Finite Group Databasebeta

← #25260116

Subgroups — #25260116

Order 11008.

2766 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583468C211yesmaximal, characteristic
2#19137766C212yesmaximal, complemented
3#19137735C212yesmaximal, complemented
4#19137705C212yesmaximal, complemented
5#19137635C211yesmaximal, characteristic, complemented
6#19137632C211yesmaximal, characteristic, complemented
7#19137613C211yesmaximal, characteristic, complemented
8#19137610C211yesmaximal, characteristic, complemented
9#19137573C212yesmaximal, complemented
10#19137480C211yesmaximal, characteristic, complemented
11C22⋊C4×D172C211yesmaximal, characteristic, complemented
12#19137415C211yesmaximal, characteristic, complemented
13#19137320C212yesmaximal, complemented
14#19137318C212yesmaximal, complemented
15#19137289C211yesmaximal, characteristic, complemented
16#19137286C211yesmaximal, characteristic, complemented
17#19137257C212yesmaximal, complemented
18#19137248C212yesmaximal, complemented
19#19137184C211yesmaximal, characteristic, complemented
20C4×#13063300C211yesmaximal, characteristic, complemented
21#19137103C211yesmaximal, characteristic, complemented
22#19137081C211yesmaximal, characteristic, complemented
23C43×#2346C211yesmaximal, characteristic, complemented
24C22×#10621898C2211yescharacteristic
25C23×D172C2211yescharacteristic
26#14583468C4116yescomplemented
27C2×#13063322C2212yes—
28C2×#13063313C2212yes—
29C2×#13063300C2211yescharacteristic
30C2×#13063300C2211yescharacteristic
31C2×#13063300C2211yescharacteristic
32C2×#13063300C2211yescharacteristic
33C2×#13063295C2212yes—
34C2×#13063295C2212yes—
35C2×C4×D172C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×C4×D172C2212yescomplemented
38C2×C4×D172C2212yescomplemented
39C2×#13063287C2211yescharacteristic
40C2×#13063287C2211yescharacteristic
41C2×#13063287C2212yescomplemented
42C2×#13063287C2212yescomplemented
43C2×#13063283C2211yescharacteristic, complemented
44C2×#13063282C2211yescharacteristic, complemented
45C2×C4⋊C4×D43C2211yescharacteristic, complemented
46C2×C22⋊C4×D43C2212yes—
47C2×C22⋊C4×D43C2212yes—
48C2×C42×D43C2211yescharacteristic, complemented
49#14582803C2211yescharacteristic, complemented
50#14582803C2211yescharacteristic, complemented
51#14582803C2212yescomplemented
52#14582801C2211yescharacteristic
53#14582801C2211yescharacteristic
54#14582801C2212yescomplemented
55#14582801C2212yescomplemented
56#14582800C2211yescharacteristic
57#14582800C2211yescharacteristic
58#14582800C2212yescomplemented
59#14582800C2212yescomplemented
60#14582799C2211yescharacteristic
61#14582799C2211yescharacteristic
62#14582799C2212yes—
63#14582798C2211yescharacteristic, complemented
64#14582798C2211yescharacteristic, complemented
65#14582792C2212yes—
66#14582792C2212yes—
67#14582791C2212yescomplemented
68#14582791C2212yescomplemented
69#14582790C2212yescomplemented
70#14582790C2212yescomplemented
71#14582789C2212yescomplemented
72#14582789C2212yescomplemented
73#14582788C2212yescomplemented
74#14582788C2212yescomplemented
75#14582777C2212yes—
76#14582777C2212yes—
77#14582777C2212yes—
78#14582777C2212yes—
