Finite Group Databasebeta

← #72312143

Subgroups — #72312143

Order 2048.

At least 6750 conjugacy classes of subgroups; only the 2484 normal subgroups are shown.

The subgroup lattice has 806 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72312134C212yesmaximal, complemented
2#72312129C212yesmaximal, complemented
3#72312125C212yesmaximal, complemented
4#72312121C218yesmaximal, complemented
5#72312116C218yesmaximal, complemented
6#72312114C211yesmaximal, characteristic, complemented
7#72312112C211yesmaximal, characteristic, complemented
8#72312108C211yesmaximal, characteristic, complemented
9#72312044C211yesmaximal, characteristic, complemented
10#72311906C211yesmaximal, characteristic, complemented
11#72281894C211yesmaximal, characteristic, complemented
12#72257760C212yesmaximal, complemented
13#72257321C211yesmaximal, characteristic
14C2×#62812C2211yescharacteristic
15C22×#3481C2211yescharacteristic
16C2×#60282C2211yescharacteristic, complemented
17#7737817C412yescomplemented
18#7737817C412yescomplemented
19#7737652C412yescomplemented
20#7737411C412yescomplemented
21#7734385C2214yes—
22#7733277C2214yes—
23#7636581C414yescomplemented
24D4×#525C414yescomplemented
25#7628578C2211yescharacteristic
26#7628578C2211yescharacteristic
27#7628157C2211yescharacteristic
28#7628157C2211yescharacteristic
29#7625999C2211yescharacteristic
30#7625424C2211yescharacteristic, complemented
31#6374676C2212yescomplemented
32#6370997C2212yescomplemented
33#6370997C2212yescomplemented
34#6370937C2211yescharacteristic, complemented
35#6370937C2212yescomplemented
36#6343655C2218yescomplemented
37#6343377C2212yes—
38#6343377C2212yes—
39#6343377C2212yescomplemented
40#6342561C2211yescharacteristic, complemented
41#6342561C2212yescomplemented
42#201867C2218yescomplemented
43#201674C2218yescomplemented
44#201468C2214yescomplemented
45#201464C2214yescomplemented
46#194658C2214yescomplemented
47#194657C2214yescomplemented
48#185659C2218yescomplemented
49#185481C2218yescomplemented
50#185475C2218yescomplemented
51#181777C2212yescomplemented
52#181358C2212yescomplemented
53#181343C2212yescomplemented
54#181122C2212yescomplemented
55#113656C2218yescomplemented
56#113655C2218yescomplemented
57#112305C22116yescomplemented
58#107568C22116yescomplemented
59C2×#3499C2×C412yes—
60C2×#3499D412yes—
61C2×#3498C2×C412yes—
62C2×#3498D412yes—
63C2×#3497D412yes—
64C2×#3496D412yes—
65C2×#3496C2314yes—
66C22×#559C2×C411yescharacteristic, complemented
67C22×#553C2312yes—
68C22×#554C2×C411yescharacteristic, complemented
69C22×#554C2×C411yescharacteristic, complemented
70C2×D4×#41C2×C414yes—
71C2×D4×#41D414yes—
72C22×#546C2312yes—
73C22×D42C2×C411yescharacteristic, complemented
74C22×#532D414yes—
75C22×#532C2311yescharacteristic
76C22×#532C2311yescharacteristic
77C22×#529C2×C412yescomplemented
78C22×C4×#41C2311yescharacteristic
79C22×C4×#41C2311yescharacteristic
80C22×C4×#41C2311yescharacteristic
81C23×C4×D4C2×C412yescomplemented
82C2×#2973C2314yes—
