Finite Group Databasebeta

← #72338249

Subgroups — #72338249

Order 2048.

At least 7951 conjugacy classes of subgroups; only the 2476 normal subgroups are shown.

The subgroup lattice has 897 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72338248C2116yesmaximal, complemented
2#72338235C211yesmaximal, characteristic, complemented
3#72338230C211yesmaximal, characteristic, complemented
4#72338226C211yesmaximal, characteristic, complemented
5#72338224C211yesmaximal, characteristic, complemented
6#72338214C211yesmaximal, characteristic, complemented
7#72338213C211yesmaximal, characteristic, complemented
8#72338208C211yesmaximal, characteristic, complemented
9#72337526C211yesmaximal, characteristic, complemented
10#72316807C211yesmaximal, characteristic, complemented
11#72316741C211yesmaximal, characteristic, complemented
12#72316683C211yesmaximal, characteristic, complemented
13C2×#10577334C211yesmaximal, characteristic
14#72257773C211yesmaximal, characteristic, complemented
15#72257772C211yesmaximal, characteristic, complemented
16#72226726C211yesmaximal, characteristic, complemented
17C22×#3549C2211yescharacteristic
18C2×#62812C2211yescharacteristic
19#10577334C418yescomplemented
20#10577334C2218yes—
21C2×#61682C414yescomplemented
22C2×#61679C414yescomplemented
23C2×#60803C2211yescharacteristic
24C2×#60803C2211yescharacteristic
25C2×#60561C2211yescharacteristic
26C2×#60561C2211yescharacteristic
27C2×#60232C2211yescharacteristic
28C2×#60144C2211yescharacteristic, complemented
29#7625999C2211yescharacteristic, complemented
30#6393503C2218yescomplemented
31#6374554C2211yescharacteristic
32#6374554C2211yescharacteristic, complemented
33#6374317C2211yescharacteristic, complemented
34#6372442C2211yescharacteristic
35#6372442C2211yescharacteristic, complemented
36#6372442C2211yescharacteristic, complemented
37#6372358C2211yescharacteristic, complemented
38#6370997C2211yescharacteristic, complemented
39#6370937C2211yescharacteristic, complemented
40#6344036C2211yescharacteristic
41#6344036C2211yescharacteristic, complemented
42C2×#17745C2211yescharacteristic, complemented
43#6343804C2211yescharacteristic, complemented
44#6343377C2211yescharacteristic
45#6343377C2211yescharacteristic, complemented
46#6343377C2211yescharacteristic, complemented
47#6343377C2211yescharacteristic, complemented
48C2×#17451C2211yescharacteristic, complemented
49#202021C2218yescomplemented
50#200904C2218yescomplemented
51#198957C2218yescomplemented
52#195355C2218yescomplemented
53#187428C2218yescomplemented
54#186289C2218yescomplemented
55#185340C2218yescomplemented
56#181791C2211yescharacteristic, complemented
57#181375C2211yescharacteristic, complemented
58#181222C2211yescharacteristic, complemented
59#181220C2211yescharacteristic, complemented
60#181175C2211yescharacteristic, complemented
61#181122C2211yescharacteristic, complemented
62#181055C2211yescharacteristic, complemented
63#180880C2211yescharacteristic, complemented
64#115392C2218yescomplemented
65#114223C2218yescomplemented
66#113989C2218yescomplemented
67#113022C2218yescomplemented
68#108044C2218yescomplemented
69#107826C2218yescomplemented
70#62812C2×C414yescomplemented
71#62812C2314yes—
72C2×#3497C2×C412yescomplemented
73C2×#3496C2×C412yescomplemented
74C2×#3549C2×C414yes—
75C2×#3549C2×C414yes—
76C2×#3549D414yes—
77C2×#3549D414yes—
78C2×#3549D414yes—
79C2×#3549C2314yes—
80C22×#555D412yes—
81C22×D42D412yes—
82C22×#532C2311yescharacteristic
83C22×#532C2311yescharacteristic
84C22×#532C2311yescharacteristic
85C22×#532C2311yescharacteristic
86C22×C4×#41C2311yescharacteristic
87#61682C2×C4132yescomplemented
88#61679C2×C4132yescomplemented
89#60803C2×C414yes—
90#60803C2×C414yescomplemented
