117#12112yes—
327C2×#117#12311yescharacteristic
328C2×#117#12311yescharacteristic
329C2×#117#12312yes—
330C2×#117#12312yes—
331C2×#117C23×C411yescharacteristic
332C2×#117C23×C412yes—
333C2×#117C22×D412yes—
334C2×#117C22×D411yescharacteristic
335C2×#117C22×D411yescharacteristic
336C2×#117C22×D412yes—
337C2×#117C22×D411yescharacteristic
338C2×#117C22×D412yes—
339C2×#117C22×D412yes—
340C2×#117C22×D412yes—
341C2×#117C22×D412yes—
342C2×#117C22×D411yescharacteristic
343C2×#117C2×#4112yes—
344C2×#117C2×#4112yes—
345C2×#117C2×#4112yes—
346C2×#117C2511yescharacteristic
347C22×C4⋊C4C4×D412yes—
348C22×C4⋊C4C4×D412yes—
349C22×C4⋊C4C4×D412yes—
350C22×C4⋊C4#12112yes—
351C22×C4⋊C4#12112yes—
352C22×C4⋊C4#12112yes—
353C22×C4⋊C4#12312yes—
354C22×C4⋊C4#12312yes—
355C22×C4⋊C4#12312yes—
356C22×C4⋊C4C2×#4112yes—
357C22×C4⋊C4C2×#4112yes—
358C22×C4⋊C4C2×#4112yes—
359C22×C22⋊C4C2×C22⋊C412yes—
360C22×C22⋊C4C2×C22⋊C412yes—
361C22×C22⋊C4C2×C22⋊C411yescharacteristic
362C22×C22⋊C4C2×C22⋊C411yescharacteristic
363C22×C22⋊C4C2×C22⋊C412yes—
364C22×C22⋊C4C2×C22⋊C412yes—
365C22×C22⋊C4C2×C22⋊C411yescharacteristic
366C22×C22⋊C4C2×C22⋊C411yescharacteristic
367C22×C22⋊C4C2×C22⋊C412yes—
368C22×C22⋊C4C2×C22⋊C411yescharacteristic
369C22×C22⋊C4C2×C22⋊C412yes—
370C22×C22⋊C4C2×C22⋊C411yescharacteristic
371C22×C22⋊C4C4×D412yes—
372C22×C22⋊C4C4×D412yes—
373C22×C22⋊C4C4×D412yes—
374C22×C22⋊C4#12112yes—
375C22×C22⋊C4#12112yes—
376C22×C22⋊C4#12112yes—
377C22×C22⋊C4C23×C412yes—
378C22×C22⋊C4C23×C411yescharacteristic
379C22×C22⋊C4C22×D411yescharacteristic
380C22×C22⋊C4C22×D412yes—
381C22×C42C4×D412yes—
382C22×C42C4×D412yes—
383C22×C42C4×D412yes—
384C22×C42#12012yes—
385C22×C42#12012yes—
386C22×C42#12012yes—
387C22×C42#12112yes—
388C22×C42#12112yes—
389C22×C42#12112yes—
390C22×C42C22×D412yes—
391C22×C42C22×D412yes—
392C22×C42C22×D412yes—
393C2×#97C22×D418yescomplemented
394C2×C4×C8C22×D418yescomplemented
395#381C2×C22⋊C412yes—
396#381C2×C22⋊C412yes—
397#381C2×C22⋊C412yes—
398#381C2×C22⋊C411yescharacteristic
399#381C2×C22⋊C411yescharacteristic
400#381C2×C22⋊C412yes—
401#381C2×C22⋊C412yes—
402#381C2×C22⋊C412yes—
403#381C2×C22⋊C412yes—
404#381C2×C22⋊C412yes—
405#381C2×C22⋊C412yes—
406#381C2×C22⋊C412yes—
407#381C2×C22⋊C411yescharacteristic
408#381C2×C22⋊C411yescharacteristic
409#381C23×C412yes—
410#381C23×C411yescharacteristic
411#381C23×C411yescharacteristic
412#381C22×D412yes—
413#381C22×D411yescharacteristic
414#381C22×D411yescharacteristic
415#379C2×C22⋊C411yescharacteristic
416#379C2×C22⋊C412yes—
417#379C2×C22⋊C412yes—
418#379C2×C22⋊C412yes—
419#379C2×C22⋊C412yes—
420#379C2×C22⋊C411yescharacteristic
421#379C2×C22⋊C412yes—
422#379C2×C22⋊C412yes—
423#379C2×C22⋊C411yescharacteristic
424#379C2×C22⋊C412yes—
425#379C2×C22⋊C412yes—
426#379C2×C22⋊C412yes—
427#379C2×C22⋊C412yes—
428#379C2×C22⋊C411yescharacteristic
429#379C23×C411yescharacteristic
430#379C23×C412yes—
431#379C23×C411yescharacteristic
432#379C22×D411yescharacteristic
433#379C22×D412yes—
434#379C22×D411yescharacteristic
435#342C23×C414yes—
436#342C23×C414yes—
437C25#38612yes—
438C25#38611yescharacteristic