83C2×#2920C2312yes—
84C2×#2920C2312yes—
85#38907C2×C418yescomplemented
86#38906C2×C418yescomplemented
87#38905C2×C418yescomplemented
88#38904C2×C418yescomplemented
89#36624C2×C414yescomplemented
90#36103C2×C418yescomplemented
91#36102C2×C418yescomplemented
92D4×#123C2×C418yescomplemented
93D4×#120C2×C418yescomplemented
94#35262C2312yes—
95#35250C2312yes—
96#35249C2×C412yescomplemented
97#35249C2×C412yescomplemented
98#35237C2×C412yescomplemented
99#35237C2×C412yescomplemented
100#35076C2314yes—
101#34971C2×C412yes—
102#34971C2×C412yes—
103#34971D412yes—
104#34963C2×C412yes—
105#34963C2×C412yes—
106#34963D412yes—
107#34956C2314yes—
108#34955C2×C412yescomplemented
109#34952C2×C412yes—
110#34952D412yes—
111#34936C2×C412yescomplemented
112#34935C2×C412yes—
113#34935D412yes—
114#34909D414yes—
115#34875D414yes—
116#34875D414yes—
117#34809D412yes—
118#34809D412yes—
119#34809C2312yes—
120#34736D412yes—
121#34736D412yes—
122#34736C2312yes—
123#34547D414yes—
124#34365C2×C412yescomplemented
125#34364C2×C412yescomplemented
126#34363C2314yes—
127#34185C2314yes—
128D4×#117C2×C414yescomplemented
129C4×#525C2×C414yes—
130#34012C2312yes—
131#34012C2311yescharacteristic
132#34012C2311yescharacteristic
133#34012C2312yes—
134#21767C2318yes—
135#20722C2314yes—
136#20722C2318yes—
137#20705C2314yes—
138#20705C2314yes—
139#20605C2314yes—
140#20605C2314yes—
141#17583D418yescomplemented
142#17577C2318yes—
143#17577C2318yes—
144#17577C2318yes—
145#17544D418yescomplemented
146#17362C2314yes—
147#17362C2318yes—
148#8104C2318yes—
149#8102C2318yes—
150#8049C2318yes—
151#7946C2318yes—
152C23×#41C2×D411yescharacteristic
153C23×#41C2×D411yescharacteristic
154C23×#41C2411yescharacteristic
155C24×D4C22×C412yes—
156C2×#550C22⋊C414yes—
157C2×#550C22⋊C414yes—
158C2×D4×Q8C22⋊C414yes—
159C2×D4×Q8C22⋊C414yes—
160C2×#547C22⋊C414yes—
161C2×#547C22⋊C414yes—
162C2×#547C22×C418yes—
163C2×#547C2×D418yes—
164C2×D42C22⋊C414yes—
165C2×D42C22⋊C414yes—
166C2×D42C22×C418yes—
167C2×D42C2×D418yes—
168C2×#532C22⋊C418yes—
169C2×#532C22⋊C414yes—
170C2×#532C22⋊C414yes—
171C2×#532C22×C412yes—
172C2×#532C22×C412yes—
173C2×#532C2×D412yes—
174C2×#532C2×D412yes—
175C2×#532C2×D418yes—
176C2×#532C2×D412yes—
177C2×#532C2×D412yes—
178C2×#532C2×D412yes—
179C2×#532C2×D412yes—
180C2×#532C2×D414yes—
181C2×#532C2×D414yes—
182C2×#532#4114yes—
183C2×#532#4114yes—
184C22×C4⋊Q8C22⋊C414yes—
185C22×C4⋊Q8C22×C411yescharacteristic
186C22×C4⋊Q8C2×D411yescharacteristic
187C22×#127C22⋊C414yes—
188C22×#127C22×C411yescharacteristic
189C22×#127C2×D411yescharacteristic
190C22×#125C22×C412yes—
191C22×#124C22×C412yes—
192C2×#525C22⋊C414yes—
193C22×C22⋊Q8C22×C412yes—
194C22×#121C22×C412yes—
195C22×#121C2×D418yes—
196C22×#121C2412yes—
197C22×#121C2412yes—
198C2×C4×#41C22×C412yes—
199C2×C4×#41C22×C412yes—
200C2×C4×#41C2×D412yes—
201C2×C4×#41C2×D412yes—
202C2×C4×#41C2×D412yes—
203C2×C4×#41C2×D412yes—
204C2×C4×#41C2×D412yes—
205C2×C4×#41C2×D412yes—
206C2×C4×#41C2×D412yes—
207C2×C4×#41C2×D412yes—