91#60803D414yes—
92#60803D414yes—
93#60803C2314yes—
94#60803C2314yes—
95C2×#3214C2×C414yescomplemented
96C2×#3207C2×C414yes—
97C2×#3206D412yes—
98C2×#3205D412yes—
99C2×#3151D412yes—
100C2×#3141D412yes—
101#60561C2×C414yes—
102#60561C2×C414yescomplemented
103#60561D414yes—
104#60561D414yes—
105#60561C2314yes—
106#60561C2314yes—
107C2×#3112C2×C412yes—
108C2×#3109C2×C412yes—
109C2×#3103C2×C412yescomplemented
110C2×#3103D412yes—
111C2×#3100C2×C412yescomplemented
112C2×#3100D412yes—
113C2×#3094D412yes—
114C2×#3006D412yes—
115#60232C2×C414yescomplemented
116#60232C2314yes—
117C2×#2981C2×C414yescomplemented
118C2×#2932C2314yescomplemented
119C2×#2920C2311yescharacteristic
120C2×#2920C2311yescharacteristic
121C2×#2920C2311yescharacteristic
122C2×#2920C2311yescharacteristic
123C2×#2920C2311yescharacteristic
124C22×#423C2311yescharacteristic
125C22×C4×M16C2311yescharacteristic
126#34369C2314yescomplemented
127#34012C2311yescharacteristic
128#34012C2311yescharacteristic
129#34012C2311yescharacteristic
130#21891C2314yes—
131#21891C2314yescomplemented
132#21884D414yes—
133#21816C2314yescomplemented
134#21408C2314yes—
135#21408C2314yescomplemented
136#21408C2314yescomplemented
137#21401D414yes—
138#21379C2314yescomplemented
139#21313D412yes—
140#21260D412yes—
141#20973D412yes—
142#20973D412yes—
143#20748C2314yescomplemented
144#20723C2314yescomplemented
145#17745C2314yescomplemented
146#17743C2314yes—
147#17731C2314yescomplemented
148#17671C2314yescomplemented
149#17595C2314yes—
150#17595C2314yescomplemented
151#17589C2314yescomplemented
152#17561C2314yescomplemented
153#17451C2314yescomplemented
154#8113C2314yescomplemented
155#8077C2314yescomplemented
156#7977C2314yescomplemented
157#7976C2314yescomplemented
158#7962C2314yescomplemented
159#7945C2314yescomplemented
160#7919C2314yescomplemented
161#7861C2314yescomplemented
162C23×#41C2×D411yescharacteristic
163C23×M16C2×D411yescharacteristic
164C23×M16C2×D411yescharacteristic
165#3549C22⋊C4116yes—
166#3549C22⋊C4116yes—
167#3549C22×C4116yes—
168#3549C2×D4116yes—
169#3497C22×C418yes—
170#3496C22×C418yes—
171C2×#555C22⋊C418yes—
172C2×#555C22⋊C418yes—
173C2×#555C2×D418yes—
174C2×D42C22⋊C418yes—
175C2×D42C22⋊C418yes—
176C2×D42C2×D418yes—
177C2×#532C22×C412yes—
178C2×#532C22×C412yes—
179C2×#532C22×C412yes—
180C2×#532C22×C412yes—
181C2×#532C22×C412yes—
182C2×#532C22×C412yes—
183C2×#532C22×C412yes—
184C2×#532C22×C412yes—
185C2×#532C2×D412yes—
186C2×#532C2×D412yes—
187C2×#532C2×D412yes—
188C2×#532C2×D412yes—
189C2×#532C2×D412yes—
190C2×#532C2×D412yes—
191C2×#532C2×D412yes—
192C2×#532C2×D412yes—
193C2×#532C2×D412yes—
194C2×#532C2×D412yes—
195C2×#532C2×D412yes—
196C2×#532C2×D412yes—
197C2×#532C2×D412yes—
198C2×#532C2×D412yes—
199C2×#532C2×D412yes—
200C2×#532C2×D412yes—
201C2×#532C2×D412yes—
202C2×#532C2×D412yes—
203C2×#532C2×D412yes—
204C2×#532C2×D412yes—
205C2×#532#4112yes—
206C2×#532#4112yes—
207C2×#532#4112yes—
208C2×#532#4112yes—
209C2×#532C2412yes—
210C2×#532C2412yes—
211C2×#532C2412yes—
212C2×#532C2412yes—
213C22×C4⋊Q8C2×D411yescharacteristic
214C22×C4⋊Q8C2×D411yescharacteristic
215C22×C4⋊Q8C2×D411yescharacteristic
216C22×C4⋊Q8C2×D411yescharacteristic
217C22×#127C2×D411yescharacteristic
218C22×#127C2×D411yescharacteristic
219C22×#127C2×D411yescharacteristic
220C22×#127C2×D411yescharacteristic
221C22×#121C2×D412yes—
222C22×#121C2×D412yes—
223C2×C4×#41C22×C412yes—
224C2×C4×#41C2×D412yes—
225C2×C4×#41C2×D412yes—
226C2×C4×#41C2412yes—
227C22×C4×Q8C22×C411yescharacteristic
228C22×C4×Q8C2×D411yescharacteristic
229C22×C4×D4C22×C411yescharacteristic
230C22×C4×D4C2×D411yescharacteristic
231C22×C4×D4C2×D412yes—
232C22×C4×D4C2×D412yes—
233C22×#117C2×D411yescharacteristic
234C23×C42C2411yescharacteristic