79#14582777C2212yescomplemented
80#14582777C2212yescomplemented
81#14582777C2212yescomplemented
82#14582777C2212yescomplemented
83#14582777C2211yescharacteristic, complemented
84#14582777C2212yescomplemented
85#14582777C2212yescomplemented
86#14582777C2212yescomplemented
87#14582777C2211yescharacteristic, complemented
88#14582777C2212yescomplemented
89#14582777C2212yescomplemented
90#14582775C2212yes—
91#14582775C2211yescharacteristic
92#14582775C2211yescharacteristic
93#14582773C2212yescomplemented
94#14582773C2212yescomplemented
95#14582770C2212yescomplemented
96#14582770C2212yescomplemented
97#14582765C2212yescomplemented
98#14582759C2211yescharacteristic
99#14582756C2211yescharacteristic, complemented
100#14582756C2211yescharacteristic, complemented
101#14582754C2212yes—
102#14582754C2212yes—
103C4⋊C4×Dic43C2211yescharacteristic, complemented
104C4⋊C4×Dic43C2211yescharacteristic, complemented
105C4×(C2×D43)⋊C4C2212yescomplemented
106C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
107C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D43)⋊C4C2212yescomplemented
109C4×C22⋊Dic43C2211yescharacteristic
110#14582746C2212yescomplemented
111#14582746C2212yescomplemented
112#14582745C2212yescomplemented
113C2×#117×C43C2211yescharacteristic
114C43×#389C2211yescharacteristic, complemented
115C43×#389C2211yescharacteristic, complemented
116C43×#388C2212yes—
117C43×#388C2212yes—
118C43×#382C2212yescomplemented
119C43×#380C2211yescharacteristic
120C4×C4⋊C4×C43C2211yescharacteristic, complemented
121C4×C4⋊C4×C43C2211yescharacteristic, complemented
122C4×C22⋊C4×C43C2211yescharacteristic
123C43×#376C2212yescomplemented
124C24×D43C2312yes—
125C2×#10621898—42no—
126C2×#10621898—42no—
127C2×#10621898C2×C418yescomplemented
128C22×Dic86C2311yescharacteristic
129C22×D172—42no—
130C22×D172—42no—
131C22×D172C2×C418yescomplemented
132C22×D172C2311yescharacteristic
133C22×D172C2311yescharacteristic
134C22×D172C2312yes—
135C22×D172C2312yes—
136C22×D172C2312yes—
137C22×D172C2312yes—
138C22×D172C2312yes—
139C22×D172C2311yescharacteristic
140C22×C22⋊D43C2311yescharacteristic
141C22×C22⋊D43C2311yescharacteristic
142C22×C4×D43C2311yescharacteristic
143C22×C4×D43C2311yescharacteristic
144C22×C4×D43C2311yescharacteristic
145C22×C4×D43C2311yescharacteristic
146C22×C4×D43C2312yes—
147C22×C4×D43C2312yes—
148C22×C4×D43C2312yes—
149C22×C4×D43C2312yes—
150C22×C4×D43C2312yes—
151#13063322C2×C4116yescomplemented
152#13063313C2×C4116yescomplemented
153#13063300C2×C418yescomplemented
154#13063300C2×C418yescomplemented
155#13063300C2×C418yescomplemented
156#13063300C2×C418yescomplemented
157#13063295C2×C4116yescomplemented
158#13063295C2×C4116yescomplemented
159C4×D172—42no—
160C4×D172—42no—
161C4×D172—44no—
162C4×D172—44no—
163#13063287—44no—
164#13063287—42no—
165#13063287—42no—
166#13063287—44no—
167#13063283—42no—
168#13063282—42no—
169C2×C4⋊Dic43C2311yescharacteristic
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2312yes—
172C2×C4⋊Dic43C2312yes—
173C2×Dic43⋊C4C2311yescharacteristic
174C2×Dic43⋊C4C2312yes—
175C2×Dic43⋊C4C2311yescharacteristic
176C4⋊C4×D43—42no—
177C2×C22⋊Dic43C2311yescharacteristic