208C2×C4×#41C2×D412yes—
209C2×C4×#41C2×D412yes—
210C22×C4×Q8C22×C411yescharacteristic
211C22×C4×Q8C22×C411yescharacteristic
212C22×C4×Q8C22×C411yescharacteristic
213C22×C4×Q8C2×D411yescharacteristic
214C22×C4×Q8C2×D411yescharacteristic
215C22×C4×Q8C2×D411yescharacteristic
216C22×C4×D4C22⋊C418yes—
217C22×C4×D4C22×C411yescharacteristic
218C22×C4×D4C22×C411yescharacteristic
219C22×C4×D4C22×C412yes—
220C22×C4×D4C22×C412yes—
221C22×C4×D4C22×C412yes—
222C22×C4×D4C22×C411yescharacteristic
223C22×C4×D4C2×D412yes—
224C22×C4×D4C2×D412yes—
225C22×C4×D4C2×D411yescharacteristic
226C22×C4×D4C2×D412yes—
227C22×C4×D4C2×D411yescharacteristic
228C22×C4×D4C2×D411yescharacteristic
229C22×C4×D4C2412yes—
230C22×C4×D4C2412yes—
231C22×#117C2×D412yes—
232C22×#117C2×D412yes—
233C22×#117C2×D411yescharacteristic
234C22×#117C2×D411yescharacteristic
235C22×#117C2411yescharacteristic
236C23×C4⋊C4C22×C412yes—
237C23×C42C22×C412yes—
238C23×C42C2×D412yes—
239C23×C42C2411yescharacteristic
240#2920C2×D414yescomplemented
241#2920C2×D414yescomplemented
242C2×#407C2414yes—
243C2×#407C2414yes—
244#2854C22×C418yes—
245#2847C22×C418yes—
246#2599C22⋊C418yes—
247#2598C22⋊C418yes—
248#2581C22⋊C414yes—
249#2580C22⋊C414yes—
250#2579C2×D418yes—
251#2536C22⋊C414yes—
252#2535C22⋊C414yes—
253#2534C2×D418yes—
254#2504C22×C414yes—
255#2501C22×C414yes—
256#2487C22⋊C414yes—
257#2487C22×C414yes—
258#2486C22⋊C414yes—
259#2486C22×C414yes—
260#2484C22⋊C414yes—
261#2484C2×D414yes—
262#2483C2×D414yes—
263#2482C22⋊C414yes—
264#2482C2×D414yes—
265#2436C22×C414yes—
266#2433C22×C414yes—
267#2409C22⋊C414yes—
268#2409C22×C414yes—
269#2408C22⋊C414yes—
270#2408C22×C414yes—
271#2406C22⋊C414yes—
272#2406C2×D414yes—
273#2405C2×D414yes—
274#2405C2×D414yes—
275#2404C22⋊C414yes—
276#2404C2×D414yes—
277#2403C2×D414yes—
278#2399C22⋊C414yes—
279#2398C22⋊C414yes—
280#2398C22⋊C414yes—
281#2397C22⋊C414yes—
282#2396C22⋊C418yes—
283#2395C2×D418yes—
284#2392C22⋊C418yes—
285#2388C2×D418yes—
286#2344C22×C418yes—
287D4×C22⋊C4C22×C418yes—
288C4×#123C22⋊C418yes—
289C4×#123C22×C418yes—
290C4×#120C22⋊C418yes—
291C4×#120C22×C418yes—
292#2297C22⋊C414yes—
293#2296C22⋊C414yes—
294#2285C22×C412yes—
295#2285C2×D412yes—
296#2283C22×C412yes—
297#2283C22×C412yes—
298#2283C2×D412yes—
299#2283C2×D412yes—
300#2283C2×D412yes—
301#2283C2×D412yes—
302#2283C2×D414yescomplemented
303#2280C22⋊C414yes—
304#2280C2×D412yes—
305#2280C2×D412yes—
306#2280C2414yes—
307#2280C2412yes—
308#2280C2414yes—
309#2280C2412yes—
310C4×#117C22×C412yes—
311C4×#117C2×D412yes—
312C4×#117C2×D414yescomplemented
313#1507C2×D4132yescomplemented
314C22×#41C2×C22⋊C412yes—
315C22×#41C2×C22⋊C412yes—
316C22×#41#12012yes—
317C22×#41#12012yes—
318C22×#41C22×D412yes—
319C22×#41C22×D412yes—
320C23×Q8C2×C22⋊C411yescharacteristic
321C23×Q8#12011yescharacteristic
322C23×Q8C23×C411yescharacteristic
323C23×D4C2×C22⋊C411yescharacteristic
324C23×D4C2×C22⋊C418yes—
325C23×D4#12011yescharacteristic
326C23×D4C23×C411yescharacteristic
327C23×D4C23×C412yes—
328C23×D4C22×D412yes—