235#3214C22×C4116yes—
236#3207C22⋊C4116yes—
237#3207C22×C4116yes—
238#3206C22⋊C418yes—
239#3206C2×D418yes—
240#3205C22⋊C418yes—
241#3205C2×D418yes—
242#3151C22⋊C418yes—
243#3151C2×D418yes—
244C2×#493C22⋊C414yes—
245C2×#492C22⋊C414yes—
246#3141C22⋊C418yes—
247#3141C2×D418yes—
248C2×#487C22⋊C414yes—
249C2×#486C22⋊C414yes—
250#3112C22⋊C418yes—
251#3112C22×C418yes—
252#3109C22⋊C418yes—
253#3109C22×C418yes—
254#3103C22⋊C418yes—
255#3103C22×C418yes—
256#3103C2×D418yes—
257#3100C22⋊C418yes—
258#3100C22×C418yes—
259#3100C2×D418yes—
260#3094C22⋊C418yes—
261#3094C2×D418yes—
262C2×#481C22⋊C414yes—
263C2×#480C22⋊C414yes—
264#3006C22⋊C418yes—
265#3006C2×D418yes—
266C2×#448C22⋊C414yes—
267C2×#447C22⋊C414yes—
268#2981C22×C4116yes—
269#2920C22×C412yes—
270#2920C22×C412yes—
271#2920C2×D412yes—
272#2920C2×D412yes—
273#2920C2×D412yes—
274#2920C2×D412yes—
275#2920C2412yes—
276#2920C2412yes—
277#2920C2412yes—
278#2920C2412yes—
279C2×#432C22×C412yes—
280C2×#432C2412yes—
281C2×#431C22×C412yes—
282C2×#431C2×D412yes—
283C2×#431C2×D412yes—
284C2×#423C2×D412yes—
285C2×#423C2412yes—
286C22×C4⋊C8C2×D412yes—
287C2×#407C2×D412yes—
288C2×C4×M16C2×D412yes—
289C22×#97C2412yes—
290C22×C4×C8C2×D412yes—
291#2285C2×D412yes—
292#2285C2×D412yes—
293#2283C2412yes—
294#2283C2412yes—
295#2283C2412yes—
296#2280C2×D412yes—
297C4×#117C2×D412yes—
298#1988C2×D418yes—
299#1982C2×D418yes—
300#1893C2×D418yes—
301#1893C2×D418yes—
302C22×#41C2×C22⋊C412yes—
303C22×#41C22×D412yes—
304C23×Q8C2×C22⋊C411yescharacteristic
305C23×D4C2×C22⋊C411yescharacteristic
306C23×D4#12012yes—
307C23×D4#12012yes—
308C24×C4C22×D411yescharacteristic
309C24×C4C22×D411yescharacteristic
310C24×C4H(5,𝔽2)11yescharacteristic
311C23×C8C22×D412yes—
312C23×C8C22×D412yes—
313#555C2×C22⋊C4132yes—
314D42C2×C22⋊C4132yes—
315#532C2×C22⋊C414yes—
316#532C2×C22⋊C414yes—
317#532C2×C22⋊C414yes—
318#532C2×C22⋊C414yes—
319#532C2×C22⋊C414yes—
320#532C2×C22⋊C414yes—
321#532C2×C22⋊C414yes—
322#532C2×C22⋊C414yes—
323#532C2×C22⋊C414yes—
324#532C2×C22⋊C414yes—
325#532C2×C22⋊C414yes—
326#532C2×C22⋊C414yes—
327#532C4×D414yes—
328#532C4×D414yes—
329#532C4×D414yes—
330#532C4×D414yes—
331#532#12014yes—
332#532#12014yes—
333#532#12014yes—
334#532#12014yes—
335#532#12014yes—
336#532#12014yes—
337#532#12114yes—
338#532#12114yes—
339#532#12114yes—
340#532#12114yes—
341#532#12314yes—
342#532#12314yes—
343#532C23×C414yes—
344#532C23×C414yes—
345#532C23×C414yes—
346#532C23×C414yes—
347#532C22×D414yes—
348#532C22×D414yes—
349#532C22×D414yes—
350#532C22×D414yes—
351#532C22×D414yes—
352#532C22×D414yes—
353#532C2×#4114yes—
354#532C2×#4114yes—
355C2×C4⋊Q8C2×C22⋊C412yes—
356C2×C4⋊Q8C2×C22⋊C412yes—
357C2×C4⋊Q8C2×C22⋊C412yes—
358C2×C4⋊Q8C2×C22⋊C412yes—
359C2×C4⋊Q8C2×C22⋊C412yes—
360C2×C4⋊Q8C2×C22⋊C412yes—
361C2×C4⋊Q8C4×D412yes—
362C2×C4⋊Q8C4×D412yes—
363C2×C4⋊Q8#12012yes—
364C2×C4⋊Q8#12012yes—
365C2×C4⋊Q8#12012yes—
366C2×C4⋊Q8#12012yes—
367C2×C4⋊Q8#12112yes—
368C2×C4⋊Q8#12112yes—
369C2×C4⋊Q8C22×D412yes—
370C2×C4⋊Q8C22×D412yes—
371C2×C4⋊Q8C22×D412yes—
372C2×C4⋊Q8C22×D412yes—
373C2×#127C2×C22⋊C412yes—
374C2×#127C2×C22⋊C412yes—
375C2×#127C2×C22⋊C412yes—
376C2×#127C2×C22⋊C412yes—
377C2×#127C2×C22⋊C412yes—
378C2×#127C2×C22⋊C412yes—
379C2×#127C4×D412yes—
380C2×#127C4×D412yes—
381C2×#127#12012yes—
382C2×#127#12012yes—
383C2×#127#12012yes—
384C2×#127#12012yes—
385C2×#127#12112yes—
386C2×#127#12112yes—
387C2×#127C22×D412yes—
388C2×#127C22×D412yes—
389C2×#127C22×D412yes—
390C2×#127C22×D412yes—
391C2×#121C2×C22⋊C414yes—
392C2×#121C2×C22⋊C414yes—
393C2×#121C4×D414yes—
394C2×#121C4×D414yes—
395C2×#121#12014yes—
396C2×#121#12014yes—
397C2×#121#12014yes—
398C2×#121#12014yes—
399C2×#121#12114yes—
400C2×#121#12114yes—
401C2×#121C22×D414yes—