178C2×C22⋊Dic43C2312yes—
179C2×C22⋊Dic43C2311yescharacteristic
180C2×(C2×D43)⋊C4C2312yes—
181C2×(C2×D43)⋊C4C2312yes—
182C2×(C2×D43)⋊C4C2311yescharacteristic
183C2×(C2×D43)⋊C4C2311yescharacteristic
184C2×(C2×D43)⋊C4C2312yes—
185C2×(C2×D43)⋊C4C2312yes—
186C2×(C2×D43)⋊C4C2312yes—
187C2×(C2×D43)⋊C4C2312yes—
188C2×(C2×D43)⋊C4C2312yes—
189C2×(C2×D43)⋊C4C2312yes—
190C2×(C2×D43)⋊C4C2312yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2312yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2311yescharacteristic
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2311yescharacteristic
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2311yescharacteristic
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2311yescharacteristic
201C2×(C2×D43)⋊C4C2312yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2312yes—
204C2×(C2×D43)⋊C4C2312yes—
205C22⋊C4×D43—44no—
206C22⋊C4×D43—44no—
207C2×C4×Dic43C2312yes—
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2312yes—
211C2×C4×Dic43C2311yescharacteristic
212C2×C4×Dic43C2312yes—
213C2×C4×Dic43C2311yescharacteristic
214C42×D43—42no—
215C43⋊#95C2311yescharacteristic
216C43⋊#95C2312yes—
217C43⋊#95C2311yescharacteristic
218C43⋊#95C2312yes—
219C43⋊#95C2312yes—
220C43⋊#95C2312yes—
221C43⋊#95C2312yes—
222C43⋊#95C2311yescharacteristic
223C43⋊#95C2311yescharacteristic
224C43⋊#95C2312yes—
225C43⋊#95C2311yescharacteristic
226C43⋊#95C2312yes—
227C43⋊#95C2311yescharacteristic
228C23×C4×C43C2311yescharacteristic
229#117×C43C2×C418yescomplemented
230C2×C4⋊C4×C43C2311yescharacteristic
231C2×C4⋊C4×C43C2311yescharacteristic
232C2×C4⋊C4×C43C2312yes—
233C2×C4⋊C4×C43C2312yes—
234C2×C4⋊C4×C43C2311yescharacteristic
235C2×C4⋊C4×C43C2311yescharacteristic
236C2×C22⋊C4×C43C2311yescharacteristic
237C2×C22⋊C4×C43C2312yes—
238C2×C22⋊C4×C43C2311yescharacteristic
239C2×C22⋊C4×C43C2312yes—
240C2×C42×C43C2312yes—
241C2×C42×C43C2311yescharacteristic
242C2×C42×C43C2311yescharacteristic
243C2×C42×C43C2312yes—
244C2×C42×C43C2312yes—
245#95×C43C2312yes—
246#95×C43C2312yes—
247#95×C43C2312yes—
248#95×C43C2311yescharacteristic
249#95×C43C2312yes—
250#95×C43C2311yescharacteristic
251#95×C43C2312yes—
252C24×C43C2411yescharacteristic
253C23×D43—42no—
254C23×D43—42no—
255C23×D43—42no—
256C23×D43—42no—
257C23×D43—42no—
258C23×D43—42no—
259C23×D43C22×C418yes—
260C23×D43C2412yes—
261C23×D43C2412yes—
262C23×D43C2411yescharacteristic
263C23×D43C2411yescharacteristic
264C22×C4×C43—22no—
265C22×C4×C43—22no—
266C22×C4×C43C22×C414yes—
267C22×C4×C43C2411yescharacteristic
268C22×C4×C43C2411yescharacteristic
269C22×C4×C43C2412yes—
270C22×C4×C43C2411yescharacteristic
271C22×C4×C43C2412yes—
272C22×C4×C43C2411yescharacteristic
273C22×C4×C43C2412yes—
274C22×C4×C43C2412yes—
275C22×C4×C43C2411yescharacteristic
276C22×C4×C43C2411yescharacteristic
277C2×C22⋊D43—41no—
278C2×C22⋊D43—41no—
279C2×C22⋊D43—41no—
280C2×C22⋊D43—41no—
281C2×C22⋊D43C22×C414yes—
282C2×C22⋊D43C22×C414yes—
283C22×Dic43C2411yescharacteristic
284C22×Dic43C2411yescharacteristic
285C22×Dic43C2412yes—
286C22×Dic43C2411yescharacteristic
287C22×Dic43C2412yes—
288C22×Dic43C2411yescharacteristic