329C23×D4C22×D412yes—
330C23×D4C22×D412yes—
331C24×C4C2×C22⋊C412yes—
332C24×C4C2×C22⋊C412yes—
333C24×C4#12012yes—
334C24×C4#12012yes—
335C24×C4C23×C412yes—
336C24×C4C22×D412yes—
337C24×C4C22×D411yescharacteristic
338C24×C4C22×D411yescharacteristic
339C24×C4C2511yescharacteristic
340#532#12014yes—
341#532#12014yes—
342#532#12018yes—
343#532#12118yes—
344#532#12118yes—
345#532#12118yes—
346#532#12118yes—
347#532#12314yes—
348#532#12314yes—
349#532#12318yes—
350C2×C4⋊Q8C2×C22⋊C412yes—
351C2×C4⋊Q8C2×C22⋊C412yes—
352C2×C4⋊Q8C2×C22⋊C418yes—
353C2×C4⋊Q8C2×C22⋊C412yes—
354C2×C4⋊Q8C2×C22⋊C412yes—
355C2×C4⋊Q8C4×D414yes—
356C2×C4⋊Q8C4×D414yes—
357C2×#127C2×C22⋊C412yes—
358C2×#127C2×C22⋊C412yes—
359C2×#127C2×C22⋊C418yes—
360C2×#127C2×C22⋊C412yes—
361C2×#127C2×C22⋊C412yes—
362C2×#127C4×D414yes—
363C2×#127C4×D414yes—
364C2×#123C2×C22⋊C418yes—
365C2×#121C2×C22⋊C418yes—
366C2×#121C2×C22⋊C418yes—
367C2×#121C23×C414yes—
368C2×#121C22×D414yes—
369C2×#121C22×D414yes—
370C2×#121C22×D414yes—
371C2×#121C22×D418yes—
372C2×#121C2×#4118yes—
373C2×#120C2×C22⋊C418yes—
374C2×C4×Q8C2×C22⋊C412yes—
375C2×C4×Q8C2×C22⋊C412yes—
376C2×C4×Q8C2×C22⋊C412yes—
377C2×C4×Q8C2×C22⋊C412yes—
378C2×C4×Q8C2×C22⋊C412yes—
379C2×C4×Q8C2×C22⋊C412yes—
380C2×C4×Q8C2×C22⋊C412yes—
381C2×C4×Q8C2×C22⋊C412yes—
382C2×C4×Q8#12012yes—
383C2×C4×Q8#12012yes—
384C2×C4×Q8#12012yes—
385C2×C4×Q8#12012yes—
386C2×C4×D4C2×C22⋊C414yes—
387C2×C4×D4C2×C22⋊C414yes—
388C2×C4×D4C2×C22⋊C412yes—
389C2×C4×D4C2×C22⋊C412yes—
390C2×C4×D4C2×C22⋊C412yes—
391C2×C4×D4C2×C22⋊C412yes—
392C2×C4×D4C2×C22⋊C418yes—
393C2×C4×D4C2×C22⋊C418yes—
394C2×C4×D4C2×C22⋊C414yes—
395C2×C4×D4C2×C22⋊C414yes—
396C2×C4×D4C2×C22⋊C412yes—
397C2×C4×D4C2×C22⋊C412yes—
398C2×C4×D4C2×C22⋊C412yes—
399C2×C4×D4C2×C22⋊C412yes—
400C2×C4×D4C2×C22⋊C414yes—
401C2×C4×D4C2×C22⋊C414yes—
402C2×C4×D4C4×D418yes—
403C2×C4×D4C4×D418yes—
404C2×C4×D4#12012yes—
405C2×C4×D4#12012yes—
406C2×C4×D4#12012yes—
407C2×C4×D4#12012yes—
408C2×C4×D4#12014yes—
409C2×C4×D4#12014yes—
410C2×C4×D4C23×C414yes—
411C2×C4×D4C22×D414yes—
412C2×C4×D4C22×D414yes—
413C2×C4×D4C22×D414yes—
414C2×#117C2×C22⋊C414yes—
415C2×#117C2×C22⋊C414yes—
416C2×#117C2×C22⋊C414yes—
417C2×#117C2×C22⋊C412yes—
418C2×#117C2×C22⋊C412yes—
419C2×#117#12014yes—
420C2×#117#12014yes—
421C2×#117#12012yes—
422C2×#117#12012yes—
423C2×#117C22×D412yes—
424C2×#117C22×D412yes—
425C22×C4⋊C4C2×C22⋊C411yescharacteristic
426C22×C4⋊C4C2×C22⋊C411yescharacteristic
427C22×C4⋊C4C2×C22⋊C412yes—
428C22×C4⋊C4C2×C22⋊C418yes—
429C22×C4⋊C4#12012yes—
430C22×C4⋊C4#12011yescharacteristic
431C22×C4⋊C4#12011yescharacteristic
432C22×C4⋊C4C23×C411yescharacteristic
433C22×C4⋊C4C23×C411yescharacteristic
434C22×C4⋊C4C23×C412yes—
435C22×C4⋊C4C22×D412yes—
436C22×C4⋊C4C22×D412yes—
437C22×C4⋊C4C22×D412yes—
438C22×C22⋊C4C2×C22⋊C412yes—
439C22×C22⋊C4#12012yes—
440C22×C22⋊C4C22×D412yes—
441C22×C22⋊C4C22×D412yes—
442C22×C22⋊C4C22×D412yes—
443C22×C22⋊C4C22×D412yes—
444C22×C42C2×C22⋊C412yes—
445C22×C42C2×C22⋊C412yes—