402C2×#121C22×D414yes—
403C2×C4×Q8C2×C22⋊C412yes—
404C2×C4×Q8C2×C22⋊C412yes—
405C2×C4×Q8C23×C412yes—
406C2×C4×Q8C22×D412yes—
407C2×C4×D4C2×C22⋊C412yes—
408C2×C4×D4C2×C22⋊C412yes—
409C2×C4×D4C2×C22⋊C414yes—
410C2×C4×D4C2×C22⋊C414yes—
411C2×C4×D4C2×C22⋊C414yes—
412C2×C4×D4C2×C22⋊C414yes—
413C2×C4×D4#12014yes—
414C2×C4×D4#12014yes—
415C2×C4×D4#12014yes—
416C2×C4×D4#12014yes—
417C2×C4×D4#12314yes—
418C2×C4×D4#12314yes—
419C2×C4×D4C23×C412yes—
420C2×C4×D4C22×D412yes—
421C2×C4×D4C22×D414yes—
422C2×C4×D4C22×D414yes—
423C2×#117C2×C22⋊C412yes—
424C2×#117C22×D412yes—
425C22×C4⋊C4C2×C22⋊C411yescharacteristic
426C22×C4⋊C4C2×C22⋊C411yescharacteristic
427C22×C4⋊C4#12012yes—
428C22×C4⋊C4#12012yes—
429C22×C42C23×C411yescharacteristic
430C22×C42C23×C411yescharacteristic
431C22×C42C22×D411yescharacteristic
432C22×C42C22×D411yescharacteristic
433C22×C42C22×D411yescharacteristic
434C22×C42C22×D411yescharacteristic
435C22×C42C22×D411yescharacteristic
436C22×C42C22×D411yescharacteristic
437C22×C42C22×D411yescharacteristic
438C22×C42C22×D411yescharacteristic
439C22×C42C22×D411yescharacteristic
440C22×C42C22×D411yescharacteristic
441C22×C42C22×D411yescharacteristic
442C22×C42C22×D411yescharacteristic
443C22×C42C22×D411yescharacteristic
444C22×C42C22×D411yescharacteristic
445C22×C42C2×#4111yescharacteristic
446C22×C42C2×#4111yescharacteristic
447C22×C42C2×#4111yescharacteristic
448C22×C42C2×#4111yescharacteristic
449C22×C42H(5,𝔽2)11yescharacteristic
450C22×C42H(5,𝔽2)11yescharacteristic
451C22×C42H(5,𝔽2)11yescharacteristic
452C22×C42H(5,𝔽2)11yescharacteristic
453C22×C42H(5,𝔽2)11yescharacteristic
454C22×C42H(5,𝔽2)11yescharacteristic
455C22×C42H(5,𝔽2)11yescharacteristic
456C22×C42C2511yescharacteristic
457#493C2×C22⋊C4116yes—
458#492C2×C22⋊C4116yes—
459#487C2×C22⋊C4116yes—
460#486C2×C22⋊C4116yes—
461#481C2×C22⋊C4116yes—
462#480C2×C22⋊C4116yes—
463#448C2×C22⋊C4116yes—
464#447C2×C22⋊C4116yes—
465#432C2×C22⋊C414yes—
466#432C23×C414yes—
467#431C2×C22⋊C414yes—
468#431C2×C22⋊C414yes—
469#431C2×C22⋊C414yes—
470#431C23×C414yes—
471#431C22×D414yes—
472#431C22×D414yes—
473C2×C4⋊C8C22×D414yes—
474#407C2×C22⋊C414yes—
475#407C22×D414yes—
476C2×C22⋊C8C2×C22⋊C414yes—
477C4×M16C2×C22⋊C414yes—
478C4×M16C22×D414yes—
479C2×C4×C8C2×C22⋊C414yes—
480#380C22×D414yes—
481C4×C4⋊C4C22×D414yes—
482C25D4211yescharacteristic
483C22×Q8C22×C22⋊C412yes—
484C22×D4#37914yes—
485C22×D4#37914yes—
486C22×D4#38614yes—
487C22×D4#38614yes—
488C22×D4C22×C22⋊C412yes—
489C22×D4C2×#12014yes—
490C22×D4C2×#12014yes—
491C23×C4C22×C22⋊C411yescharacteristic
492C23×C4C22×C22⋊C411yescharacteristic
493C23×C4C2×C4×D411yescharacteristic
494C23×C4C2×C4×D411yescharacteristic
495C23×C4#51811yescharacteristic
496C23×C4#51811yescharacteristic
497C23×C4C2×#12011yescharacteristic
498C23×C4C2×#12011yescharacteristic
499C23×C4C2×#12011yescharacteristic
500C23×C4C2×#12011yescharacteristic
501C23×C4C2×#12011yescharacteristic
502C23×C4C2×#12011yescharacteristic
503C23×C4C2×#12111yescharacteristic
504C23×C4C2×#12111yescharacteristic
505C23×C4#53411yescharacteristic
506C23×C4#53411yescharacteristic
507C23×C4#53411yescharacteristic
508C23×C4#53411yescharacteristic
509C23×C4D4211yescharacteristic
510C23×C4D4211yescharacteristic
511C23×C4D4211yescharacteristic
512C23×C4D4211yescharacteristic
513C23×C4D4211yescharacteristic
514C23×C4D4211yescharacteristic
515C23×C4D4211yescharacteristic
516C23×C4D4211yescharacteristic
517C23×C4D4211yescharacteristic
518C23×C4D4211yescharacteristic
519C23×C4D4211yescharacteristic
520C23×C4D4211yescharacteristic
521C23×C4D4211yescharacteristic
522C23×C4#54611yescharacteristic
523C23×C4#54611yescharacteristic
524C23×C4#54611yescharacteristic
525C23×C4#54611yescharacteristic