289C22×Dic43C2411yescharacteristic
290C22×Dic43C2411yescharacteristic
291#10621898—416no—
292C2×D172—22no—
293C2×D172—22no—
294C2×D172—22no—
295C2×D172—22no—
296C2×D172—42no—
297C2×D172—42no—
298C2×D172—42no—
299C2×D172—42no—
300C2×D172—42no—
301C2×D172—42no—
302C2×D172—42no—
303C2×D172—42no—
304C2×D172—42no—
305C2×D172—42no—
306C2×D172—41no—
307C2×D172—41no—
308C2×D172—416no—
309C2×D172C22×C414yes—
310C2×D172C22×C414yes—
311C2×D172C22×C418yes—
312C2×D172C22×C418yes—
313C2×D172C22×C418yes—
314C2×D172C22×C418yes—
315C2×D172C22×C418yes—
316C2×D172C22×C414yes—
317C2×C4×D43—22no—
318C2×C4×D43—22no—
319C2×C4×D43—22no—
320C2×C4×D43—22no—
321C2×C4×D43—22no—
322C2×C4×D43—22no—
323C2×C4×D43—24no—
324C2×C4×D43—24no—
325C2×C4×D43—41no—
326C2×C4×D43—41no—
327C2×C4×D43—41no—
328C2×C4×D43—41no—
329C2×C4×D43—42no—
330C2×C4×D43—42no—
331C2×C4×D43—42no—
332C2×C4×D43—42no—
333C2×C4×D43—42no—
334C2×C4×D43—42no—
335C2×C4×D43—42no—
336C2×C4×D43—42no—
337C2×C4×D43—42no—
338C2×C4×D43—42no—
339C2×C4×D43—42no—
340C2×C4×D43—42no—
341C2×C4×D43—42no—
342C2×C4×D43C22×C414yes—
343C2×C4×D43C22×C414yes—
344C2×Dic86—41no—
345C2×Dic86—41no—
346C2×Dic86C22×C414yes—
347C4⋊C4×C43—22no—
348C4⋊C4×C43—22no—
349C4⋊C4×C43—42no—
350C4⋊C4×C43—42no—
351C4⋊C4×C43C22×C414yes—
352C4⋊C4×C43C22×C414yes—
353C22⋊C4×C43—22no—
354C22⋊C4×C43—41no—
355C22⋊C4×C43—42no—
356C22⋊C4×C43C22×C418yes—
357C42×C43—22no—
358C42×C43—22no—
359C42×C43—24no—
360C42×C43—42no—
361C42×C43C22×C418yes—
362C22⋊Dic43—22no—
363C22⋊Dic43—42no—
364C22⋊Dic43—41no—
365(C2×D43)⋊C4—24no—
366(C2×D43)⋊C4—22no—
367(C2×D43)⋊C4—24no—
368(C2×D43)⋊C4—22no—
369(C2×D43)⋊C4—42no—
370(C2×D43)⋊C4—42no—
371(C2×D43)⋊C4—41no—
372(C2×D43)⋊C4—41no—
373(C2×D43)⋊C4—42no—
374(C2×D43)⋊C4—42no—
375(C2×D43)⋊C4—41no—
376(C2×D43)⋊C4—41no—
377(C2×D43)⋊C4—42no—
378(C2×D43)⋊C4—42no—
379(C2×D43)⋊C4—42no—
380(C2×D43)⋊C4—42no—
381(C2×D43)⋊C4—42no—
382(C2×D43)⋊C4—42no—
383(C2×D43)⋊C4—42no—
384(C2×D43)⋊C4—42no—
385(C2×D43)⋊C4—42no—
386(C2×D43)⋊C4C22×C418yes—
387(C2×D43)⋊C4C22×C418yes—
388(C2×D43)⋊C4C22×C418yes—
389(C2×D43)⋊C4C22×C418yes—
390C4⋊Dic43—22no—
391C4⋊Dic43—22no—
392C4⋊Dic43—42no—
393C4⋊Dic43—42no—
394Dic43⋊C4—42no—
395Dic43⋊C4—41no—
396Dic43⋊C4—41no—
397C4×Dic43—22no—
398C4×Dic43—22no—
399C4×Dic43—24no—
400C4×Dic43—41no—
401C4×Dic43—41no—
402C4×Dic43—42no—
403C4×Dic43—42no—
404C23×C43—21no—
405C23×C43—21no—
406C23×C43—21no—
407C23×C43—21no—
408C23×C43—21no—
409C23×C43—21no—
410C23×C43C23×C412yes—
411C23×C43C2511yescharacteristic
412C22×D43—22no—
413C22×D43—22no—
414C22×D43—21no—
415C22×D43—21no—
416C22×D43—21no—
417C22×D43—21no—
418C22×D43—21no—
419C22×D43—21no—
420C22×D43—22no—
421C22×D43—22no—
422C22×D43—22no—
423C22×D43—22no—
424C22×D43—22no—
425C22×D43—22no—
426C22×D43—21no—
427C22×D43—21no—
428C22×D43—21no—
429C22×D43—21no—
430C22×D43—22no—
431C22×D43—22no—
432C22×D43—21no—
433C22×D43—21no—
434C22×D43—22no—
435C22×D43—22no—
436C22×D43—48no—
437C22×D43—48no—
438C22×D43—48no—
439C22×D43—84no—
440C22×D43—84no—
441C22×D43—84no—
442C22×D43—84no—
443C22×D43C23×C414yes—
444C22×D43C23×C414yes—
445C22×D43C23×C412yes—
446C22×D43C23×C412yes—
447C2×C4×C43—22no—