446C22×C42C2×C22⋊C414yes—
447C22×C42C2×C22⋊C414yes—
448C22×C42#12014yes—
449C22×C42#12014yes—
450C22×C42#12012yes—
451C22×C42#12012yes—
452C22×C42C23×C412yes—
453C22×C42C23×C411yescharacteristic
454C22×C42C23×C411yescharacteristic
455C22×C42C22×D412yes—
456C22×C42C22×D411yescharacteristic
457C22×C42C22×D411yescharacteristic
458C22×C42C22×D411yescharacteristic
459C22×C42C22×D411yescharacteristic
460C22×C42C22×D411yescharacteristic
461C22×C42C22×D411yescharacteristic
462C22×C42C22×D411yescharacteristic
463C22×C42C22×D411yescharacteristic
464C22×C42C22×D412yes—
465C22×C42C22×D412yes—
466C22×C42C22×D411yescharacteristic
467C22×C42C22×D411yescharacteristic
468C22×C42C2×#4112yes—
469C22×C42C2×#4112yes—
470C22×C42H(5,𝔽2)12yes—
471C22×C42H(5,𝔽2)12yes—
472C22×C42H(5,𝔽2)12yes—
473C22×C42H(5,𝔽2)12yes—
474#407C22×D418yes—
475#400C2×C22⋊C418yes—
476#399C2×C22⋊C418yes—
477#398C2×C22⋊C418yes—
478#397C2×C22⋊C418yes—
479#395C2×C22⋊C418yes—
480#394C2×C22⋊C418yes—
481#393C2×C22⋊C418yes—
482#392C2×C22⋊C418yes—
483#386C2×C22⋊C418yes—
484#386C2×C22⋊C418yes—
485#385C2×C22⋊C418yes—
486#385C2×C22⋊C418yes—
487#383C2×C22⋊C414yes—
488#382C2×C22⋊C414yes—
489#381C2×C22⋊C414yes—
490#381C2×C22⋊C418yes—
491#381C22×D414yes—
492#380C2×C22⋊C414yes—
493#380C23×C414yes—
494#380C22×D414yes—
495#379C2×C22⋊C418yes—
496#379C22×D414yes—
497C4×C4⋊C4C2×C22⋊C414yes—
498C4×C22⋊C4C2×C22⋊C414yes—
499C4×C22⋊C4C23×C414yes—
500C4×C22⋊C4C22×D418yes—
501C4×C22⋊C4C22×D414yes—
502#376C2×C22⋊C414yes—
503C25C22×C22⋊C412yes—
504C25C2×#12012yes—
505C25C23×D411yescharacteristic
506C22×Q8#37912yes—
507C22×Q8#37912yes—
508C22×Q8C22×C22⋊C412yes—
509C22×D4#37912yes—
510C22×D4#37912yes—
511C22×D4C22×C22⋊C412yes—
512C22×D4C22×C22⋊C414yes—
513C22×D4C22×C22⋊C414yes—
514C22×D4C22×C22⋊C414yes—
515C22×D4C2×C4×D418yes—
516C22×D4C2×#12014yes—
517C23×C4#37914yes—
518C23×C4#37914yes—
519C23×C4#37914yes—
520C23×C4#37914yes—
521C23×C4C22×C22⋊C411yescharacteristic
522C23×C4C22×C22⋊C412yes—
523C23×C4C22×C22⋊C412yes—
524C23×C4C22×C22⋊C412yes—
525C23×C4C22×C22⋊C414yes—
526C23×C4C22×C22⋊C411yescharacteristic
527C23×C4C22×C22⋊C411yescharacteristic
528C23×C4C22×C22⋊C411yescharacteristic
529C23×C4C2×#12011yescharacteristic
530C23×C4C2×#12011yescharacteristic
531C23×C4C2×#12012yes—
532C23×C4C2×#12014yes—
533C23×C4C2×#12012yes—
534C23×C4C2×#12012yes—
535C23×C4C2×#12011yescharacteristic
536C23×C4C2×#12011yescharacteristic
537C23×C4C2×#12011yescharacteristic
538C23×C4C2×#12011yescharacteristic
539C23×C4C2×#12011yescharacteristic
540C23×C4C2×#12011yescharacteristic
541C23×C4D4212yes—
542C23×C4D4212yes—
543C23×C4D4212yes—
544C23×C4D4212yes—
545C23×C4#54612yes—
546C23×C4#54612yes—
547C23×C4#54612yes—
548C23×C4#54612yes—
549C23×C4C24×C411yescharacteristic
550C23×C4C23×D411yescharacteristic
551C23×C4C23×D411yescharacteristic
552C23×C4C23×D411yescharacteristic
553C23×C4C23×D411yescharacteristic
554C23×C4C23×D412yes—
555C23×C4C23×D411yescharacteristic
556C23×C4C22×#4112yes—
557C23×C4C2×H(5,𝔽2)12yes—
558C23×C4C2×H(5,𝔽2)12yes—