526C23×C4#54611yescharacteristic
527C23×C4#54611yescharacteristic
528C23×C4#54611yescharacteristic
529C23×C4#54611yescharacteristic
530C23×C4C23×D411yescharacteristic
531C23×C4C23×D411yescharacteristic
532C23×C4C2×H(5,𝔽2)11yescharacteristic
533C4⋊Q8#37914yes—
534C4⋊Q8#37914yes—
535C4⋊Q8#38614yes—
536C4⋊Q8#38614yes—
537C4⋊Q8C22×C22⋊C414yes—
538C4⋊Q8C22×C22⋊C414yes—
539C4⋊Q8C22×C22⋊C414yes—
540C4⋊Q8C2×C4×D414yes—
541C4⋊Q8C2×#12014yes—
542C4⋊Q8C2×#12114yes—
543#127#37914yes—
544#127#37914yes—
545#127#38614yes—
546#127#38614yes—
547#127C22×C22⋊C414yes—
548#127C22×C22⋊C414yes—
549#127C22×C22⋊C414yes—
550#127C2×C4×D414yes—
551#127C2×#12014yes—
552#127C2×#12114yes—
553#121#37918yes—
554#121#37918yes—
555#121#38618yes—
556#121#38618yes—
557#121C22×C22⋊C418yes—
558#121C2×C4×D418yes—
559#121C2×#12018yes—
560#121C2×#12118yes—
561C4×D4#37918yes—
562C4×D4#37918yes—
563C4×D4#38618yes—
564C4×D4#38618yes—
565C4×D4C22×C22⋊C418yes—
566C4×D4C22×C22⋊C418yes—
567C4×D4C2×#12018yes—
568C4×D4C2×#12318yes—
569C2×C4⋊C4#37914yes—
570C2×C4⋊C4#37914yes—
571C2×C4⋊C4#38614yes—
572C2×C4⋊C4#38614yes—
573C2×C4⋊C4C22×C22⋊C412yes—
574C2×C4⋊C4C22×C22⋊C412yes—
575C2×C4⋊C4C2×#12014yes—
576C2×C4⋊C4C2×#12014yes—
577C2×C42C22×C22⋊C411yescharacteristic
578C2×C42C22×C22⋊C411yescharacteristic
579C2×C42C22×C22⋊C411yescharacteristic
580C2×C42C22×C22⋊C411yescharacteristic
581C2×C42C22×C22⋊C411yescharacteristic
582C2×C42C22×C22⋊C411yescharacteristic
583C2×C42C22×C22⋊C411yescharacteristic
584C2×C42C22×C22⋊C411yescharacteristic
585C2×C42C22×C22⋊C411yescharacteristic
586C2×C42C22×C22⋊C411yescharacteristic
587C2×C42C2×C4×D411yescharacteristic
588C2×C42C2×C4×D411yescharacteristic
589C2×C42C2×C4×D411yescharacteristic
590C2×C42C2×C4×D411yescharacteristic
591C2×C42C2×C4×D411yescharacteristic
592C2×C42C2×C4×D411yescharacteristic
593C2×C42#51811yescharacteristic
594C2×C42#51811yescharacteristic
595C2×C42#51811yescharacteristic
596C2×C42#51811yescharacteristic
597C2×C42#51811yescharacteristic
598C2×C42#51811yescharacteristic
599C2×C42C2×#12011yescharacteristic
600C2×C42C2×#12011yescharacteristic
601C2×C42C2×#12011yescharacteristic
602C2×C42C2×#12011yescharacteristic
603C2×C42C2×#12011yescharacteristic
604C2×C42C2×#12011yescharacteristic
605C2×C42C2×#12011yescharacteristic
606C2×C42C2×#12011yescharacteristic
607C2×C42C2×#12011yescharacteristic
608C2×C42C2×#12011yescharacteristic
609C2×C42C2×#12011yescharacteristic
610C2×C42C2×#12011yescharacteristic
611C2×C42C2×#12011yescharacteristic
612C2×C42C2×#12011yescharacteristic
613C2×C42C2×#12111yescharacteristic
614C2×C42C2×#12111yescharacteristic
615C2×C42C2×#12111yescharacteristic
616C2×C42C2×#12111yescharacteristic
617C2×C42C2×#12111yescharacteristic
618C2×C42C2×#12111yescharacteristic
619C2×C42C2×#12311yescharacteristic
620C2×C42C2×#12311yescharacteristic
621C2×C42C2×#12311yescharacteristic
622C2×C42C2×#12311yescharacteristic
623C2×C42#53411yescharacteristic
624C2×C42#53411yescharacteristic
625C2×C42#53411yescharacteristic
626C2×C42#53411yescharacteristic
627C2×C42#53411yescharacteristic
628C2×C42#53411yescharacteristic
629C2×C42#53411yescharacteristic
630C2×C42#53411yescharacteristic
631C2×C42#53411yescharacteristic
632C2×C42#53411yescharacteristic
633C2×C42#53411yescharacteristic
634C2×C42#53411yescharacteristic
635C2×C42D4211yescharacteristic
636C2×C42D4211yescharacteristic
637C2×C42D4211yescharacteristic
638C2×C42D4211yescharacteristic
639C2×C42D4211yescharacteristic
640C2×C42D4211yescharacteristic
641C2×C42D4211yescharacteristic
642C2×C42D4211yescharacteristic
643C2×C42D4211yescharacteristic
644C2×C42D4211yescharacteristic
645C2×C42D4211yescharacteristic
646C2×C42D4211yescharacteristic
647C2×C42D4211yescharacteristic
648C2×C42D4211yescharacteristic