448C2×C4×C43—21no—
449C2×C4×C43—22no—
450C2×C4×C43—21no—
451C2×C4×C43—21no—
452C2×C4×C43—22no—
453C2×C4×C43—22no—
454C2×C4×C43—21no—
455C2×C4×C43—28no—
456C2×C4×C43—21no—
457C2×C4×C43—22no—
458C2×C4×C43—21no—
459C2×C4×C43—21no—
460C2×C4×C43—22no—
461C2×C4×C43—22no—
462C2×C4×C43—21no—
463C2×C4×C43—22no—
464C2×C4×C43—21no—
465C2×C4×C43—22no—
466C2×C4×C43—21no—
467C2×C4×C43—21no—
468C2×C4×C43—22no—
469C2×C4×C43—21no—
470C2×C4×C43—21no—
471C2×C4×C43C23×C414yes—
472C2×C4×C43C23×C414yes—
473C2×C4×C43C23×C412yes—
474C2×C4×C43C23×C412yes—
475C2×C4×C43H(5,𝔽2)12yes—
476C2×C4×C43H(5,𝔽2)12yes—
477C2×C4×C43H(5,𝔽2)12yes—
478C22⋊D43—44no—
479C22⋊D43—44no—
480C2×Dic43—21no—
481C2×Dic43—21no—
482C2×Dic43—21no—
483C2×Dic43—21no—
484C2×Dic43—21no—
485C2×Dic43—21no—
486C2×Dic43—21no—
487C2×Dic43—21no—
488C2×Dic43—21no—
489C2×Dic43—22no—
490C2×Dic43—22no—
491C2×Dic43—22no—
492C2×Dic43—21no—
493C2×Dic43—21no—
494C2×Dic43—22no—
495C2×Dic43—22no—
496C2×Dic43—21no—
497C2×Dic43—21no—
498C2×Dic43—22no—
499C2×Dic43—21no—
500C2×Dic43—21no—
501C2×Dic43C23×C412yes—
502C2×Dic43C23×C412yes—
503C2×Dic43H(5,𝔽2)12yes—
504D172—28no—
505D172—28no—
506D172—48no—
507D172—48no—
508D172—48no—
509D172—48no—
510D172—48no—
511D172—44no—
512C4×D43—28no—
513C4×D43—28no—
514C4×D43—44no—
515C4×D43—44no—
516C4×D43—84no—
517C4×D43—84no—
518C4×D43—84no—
519C4×D43—84no—
520C4×D43—84no—
521Dic86—44no—
522#34415—431nomaximal, Sylow
523C22×C43—22no—
524C22×C43—22no—
525C22×C43—22no—
526C22×C43—41no—
527C22×C43—41no—
528C22×C43—41no—
529C22×C43—41no—
530C22×C43C24×C411yescharacteristic
531C22×C43C2×H(5,𝔽2)11yescharacteristic
532C22×C43C2×H(5,𝔽2)11yescharacteristic
533C22×C43C2×H(5,𝔽2)11yescharacteristic
534C22×C43C2×H(5,𝔽2)11yescharacteristic
535C22×C43#58511yescharacteristic
536C22×C43#58511yescharacteristic
537C2×D43—24no—
538C2×D43—24no—
539C2×D43—22no—
540C2×D43—22no—
541C2×D43—24no—
542C2×D43—24no—
543C2×D43—24no—
544C2×D43—24no—
545C2×D43—22no—
546C2×D43—22no—
547C2×D43—22no—
548C2×D43—22no—
549C2×D43—41no—
550C2×D43—41no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—41no—
556C2×D43—41no—
557C2×D43—41no—
558C2×D43—42no—
559C2×D43—42no—
560C2×D43—41no—
561C2×D43—41no—
562C2×D43—41no—
563C2×D43—42no—
564C2×D43—42no—
565C2×D43—816no—
566C4×C43—22no—
567C4×C43—24no—
568C4×C43—24no—
569C4×C43—22no—
570C4×C43—41no—
571C4×C43—42no—
572C4×C43—41no—
573C4×C43—42no—
574C4×C43—41no—
575C4×C43#51814yes—
576Dic43—22no—
577Dic43—22no—
578Dic43—22no—
579Dic43—41no—
580Dic43—42no—
581Dic43—41no—
582Dic43—42no—
583Dic43—41no—
584C2×#535—431no—
585#2379—432no—
586#2375—432no—
587#2372—432no—
588#2363—431no—
589#2363—431no—
590#2361—431no—
591#2361—431no—
592#2358—432no—
593#2346—431no—
594#2346D4311yescharacteristic, complemented
595D4×C22⋊C4—431no—
596D4×C22⋊C4—431no—
597#2328—432no—
598#2328—432no—
599#2324—431no—
600#2324—431no—
601#2321—432no—
602#2321—432no—
603#2311—431no—
604C4×#121—431no—
605C4×#121—431no—
606#2297—431no—
607C2×C43—42no—
608C2×C43C2×#51811yescharacteristic
609C2×C43C4×H(5,𝔽2)11yescharacteristic
610C2×C43C4×H(5,𝔽2)11yescharacteristic
611C2×C43#354211yescharacteristic
612C2×C43#354211yescharacteristic