559C4⋊Q8#38614yes—
560C4⋊Q8#38614yes—
561C4⋊Q8#38618yes—
562#127#38614yes—
563#127#38614yes—
564#127#38618yes—
565#121C2×#12018yes—
566#121C2×#121116yes—
567#121C2×#12318yes—
568C4×D4#38618yes—
569C4×D4#38618yes—
570C4×D4#386116yes—
571C2×C4⋊C4#37912yes—
572C2×C4⋊C4#37912yes—
573C2×C4⋊C4#37914yes—
574C2×C4⋊C4#37914yes—
575C2×C4⋊C4#37912yes—
576C2×C4⋊C4#37912yes—
577C2×C4⋊C4C22×C22⋊C412yes—
578C2×C4⋊C4C22×C22⋊C414yes—
579C2×C4⋊C4C22×C22⋊C412yes—
580C2×C4⋊C4C22×C22⋊C414yes—
581C2×C4⋊C4C22×C22⋊C414yes—
582C2×C4⋊C4C2×C4×D418yes—
583C2×C4⋊C4C2×#12014yes—
584C2×C22⋊C4#37914yes—
585C2×C22⋊C4#37914yes—
586C2×C22⋊C4C22×C22⋊C414yes—
587C2×C22⋊C4C22×C22⋊C414yes—
588C2×C22⋊C4C22×C22⋊C418yes—
589C2×C22⋊C4C2×#12014yes—
590C2×C22⋊C4C2×#12014yes—
591C2×C42#37914yes—
592C2×C42#37914yes—
593C2×C42#37914yes—
594C2×C42#37914yes—
595C2×C42C22×C22⋊C414yes—
596C2×C42C22×C22⋊C411yescharacteristic
597C2×C42C22×C22⋊C411yescharacteristic
598C2×C42C22×C22⋊C411yescharacteristic
599C2×C42C22×C22⋊C411yescharacteristic
600C2×C42C22×C22⋊C411yescharacteristic
601C2×C42C22×C22⋊C411yescharacteristic
602C2×C42C22×C22⋊C411yescharacteristic
603C2×C42C22×C22⋊C411yescharacteristic
604C2×C42C2×C4×D412yes—
605C2×C42C2×C4×D412yes—
606C2×C42C2×C4×D412yes—
607C2×C42C2×C4×D412yes—
608C2×C42#51812yes—
609C2×C42#51812yes—
610C2×C42#51812yes—
611C2×C42#51812yes—
612C2×C42C2×#12014yes—
613C2×C42C2×#12011yescharacteristic
614C2×C42C2×#12011yescharacteristic
615C2×C42C2×#12011yescharacteristic
616C2×C42C2×#12011yescharacteristic
617C2×C42C2×#12012yes—
618C2×C42C2×#12011yescharacteristic
619C2×C42C2×#12011yescharacteristic
620C2×C42C2×#12011yescharacteristic
621C2×C42C2×#12011yescharacteristic
622C2×C42C2×#12011yescharacteristic
623C2×C42C2×#12011yescharacteristic
624C2×C42C2×#12112yes—
625C2×C42C2×#12112yes—
626C2×C42C2×#12112yes—
627C2×C42C2×#12112yes—
628C2×C42C2×#12312yes—
629C2×C42C2×#12311yescharacteristic
630C2×C42C2×#12311yescharacteristic
631C2×C42#53412yes—
632C2×C42#53411yescharacteristic
633C2×C42#53411yescharacteristic
634C2×C42#53412yes—
635C2×C42#53411yescharacteristic
636C2×C42#53411yescharacteristic
637C2×C42#53412yes—
638C2×C42#53412yes—
639C2×C42#53412yes—
640C2×C42#53412yes—
641C2×C42D4212yes—
642C2×C42D4212yes—
643C2×C42D4212yes—
644C2×C42D4212yes—
645C2×C42D4212yes—
646C2×C42D4212yes—
647C2×C42D4212yes—
648C2×C42D4212yes—
649C2×C42D4212yes—
650C2×C42D4212yes—
651C2×C42D4212yes—
652C2×C42D4212yes—
653C2×C42#54612yes—
654C2×C42#54612yes—
655C2×C42#54612yes—
656C2×C42#54612yes—
657C2×C42#54612yes—
658C2×C42#54612yes—
659C2×C42#54612yes—
660C2×C42#54612yes—
661C2×C42#54612yes—
662C2×C42#54612yes—
663C2×C42#54612yes—
664C2×C42#54612yes—
665#95C22×C22⋊C418yes—
666C24C2×#37914yes—
667C24C23×C22⋊C411yescharacteristic
668C24C22×#12011yescharacteristic
669C24C22×#12011yescharacteristic
670C24C2×D4212yes—
671C24C2×#54612yes—
672C2×D4#179518yes—
673C2×D4C2×#38618yes—
674C22×C4C2×#37914yes—
675C22×C4C2×#37911yescharacteristic