649C2×C42D4211yescharacteristic
650C2×C42D4211yescharacteristic
651C2×C42D4211yescharacteristic
652C2×C42D4211yescharacteristic
653C2×C42#54611yescharacteristic
654C2×C42#54611yescharacteristic
655C2×C42#54611yescharacteristic
656C2×C42#54611yescharacteristic
657C2×C42#54611yescharacteristic
658C2×C42#54611yescharacteristic
659C2×C42#54611yescharacteristic
660C2×C42#54611yescharacteristic
661C2×C42#54611yescharacteristic
662C2×C42#54611yescharacteristic
663C2×C42#54611yescharacteristic
664C2×C42#54611yescharacteristic
665C2×C42#54611yescharacteristic
666C2×C42#54611yescharacteristic
667C2×C42#54611yescharacteristic
668C2×C42#54611yescharacteristic
669C2×C42#54611yescharacteristic
670C2×C42#54611yescharacteristic
671C2×C42#54611yescharacteristic
672C2×C42#54611yescharacteristic
673C2×C42#54611yescharacteristic
674C2×C42#54611yescharacteristic
675C2×C42#54611yescharacteristic
676C2×C42#54611yescharacteristic
677C2×C42C24×C411yescharacteristic
678C2×C42C23×D411yescharacteristic
679C2×C42C23×D411yescharacteristic
680C2×C42C23×D411yescharacteristic
681C2×C42C23×D411yescharacteristic
682C2×C42C23×D411yescharacteristic
683C2×C42C23×D411yescharacteristic
684C2×C42C22×#4111yescharacteristic
685C2×C42C22×#4111yescharacteristic
686C2×C42C2×H(5,𝔽2)11yescharacteristic
687C2×C42C2×H(5,𝔽2)11yescharacteristic
688C2×C42C2×H(5,𝔽2)11yescharacteristic
689C22⋊C8C22×C22⋊C418yes—
690C4×C8C22×C22⋊C418yes—
691C24D4×C22⋊C411yescharacteristic
692C24D4×C22⋊C411yescharacteristic
693C24#240311yescharacteristic
694C24#240311yescharacteristic
695C24#241011yescharacteristic
696C24#241011yescharacteristic
697C24C2×D4211yescharacteristic
698C2×D4C2×#37918yes—
699C2×D4C2×#38618yes—
700C22×C4C2×#37911yescharacteristic
701C22×C4C2×#37911yescharacteristic
702C22×C4C2×#37911yescharacteristic
703C22×C4C2×#37911yescharacteristic
704C22×C4C2×#38611yescharacteristic
705C22×C4C2×#38611yescharacteristic
706C22×C4C2×#38611yescharacteristic
707C22×C4C2×#38611yescharacteristic
708C22×C4#230811yescharacteristic
709C22×C4#230811yescharacteristic
710C22×C4#230811yescharacteristic
711C22×C4#230811yescharacteristic
712C22×C4D4×C22⋊C411yescharacteristic
713C22×C4D4×C22⋊C411yescharacteristic
714C22×C4D4×C22⋊C411yescharacteristic
715C22×C4D4×C22⋊C411yescharacteristic
716C22×C4D4×C22⋊C411yescharacteristic
717C22×C4D4×C22⋊C411yescharacteristic
718C22×C4D4×C22⋊C411yescharacteristic
719C22×C4D4×C22⋊C411yescharacteristic
720C22×C4D4×C22⋊C411yescharacteristic
721C22×C4D4×C22⋊C411yescharacteristic
722C22×C4D4×C22⋊C411yescharacteristic
723C22×C4D4×C22⋊C411yescharacteristic
724C22×C4D4×C22⋊C411yescharacteristic
725C22×C4D4×C22⋊C411yescharacteristic
726C22×C4D4×C22⋊C411yescharacteristic
727C22×C4D4×C22⋊C411yescharacteristic
728C22×C4D4×C22⋊C411yescharacteristic
729C22×C4D4×C22⋊C411yescharacteristic
730C22×C4#240311yescharacteristic
731C22×C4#240311yescharacteristic
732C22×C4#240311yescharacteristic
733C22×C4#240311yescharacteristic
734C22×C4#240311yescharacteristic
735C22×C4#240311yescharacteristic
736C22×C4#240311yescharacteristic
737C22×C4#240311yescharacteristic
738C22×C4#240311yescharacteristic
739C22×C4#240311yescharacteristic
740C22×C4#240511yescharacteristic
741C22×C4#240511yescharacteristic
742C22×C4#240511yescharacteristic
743C22×C4#240511yescharacteristic
744C22×C4#240511yescharacteristic
745C22×C4#240511yescharacteristic
746C22×C4#240511yescharacteristic
747C22×C4#240511yescharacteristic
748C22×C4#241011yescharacteristic
749C22×C4#241011yescharacteristic
750C22×C4#241011yescharacteristic
751C22×C4#241011yescharacteristic
752C22×C4#241011yescharacteristic
753C22×C4#241011yescharacteristic
754C22×C4#241011yescharacteristic
755C22×C4#241011yescharacteristic