613C2×C43#354911yescharacteristic
614C2×C43#355111yescharacteristic
615D43—42no—
616D43—42no—
617D43—44no—
618D43—44no—
619C22×#41—431no—
620C23×D4—431no—
621#535—4316no—
622C2×#127—432no—
623C2×#124—432no—
624C2×#121—431no—
625C2×#121—431no—
626C2×#121—431no—
627C2×#121—431no—
628C2×#120—432no—
629C2×#120—432no—
630C2×C4×D4—432no—
631C2×C4×D4—431no—
632C2×C4×D4—432no—
633C2×C4×D4—431no—
634C2×C4×D4—432no—
635C2×C4×D4—431no—
636C2×C4×D4—432no—
637C2×C4×D4—431no—
638C2×#117—431no—
639C2×#117—431no—
640C2×#117C2×D4311yescharacteristic
641C22×C4⋊C4—431no—
642C22×C22⋊C4—432no—
643C22×C22⋊C4—432no—
644C22×C42—431no—
645#391—432no—
646#391—431no—
647#391—431no—
648#390—431no—
649#390—431no—
650#390—432no—
651#390—432no—
652#390—432no—
653#390—431no—
654#390—431no—
655#390—432no—
656#390—431no—
657#390—431no—
658#390—432no—
659#389—431no—
660#389—431no—
661#389C2×D4311yescharacteristic, complemented
662#389C2×D4311yescharacteristic, complemented
663#388—432no—
664#388—432no—
665#388—432no—
666#388—432no—
667#388—432no—
668#388—432no—
669#388—432no—
670#388—432no—
671#388—432no—
672#388—432no—
673#388C2×D4312yes—
674#388C2×D4312yes—
675#386—432no—
676#386—431no—
677#386—431no—
678#386—432no—
679#386—432no—
680#386—432no—
681#386—432no—
682#386—432no—
683#386—431no—
684#386—431no—
685#386—432no—
686#386—432no—
687#386—432no—
688#386—432no—
689#386—432no—
690#386—432no—
691#386—432no—
692#386—432no—
693#385—432no—
694#385—432no—
695#385—432no—
696#385—432no—
697#382—432no—
698#382C2×D4312yescomplemented
699#380—431no—
700#380—431no—
701#380—431no—
702#380C2×D4311yescharacteristic
703#379—432no—
704#379—432no—
705C4×C4⋊C4—431no—
706C4×C4⋊C4—431no—
707C4×C4⋊C4C2×D4311yescharacteristic, complemented
708C4×C4⋊C4C2×D4311yescharacteristic, complemented
709C4×C22⋊C4—431no—
710C4×C22⋊C4—432no—
711C4×C22⋊C4—432no—
712C4×C22⋊C4—431no—
713C4×C22⋊C4—431no—
714C4×C22⋊C4—432no—
715C4×C22⋊C4—432no—
716C4×C22⋊C4C2×D4311yescharacteristic
717#376—432no—
718#376C2×D4312yescomplemented
719C43#3441511yescharacteristic, complemented, Sylow
720C25—432no—
721C2×#41—438no—
722C2×#41—1722no—
723C2×#41—1722no—
724C22×Q8—431no—
725C22×D4—431no—
726C22×D4—431no—
727C22×D4—438no—
728C22×D4—431no—
729C22×D4—431no—
730C22×D4—432no—
731C22×D4—432no—
732C22×D4—432no—
733C22×D4—432no—
734C22×D4—432no—
735C22×D4—431no—
736C22×D4—1722no—
737C22×D4—1722no—
738C23×C4—431no—
739C23×C4—431no—
740C23×C4—432no—
741C23×C4—432no—
742C23×C4—431no—
743C23×C4—431no—
744C23×C4—432no—
745C23×C4—432no—
746C23×C4—432no—
747C23×C4C22×D4311yescharacteristic
748#127—4316no—
749#124—4316no—
750#121—438no—
751#121—438no—
752#121—438no—
753#121—438no—
754#120—4316no—
755#120—4316no—
756C4×D4—1724no—
757C4×D4—1722no—
758C4×D4—1722no—
759C4×D4—1724no—
760C4×D4—1724no—
761C4×D4—1722no—
762C4×D4—1722no—
763C4×D4—1724no—
764#117—1722no—
765#117—1722no—
766#117C4×D4318yescomplemented
767C2×C4⋊C4—431no—
768C2×C4⋊C4—431no—
769C2×C4⋊C4—432no—
770C2×C4⋊C4—431no—
771C2×C4⋊C4—431no—
772C2×C4⋊C4—432no—
773C2×C4⋊C4—432no—
774C2×C4⋊C4—1722no—
775C2×C4⋊C4C22×D4311yescharacteristic
776C2×C4⋊C4C22×D4311yescharacteristic