676C22×C4C2×#37911yescharacteristic
677C22×C4C2×#37911yescharacteristic
678C22×C4C2×#37911yescharacteristic
679C22×C4C2×#37914yes—
680C22×C4C2×#37914yes—
681C22×C4C2×#37911yescharacteristic
682C22×C4C2×#37911yescharacteristic
683C22×C4C2×#37911yescharacteristic
684C22×C4C2×#37911yescharacteristic
685C22×C4D4×C22⋊C412yes—
686C22×C4D4×C22⋊C412yes—
687C22×C4D4×C22⋊C412yes—
688C22×C4D4×C22⋊C412yes—
689C22×C4D4×C22⋊C412yes—
690C22×C4D4×C22⋊C412yes—
691C22×C4D4×C22⋊C412yes—
692C22×C4D4×C22⋊C412yes—
693C22×C4#240311yescharacteristic
694C22×C4#240312yes—
695C22×C4#240311yescharacteristic
696C22×C4#240311yescharacteristic
697C22×C4#240311yescharacteristic
698C22×C4#240312yes—
699C22×C4#240511yescharacteristic
700C22×C4#240512yes—
701C22×C4#240511yescharacteristic
702C22×C4#240511yescharacteristic
703C22×C4#240511yescharacteristic
704C22×C4#240512yes—
705C22×C4#241012yes—
706C22×C4#241012yes—
707C22×C4#241012yes—
708C22×C4#241012yes—
709C22×C4#241012yes—
710C22×C4#241012yes—
711C22×C4#241012yes—
712C22×C4#241012yes—
713C22×C4C23×C22⋊C411yescharacteristic
714C22×C4C23×C22⋊C411yescharacteristic
715C22×C4C22×C4×D412yes—
716C22×C4C2×#51812yes—
717C22×C4C22×#12011yescharacteristic
718C22×C4C22×#12011yescharacteristic
719C22×C4C22×#12011yescharacteristic
720C22×C4C22×#12112yes—
721C22×C4C22×#12311yescharacteristic
722C22×C4C2×#53411yescharacteristic
723C22×C4C2×#53412yes—
724C22×C4C2×#53411yescharacteristic
725C22×C4C2×D4212yes—
726C22×C4C2×D4212yes—
727C22×C4C2×D4212yes—
728C22×C4C2×#54612yes—
729C22×C4C2×#54612yes—
730C22×C4C2×#54612yes—
731C4⋊C4C2×#38618yes—
732C42C2×#38611yescharacteristic
733C42C2×#38611yescharacteristic
734C42C2×#38611yescharacteristic
735C42C2×#38611yescharacteristic
736C42C2×#38612yes—
737C42C2×#38612yes—
738C42#230811yescharacteristic
739C42#230811yescharacteristic
740C42#230811yescharacteristic
741C42#230811yescharacteristic
742C42#230812yes—
743C42#230812yes—
744C42D4×C22⋊C412yes—
745C42D4×C22⋊C412yes—
746C42D4×C22⋊C412yes—
747C42D4×C22⋊C412yes—
748C42D4×C22⋊C412yes—
749C42D4×C22⋊C412yes—
750C42D4×C22⋊C412yes—
751C42D4×C22⋊C412yes—
752C42#240312yes—
753C42#240312yes—
754C42#240311yescharacteristic
755C42#240311yescharacteristic
756C42#240311yescharacteristic
757C42#240311yescharacteristic
758C42#240511yescharacteristic
759C42#240511yescharacteristic
760C42#240511yescharacteristic
761C42#240511yescharacteristic
762C42#240512yes—
763C42#240512yes—
764C42#241012yes—
765C42#241012yes—
766C42#241012yes—
767C42#241012yes—
768C42#241012yes—
769C42#241012yes—
770C42#241012yes—
771C42#241012yes—
772C23C2×#179518yes—
773C23C22×#37911yescharacteristic
774C23C2×D4×C22⋊C412yes—
775C23C2×#240311yescharacteristic
776C23C2×#241012yes—
777C23C2×#240511yescharacteristic
778C2×C4#1386711yescharacteristic
779C2×C4#1386711yescharacteristic
780C2×C4#1386711yescharacteristic
781C2×C4#1386711yescharacteristic
782C2×C4#1386711yescharacteristic
783C2×C4#1386711yescharacteristic
784C2×C4#1386711yescharacteristic
785C2×C4#1386712yes—