756C22×C4#241011yescharacteristic
757C22×C4#241011yescharacteristic
758C22×C4#241011yescharacteristic
759C22×C4#241011yescharacteristic
760C22×C4#241011yescharacteristic
761C22×C4#241011yescharacteristic
762C22×C4#241011yescharacteristic
763C22×C4#241011yescharacteristic
764C22×C4#241011yescharacteristic
765C22×C4#241011yescharacteristic
766C22×C4C23×C22⋊C411yescharacteristic
767C22×C4C22×C4×D411yescharacteristic
768C22×C4C2×#51811yescharacteristic
769C22×C4C22×#12011yescharacteristic
770C22×C4C22×#12011yescharacteristic
771C22×C4C22×#12011yescharacteristic
772C22×C4C22×#12111yescharacteristic
773C22×C4C2×#53411yescharacteristic
774C22×C4C2×#53411yescharacteristic
775C22×C4C2×D4211yescharacteristic
776C22×C4C2×D4211yescharacteristic
777C22×C4C2×D4211yescharacteristic
778C22×C4C2×D4211yescharacteristic
779C22×C4C2×D4211yescharacteristic
780C22×C4C2×#54611yescharacteristic
781C22×C4C2×#54611yescharacteristic
782C22×C4C2×#54611yescharacteristic
783C22×C4C2×#54611yescharacteristic
784C4⋊C4C2×#37918yes—
785C4⋊C4C2×#38618yes—
786C42C2×#37911yescharacteristic
787C42C2×#37911yescharacteristic
788C42C2×#37911yescharacteristic
789C42C2×#37911yescharacteristic
790C42C2×#38611yescharacteristic
791C42C2×#38611yescharacteristic
792C42C2×#38611yescharacteristic
793C42C2×#38611yescharacteristic
794C42#230811yescharacteristic
795C42#230811yescharacteristic
796C42#230811yescharacteristic
797C42#230811yescharacteristic
798C42D4×C22⋊C411yescharacteristic
799C42D4×C22⋊C411yescharacteristic
800C42D4×C22⋊C411yescharacteristic
801C42D4×C22⋊C411yescharacteristic
802C42D4×C22⋊C411yescharacteristic
803C42D4×C22⋊C411yescharacteristic
804C42D4×C22⋊C411yescharacteristic
805C42D4×C22⋊C411yescharacteristic
806C42D4×C22⋊C411yescharacteristic
807C42D4×C22⋊C411yescharacteristic
808C42D4×C22⋊C411yescharacteristic
809C42D4×C22⋊C411yescharacteristic
810C42#240311yescharacteristic
811C42#240311yescharacteristic
812C42#240311yescharacteristic
813C42#240311yescharacteristic
814C42#240511yescharacteristic
815C42#240511yescharacteristic
816C42#240511yescharacteristic
817C42#240511yescharacteristic
818C42#240511yescharacteristic
819C42#240511yescharacteristic
820C42#240511yescharacteristic
821C42#240511yescharacteristic
822C42#241011yescharacteristic
823C42#241011yescharacteristic
824C42#241011yescharacteristic
825C42#241011yescharacteristic
826C42#241011yescharacteristic
827C42#241011yescharacteristic
828C42#241011yescharacteristic
829C42#241011yescharacteristic
830C42#241011yescharacteristic
831C42#241011yescharacteristic
832C42#241011yescharacteristic
833C42#241011yescharacteristic
834C42C23×C22⋊C411yescharacteristic
835C42C23×C22⋊C411yescharacteristic
836C42C22×C4×D411yescharacteristic
837C42C2×#51811yescharacteristic
838C42C22×#12011yescharacteristic
839C42C22×#12011yescharacteristic
840C42C22×#12111yescharacteristic
841C42C22×#12311yescharacteristic
842C42C2×#53411yescharacteristic
843C42C2×#53411yescharacteristic
844C42C2×D4211yescharacteristic
845C42C2×D4211yescharacteristic
846C42C2×#54611yescharacteristic
847C42C2×#54611yescharacteristic
848C42C2×#54611yescharacteristic
849C42C2×#54611yescharacteristic
850C23#1386711yescharacteristic
851C23#1386711yescharacteristic
852C23#1386711yescharacteristic
853C23#1386711yescharacteristic
854C23C2×D4×C22⋊C411yescharacteristic
855C23C2×#240311yescharacteristic
856C23C2×#241011yescharacteristic
857C2×C4#1386711yescharacteristic
858C2×C4#1386711yescharacteristic
859C2×C4#1386711yescharacteristic
860C2×C4#1386711yescharacteristic
861C2×C4#1386711yescharacteristic
862C2×C4#1386711yescharacteristic
863C2×C4#1386711yescharacteristic
864C2×C4#1386711yescharacteristic
865C2×C4#1386711yescharacteristic
866C2×C4#1386711yescharacteristic