439C25#38611yescharacteristic
440C25#42114yes—
441C25C22×C22⋊C412yes—
442C25C22×C22⋊C411yescharacteristic
443C25C22×C22⋊C412yes—
444C25C22×C22⋊C411yescharacteristic
445C25C22×C22⋊C411yescharacteristic
446C23×C4#38611yescharacteristic
447C23×C4#38612yes—
448C23×C4#38612yes—
449C23×C4#38612yes—
450C23×C4#38611yescharacteristic
451C23×C4#38612yes—
452C23×C4#38612yes—
453C23×C4#38612yes—
454C23×C4#38612yes—
455C23×C4#38612yes—
456C23×C4#38612yes—
457C23×C4#38612yes—
458C23×C4#38612yes—
459C23×C4#42114yes—
460C23×C4B(4,𝔽2)12yes—
461C23×C4B(4,𝔽2)12yes—
462C23×C4B(4,𝔽2)12yes—
463C23×C4B(4,𝔽2)12yes—
464C23×C4C22×C22⋊C412yes—
465C23×C4C22×C22⋊C411yescharacteristic
466C23×C4C22×C22⋊C412yes—
467C23×C4C22×C22⋊C411yescharacteristic
468C23×C4C22×C22⋊C411yescharacteristic
469C23×C4C2×C4×D412yes—
470C23×C4C2×C4×D412yes—
471C23×C4C2×C4×D412yes—
472C23×C4C2×#12012yes—
473C23×C4C2×#12011yescharacteristic
474C23×C4C2×#12011yescharacteristic
475C23×C4C2×#12012yes—
476C23×C4C2×#12112yes—
477C23×C4C2×#12112yes—
478C23×C4C2×#12112yes—
479C23×C4C2×#12311yescharacteristic
480C23×C4C2×#12312yes—
481C23×C4C2×#12311yescharacteristic
482C23×C4C2×#12312yes—
483C23×C4C23×D411yescharacteristic
484C2×C4⋊C4#38612yes—
485C2×C4⋊C4#38612yes—
486C2×C4⋊C4#38612yes—
487C2×C4⋊C4#38612yes—
488C2×C4⋊C4#38612yes—
489C2×C4⋊C4#38612yes—
490C2×C4⋊C4C2×C4×D412yes—
491C2×C4⋊C4C2×C4×D412yes—
492C2×C4⋊C4C2×C4×D412yes—
493C2×C4⋊C4C2×#12112yes—
494C2×C4⋊C4C2×#12112yes—
495C2×C4⋊C4C2×#12112yes—
496C2×C4⋊C4C2×#12312yes—
497C2×C4⋊C4C2×#12312yes—
498C2×C4⋊C4C2×#12312yes—
499C2×C4⋊C4C22×#4112yes—
500C2×C22⋊C4#38612yes—
501C2×C22⋊C4#38612yes—
502C2×C22⋊C4#38611yescharacteristic
503C2×C22⋊C4#38611yescharacteristic
504C2×C22⋊C4#38612yes—
505C2×C22⋊C4#38612yes—
506C2×C22⋊C4#38611yescharacteristic
507C2×C22⋊C4#38611yescharacteristic
508C2×C22⋊C4C22×C22⋊C412yes—
509C2×C22⋊C4C22×C22⋊C411yescharacteristic
510C2×C22⋊C4C22×C22⋊C411yescharacteristic
511C2×C22⋊C4C22×C22⋊C412yes—
512C2×C22⋊C4C22×C22⋊C411yescharacteristic
513C2×C22⋊C4C22×C22⋊C411yescharacteristic
514C2×C22⋊C4C22×C22⋊C412yes—
515C2×C22⋊C4C22×C22⋊C411yescharacteristic
516C2×C22⋊C4C22×C22⋊C411yescharacteristic
517C2×C22⋊C4C22×C22⋊C412yes—
518C2×C22⋊C4C2×C4×D412yes—
519C2×C22⋊C4C2×C4×D412yes—
520C2×C22⋊C4C2×C4×D412yes—
521C2×C22⋊C4C2×#12112yes—
522C2×C22⋊C4C2×#12112yes—
523C2×C22⋊C4C2×#12112yes—
524C2×C22⋊C4C24×C411yescharacteristic
525C2×C22⋊C4C23×D411yescharacteristic
526C2×C42#38612yes—
527C2×C42#38612yes—
528C2×C42#38612yes—
529C2×C42#38612yes—
530C2×C42#38612yes—
531C2×C42#38612yes—
532C2×C42C2×C4×D412yes—
533C2×C42C2×C4×D412yes—
534C2×C42C2×C4×D412yes—
535C2×C42C2×#12012yes—
536C2×C42C2×#12012yes—
537C2×C42C2×#12012yes—
538C2×C42C2×#12112yes—
539C2×C42C2×#12112yes—
540C2×C42C2×#12112yes—
541C2×C42C23×D412yes—
542C24#188911yescharacteristic
543C24#188912yes—
544C24#188911yescharacteristic
545C24#191114yes—
546C24C2×#38612yes—
547C24C2×#38612yes—
548C24C2×#38611yescharacteristic
549C24C2×#38611yescharacteristic
550C24C2×#42112yes—
551C24C2×#42112yes—
552C24C2×#42112yes—
553C24C2×#42112yes—