786C2×C4#1386712yes—
787C2×C4#1386712yes—
788C2×C4#1386712yes—
789C2×C4#1386711yescharacteristic
790C2×C4C2×#179514yes—
791C2×C4C22×#38611yescharacteristic
792C2×C4C2×#230811yescharacteristic
793C2×C4C2×D4×C22⋊C412yes—
794C2×C4C2×#240311yescharacteristic
795C2×C4C2×#241012yes—
796C2×C4C2×#240511yescharacteristic
797C22C2×#1386711yescharacteristic
798C22C22×#179512yes—
799C4#35963914yes—
800C4#35964912yes—
801C4#637418612yes—
802C2C2×#35963911yescharacteristic
803C2C2×#35964911yescharacteristic
804C2#7226226511yescharacteristic
subgroupG/H
center, socleC22C2×#13867
commutatorC23×C4C24×C4
Frattini, cosocleC24×C4C25
prime radical#72257321C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C42 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72312134C2semidirect
2. #72312129C2semidirect
3. #72312125C2semidirect
4. #72312121C2semidirect
5. #72312116C2semidirect
6. #72312114C2semidirect
7. #72312112C2semidirect
8. #72312108C2semidirect
9. #72312044C2semidirect
10. #72311906C2semidirect
11. #72281894C2semidirect
12. #72257760C2semidirect
16. C2×#60282C22semidirect
17. #7737817C4semidirect
18. #7737817C4semidirect
19. #7737652C4semidirect
20. #7737411C4semidirect
23. #7636581C4semidirect
24. D4×#525C4semidirect
30. #7625424C22semidirect
31. #6374676C22semidirect
32. #6370997C22semidirect
33. #6370997C22semidirect
34. #6370937C22semidirect
35. #6370937C22semidirect
36. #6343655C22semidirect
39. #6343377C22semidirect
40. #6342561C22semidirect
41. #6342561C22semidirect
42. #201867C22semidirect
43. #201674C22semidirect
44. #201468C22semidirect
45. #201464C22semidirect
46. #194658C22semidirect
47. #194657C22semidirect
48. #185659C22semidirect
49. #185481C22semidirect
50. #185475C22semidirect
51. #181777C22semidirect
52. #181358C22semidirect
53. #181343C22semidirect
54. #181122C22semidirect
55. #113656C22semidirect
56. #113655C22semidirect
57. #112305C22semidirect
58. #107568C22semidirect
66. C22×#559C2×C4semidirect
68. C22×#554C2×C4semidirect
69. C22×#554C2×C4semidirect
73. C22×D42C2×C4semidirect
77. C22×#529C2×C4semidirect
81. C23×C4×D4C2×C4semidirect
85. #38907C2×C4semidirect
86. #38906C2×C4semidirect
87. #38905C2×C4semidirect
88. #38904C2×C4semidirect
89. #36624C2×C4semidirect
90. #36103C2×C4semidirect
91. #36102C2×C4semidirect
92. D4×#123C2×C4semidirect
93. D4×#120C2×C4semidirect
96. #35249C2×C4semidirect
97. #35249C2×C4semidirect
98. #35237C2×C4semidirect
99. #35237C2×C4semidirect
108. #34955C2×C4semidirect
111. #34936C2×C4semidirect
124. #34365C2×C4semidirect
125. #34364C2×C4semidirect
128. D4×#117C2×C4semidirect
141. #17583D4semidirect
145. #17544D4semidirect
240. #2920C2×D4semidirect
241. #2920C2×D4semidirect
302. #2283C2×D4semidirect
312. C4×#117C2×D4semidirect
313. #1507C2×D4semidirect

Maximal subgroups

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

subgroupindex
#723121342
#723121292
#723121252
#723121212
#723121162
#723121142
#723121122
#723121082
#723120442
#723119062
#722818942
#722577602
#722573212