867C2×C4#1386711yescharacteristic
868C2×C4#1386711yescharacteristic
869C2×C4#2388212yes—
870C2×C4#2388214yes—
871C2×C4#2388312yes—
872C2×C4C22×#37911yescharacteristic
873C2×C4C22×#38611yescharacteristic
874C2×C4C2×#230811yescharacteristic
875C2×C4C2×D4×C22⋊C411yescharacteristic
876C2×C4C2×D4×C22⋊C411yescharacteristic
877C2×C4C2×D4×C22⋊C411yescharacteristic
878C2×C4C2×#240311yescharacteristic
879C2×C4C2×#241011yescharacteristic
880C2×C4C2×#241011yescharacteristic
881C2×C4C2×#241011yescharacteristic
882C2×C4C2×#240511yescharacteristic
883C2×C4C2×#240511yescharacteristic
884C22#35957612yes—
885C22C2×#1386711yescharacteristic
886C22C2×#2388212yes—
887C4#35957612yes—
888C4#35964512yes—
889C4#35964512yes—
890C4#35967912yes—
891C4C2×#2388211yescharacteristic
892C4C2×#2388311yescharacteristic
893C2C2×#35957611yescharacteristic
894C2C2×#35964511yescharacteristic
895C2C2×#35967911yescharacteristic
subgroupG/H
center, socleC22C2×#13867
commutatorC2×C42C24×C4
Frattini, cosocleC22×C42C25
prime radicalC2×#10577334C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72338248C2semidirect
2. #72338235C2semidirect
3. #72338230C2semidirect
4. #72338226C2semidirect
5. #72338224C2semidirect
6. #72338214C2semidirect
7. #72338213C2semidirect
8. #72338208C2semidirect
9. #72337526C2semidirect
10. #72316807C2semidirect
11. #72316741C2semidirect
12. #72316683C2semidirect
14. #72257773C2semidirect
15. #72257772C2semidirect
16. #72226726C2semidirect
19. #10577334C4semidirect
21. C2×#61682C4semidirect
22. C2×#61679C4semidirect
28. C2×#60144C22semidirect
29. #7625999C22semidirect
30. #6393503C22semidirect
32. #6374554C22semidirect
33. #6374317C22semidirect
35. #6372442C22semidirect
36. #6372442C22semidirect
37. #6372358C22semidirect
38. #6370997C22semidirect
39. #6370937C22semidirect
41. #6344036C22semidirect
42. C2×#17745C22semidirect
43. #6343804C22semidirect
45. #6343377C22semidirect
46. #6343377C22semidirect
47. #6343377C22semidirect
48. C2×#17451C22semidirect
49. #202021C22semidirect
50. #200904C22semidirect
51. #198957C22semidirect
52. #195355C22semidirect
53. #187428C22semidirect
54. #186289C22semidirect
55. #185340C22semidirect
56. #181791C22semidirect
57. #181375C22semidirect
58. #181222C22semidirect
59. #181220C22semidirect
60. #181175C22semidirect
61. #181122C22semidirect
62. #181055C22semidirect
63. #180880C22semidirect
64. #115392C22semidirect
65. #114223C22semidirect
66. #113989C22semidirect
67. #113022C22semidirect
68. #108044C22semidirect
69. #107826C22semidirect
70. #62812C2×C4semidirect
72. C2×#3497C2×C4semidirect
73. C2×#3496C2×C4semidirect
87. #61682C2×C4semidirect
88. #61679C2×C4semidirect
90. #60803C2×C4semidirect
95. C2×#3214C2×C4semidirect
102. #60561C2×C4semidirect
109. C2×#3103C2×C4semidirect
111. C2×#3100C2×C4semidirect
115. #60232C2×C4semidirect
117. C2×#2981C2×C4semidirect
118. C2×#2932C23semidirect
126. #34369C23semidirect
131. #21891C23semidirect
133. #21816C23semidirect
135. #21408C23semidirect
136. #21408C23semidirect
138. #21379C23semidirect
143. #20748C23semidirect
144. #20723C23semidirect
145. #17745C23semidirect
147. #17731C23semidirect
148. #17671C23semidirect
150. #17595C23semidirect
151. #17589C23semidirect
152. #17561C23semidirect
153. #17451C23semidirect
154. #8113C23semidirect
155. #8077C23semidirect
156. #7977C23semidirect
157. #7976C23semidirect
158. #7962C23semidirect
159. #7945C23semidirect
160. #7919C23semidirect
161. #7861C23semidirect

Maximal subgroups

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

subgroupindex
#723382482
#723382352
#723382302
#723382262
#723382242
#723382142
#723382132
#723382082
#723375262
#723168072
#723167412
#723166832
C2×#105773342
#722577732
#722577722
#722267262