777C2×C4⋊C4C22×D4312yes—
778C2×C4⋊C4C22×D4312yes—
779C2×C4⋊C4C22×D4311yescharacteristic
780C2×C4⋊C4C22×D4311yescharacteristic
781C2×C22⋊C4—432no—
782C2×C22⋊C4—432no—
783C2×C22⋊C4—432no—
784C2×C22⋊C4—432no—
785C2×C22⋊C4—431no—
786C2×C22⋊C4—432no—
787C2×C22⋊C4—432no—
788C2×C22⋊C4—431no—
789C2×C22⋊C4—431no—
790C2×C22⋊C4—432no—
791C2×C22⋊C4—431no—
792C2×C22⋊C4—432no—
793C2×C22⋊C4—432no—
794C2×C22⋊C4—431no—
795C2×C22⋊C4—432no—
796C2×C22⋊C4—431no—
797C2×C22⋊C4—432no—
798C2×C22⋊C4—432no—
799C2×C22⋊C4—432no—
800C2×C22⋊C4—432no—
801C2×C22⋊C4—432no—
802C2×C22⋊C4—432no—
803C2×C22⋊C4—432no—
804C2×C22⋊C4—432no—
805C2×C22⋊C4—432no—
806C2×C22⋊C4—432no—
807C2×C22⋊C4—431no—
808C2×C22⋊C4—431no—
809C2×C22⋊C4—1724no—
810C2×C22⋊C4—1724no—
811C2×C22⋊C4C22×D4311yescharacteristic
812C2×C22⋊C4C22×D4312yes—
813C2×C22⋊C4C22×D4311yescharacteristic
814C2×C22⋊C4C22×D4312yes—
815C2×C42—431no—
816C2×C42—432no—
817C2×C42—431no—
818C2×C42—432no—
819C2×C42—432no—
820C2×C42—431no—
821C2×C42—431no—
822C2×C42—1722no—
823C2×C42C22×D4311yescharacteristic
824C2×C42C22×D4312yes—
825C2×C42C22×D4311yescharacteristic
826C2×C42C22×D4312yes—
827C2×C42C22×D4312yes—
828#95—431no—
829#95—432no—
830#95—432no—
831#95—432no—
832#95—431no—
833#95—431no—
834#95—432no—
835#95—432no—
836#95—431no—
837#95—431no—
838#95—431no—
839#95—432no—
840#95—432no—
841#95C22×D4311yescharacteristic
842#95C22×D4312yes—
843#95C22×D4312yes—
844#95C22×D4312yes—
845#95C22×D4311yescharacteristic
846#95C22×D4312yes—
847#95C22×D4312yes—
848C24—432no—
849C24—432no—
850C24—431no—
851C24—431no—
852C24—438no—
853C24—1722no—
854C24—1722no—
855C24—1722no—
856C24—1722no—
857C24—1722no—
858C24—1722no—
859C24C23×D4311yescharacteristic
860#41—17216no—
861C2×Q8—434no—
862C2×Q8—1721no—
863C2×Q8—1721no—
864C2×D4—434no—
865C2×D4—434no—
866C2×D4—434no—
867C2×D4—434no—
868C2×D4—438no—
869C2×D4—438no—
870C2×D4—438no—
871C2×D4—438no—
872C2×D4—438no—
873C2×D4—434no—
874C2×D4—862no—
875C2×D4—862no—
876C2×D4—862no—
877C2×D4—862no—
878C2×D4—17216no—
879C2×D4—1722no—
880C2×D4—1722no—
881C2×D4—1722no—
882C2×D4—1722no—
883C2×D4—1722no—
884C2×D4—1722no—
885C2×D4—1721no—
886C2×D4—1721no—
887C2×D4—1722no—
888C2×D4—1722no—
889C2×D4—1722no—
890C2×D4—1722no—
891C2×D4—1721no—
892C2×D4—1721no—
893C2×D4—1721no—
894C2×D4—1721no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—431no—
898C22×C4—431no—
899C22×C4—431no—
900C22×C4—434no—
901C22×C4—434no—
902C22×C4—431no—
903C22×C4—431no—
904C22×C4—432no—
905C22×C4—432no—
906C22×C4—431no—
907C22×C4—864no—
908C22×C4—862no—
909C22×C4—862no—
910C22×C4—862no—
911C22×C4—862no—
912C22×C4—862no—
913C22×C4—864no—
914C22×C4—862no—
915C22×C4—1722no—
916C22×C4—1722no—
917C22×C4—1722no—
918C22×C4—1722no—
919C22×C4—1722no—
920C22×C4—1722no—
921C22×C4—1722no—
922C22×C4—1722no—
923C22×C4—1722no—
924C22×C4—1722no—
925C22×C4—1722no—
926C22×C4—1722no—
927C22×C4—1722no—
928C22×C4—1721no—
929C22×C4—1721no—
930C22×C4—1721no—
931C22×C4—1721no—
932C22×C4C2×C4×D4314yes—
933C22×C4C23×D4312yes—
934C22×C4C23×D4311yescharacteristic
935C22×C4C23×D4311yescharacteristic
936C22×C4C23×D4312yes—
937C22×C4C23×D4311yescharacteristic
938C22×C4C23×D4311yescharacteristic