554C24C23×C22⋊C411yescharacteristic
555C22×C4#188912yes—
556C22×C4#188911yescharacteristic
557C22×C4#188911yescharacteristic
558C22×C4#188912yes—
559C22×C4#188912yes—
560C22×C4#188912yes—
561C22×C4#188912yes—
562C22×C4C2×#38611yescharacteristic
563C22×C4C2×#38612yes—
564C22×C4C2×#38611yescharacteristic
565C22×C4C2×#38612yes—
566C22×C4C2×#38612yes—
567C22×C4C2×#38612yes—
568C22×C4C2×#38612yes—
569C22×C4C2×#38612yes—
570C22×C4C2×#38612yes—
571C22×C4C2×#38612yes—
572C22×C4C2×#42112yes—
573C22×C4C2×#42112yes—
574C22×C4C2×B(4,𝔽2)12yes—
575C22×C4C2×B(4,𝔽2)12yes—
576C22×C4C2×B(4,𝔽2)12yes—
577C22×C4C2×B(4,𝔽2)12yes—
578C22×C4C2×B(4,𝔽2)12yes—
579C22×C4C2×B(4,𝔽2)12yes—
580C22×C4C22×C4×D412yes—
581C22×C4C22×#12011yescharacteristic
582C22×C4C22×#12112yes—
583C22×C4C22×#12311yescharacteristic
584C23C2×#188912yes—
585C23C2×#188911yescharacteristic
586C23C2×#188911yescharacteristic
587C23C2×#188912yes—
588C23#2097912yes—
589C23#2097912yes—
590C23C2×#191114yes—
591C23C2×#191112yes—
592C23C22×#38611yescharacteristic
593C23C22×#42111yescharacteristic
594C23C22×#42111yescharacteristic
595C2×C4C2×#188912yes—
596C2×C4C2×#188912yes—
597C2×C4C2×#188912yes—
598C2×C4C22×B(4,𝔽2)12yes—
599C22#20146212yes—
600C22#20146212yes—
601C22#49458714yes—
602C22C22×#188911yescharacteristic
603C22C2×#2097911yescharacteristic
604C22C22×#191111yescharacteristic
605C2C2×#49458712yes—
606C2C2×#20146211yescharacteristic
subgroupG/H
center, socleC22C22×#1889
commutatorC2×C22⋊C4C24×C4
Frattini, cosocleC2×#117C25
prime radicalC22×#2021C4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ C23×#117 ◁ G
LECSG ▷ C2×#117 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#480245C2semidirect
2. #72285622C2semidirect
3. #72285391C2semidirect
4. #72285266C2semidirect
5. #72284815C2semidirect
6. #72284781C2semidirect
7. #72284501C2semidirect
8. #72284275C2semidirect
24. #6386515C22semidirect
25. #6386514C22semidirect
26. #6374745C22semidirect
29. #6370175C22semidirect
31. #480245C22semidirect
32. #480245C22semidirect
33. C2×#11501C22semidirect
34. C2×#11501C22semidirect
35. #185309C22semidirect
36. #185303C22semidirect
37. #185297C22semidirect
38. #139646C22semidirect
39. #139627C22semidirect
40. #139626C22semidirect
41. #127221C22semidirect
42. #127219C22semidirect
43. #127189C22semidirect
53. C2×#2920D4semidirect
54. C2×#2920D4semidirect
101. #21910C23semidirect
102. #20717D4semidirect
103. #20717D4semidirect
110. #20529C23semidirect
111. #20528C23semidirect
112. #20377D4semidirect
119. #11501C23semidirect
120. #11501C23semidirect
121. #11501C23semidirect
122. #8348C23semidirect
123. #7214C23semidirect
170. C2×#432C2×D4semidirect
171. C2×#432C2×D4semidirect
172. C2×#431C2×D4semidirect
173. C2×#431C2×D4semidirect
174. C2×C4×M16C2×D4semidirect
175. C2×C4×M16C2×D4semidirect
259. #1750C2×D4semidirect
260. #1750C2×D4semidirect
261. #1750C2×D4semidirect
393. C2×#97C22×D4semidirect
394. C2×C4×C8C22×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#4802452
#722856222
#722853912
#722852662
#722848152
#722847812
#722845012
#722842752
C22×#239862