939C22×C4C23×D4312yes—
940C22×C4C23×D4312yes—
941C22×C4C23×D4311yescharacteristic
942C22×C4C23×D4311yescharacteristic
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—862no—
948C4⋊C4—862no—
949C4⋊C4—1722no—
950C4⋊C4—1721no—
951C4⋊C4—1721no—
952C4⋊C4—1722no—
953C4⋊C4—1722no—
954C4⋊C4C2×C4×D4314yes—
955C4⋊C4C2×C4×D4314yes—
956C22⋊C4—22no—
957C22⋊C4—42no—
958C22⋊C4—41no—
959C22⋊C4—438no—
960C22⋊C4—438no—
961C22⋊C4—438no—
962C22⋊C4—438no—
963C22⋊C4—864no—
964C22⋊C4—862no—
965C22⋊C4—862no—
966C22⋊C4—864no—
967C22⋊C4—862no—
968C22⋊C4—1722no—
969C22⋊C4—1722no—
970C22⋊C4—1721no—
971C22⋊C4—1721no—
972C22⋊C4—1722no—
973C22⋊C4—1722no—
974C22⋊C4—1722no—
975C22⋊C4—1722no—
976C22⋊C4—1722no—
977C22⋊C4—1722no—
978C22⋊C4—1722no—
979C22⋊C4—1722no—
980C22⋊C4—1722no—
981C22⋊C4—1722no—
982C22⋊C4—1721no—
983C22⋊C4—1722no—
984C22⋊C4—1721no—
985C22⋊C4—1722no—
986C22⋊C4—1721no—
987C22⋊C4C2×C4×D4318yes—
988C42—22no—
989C42—22no—
990C42—24no—
991C42—42no—
992C42—864no—
993C42—862no—
994C42—862no—
995C42—1721no—
996C42—1721no—
997C42—1722no—
998C42—1722no—
999C42C2×C4×D4318yes—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—434no—
1007C23—434no—
1008C23—432no—
1009C23—432no—
1010C23—862no—
1011C23—861no—
1012C23—861no—
1013C23—862no—
1014C23—862no—
1015C23—861no—
1016C23—861no—
1017C23—861no—
1018C23—861no—
1019C23—862no—
1020C23—862no—
1021C23—862no—
1022C23—862no—
1023C23—862no—
1024C23—861no—
1025C23—861no—
1026C23—861no—
1027C23—862no—
1028C23—861no—
1029C23—862no—
1030C23—861no—
1031C23—862no—
1032C23—861no—
1033C23—862no—
1034C23—3444no—
1035C23—3444no—
1036C23—3444no—
1037C23—3444no—
1038C23—1728no—
1039C23—1728no—
1040C23—1728no—
1041C23C22×C4×D4312yes—
1042C23C24×D4311yescharacteristic
1043Q8—1724no—
1044D4—868no—
1045D4—868no—
1046D4—1728no—
1047D4—1724no—
1048D4—1728no—
1049D4—1728no—
1050D4—1728no—
1051D4—1728no—
1052D4—1724no—
1053D4—1724no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—28no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—432no—
1079C2×C4—432no—
1080C2×C4—432no—
1081C2×C4—861no—
1082C2×C4—861no—
1083C2×C4—861no—
1084C2×C4—861no—
1085C2×C4—861no—
1086C2×C4—861no—
1087C2×C4—868no—
1088C2×C4—868no—
1089C2×C4—862no—
1090C2×C4—861no—
1091C2×C4—861no—
1092C2×C4—861no—
1093C2×C4—861no—
1094C2×C4—862no—
1095C2×C4—862no—
1096C2×C4—861no—
1097C2×C4—862no—
1098C2×C4—861no—
1099C2×C4—862no—
1100C2×C4—861no—
1101C2×C4—861no—
1102C2×C4—862no—
1103C2×C4—861no—
1104C2×C4—3444no—
1105C2×C4—3444no—
1106C2×C4—3444no—
1107C2×C4—3444no—
1108C2×C4—3444no—
1109C2×C4—1724no—
1110C2×C4—1724no—
1111C2×C4C22×C4×D4312yes—
1112C2×C4C22×C4×D4314yes—
1113C2×C4C22×C4×D4314yes—
1114C2×C4C22×C4×D4312yes—
1115C2×C4#1306337112yes—
1116C2×C4#1306337112yes—
1117C2×C4#1306337112yes—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—862no—
1126C22—862no—
1127C22—864no—
1128C22—864no—
1129C22—862no—
1130C22—862no—
1131C22—864no—
1132C22—864no—
1133C22—862no—
1134C22—862no—
1135C22—864no—
1136C22—864no—
1137C22—34416no—
1138C22—1722no—
1139C22—1721no—
1140C22—1722no—
1141C22—1721no—
1142C22—1722no—
1143C22—1721no—
1144C22—1722no—
1145C22—1721no—
1146C22—1721no—
1147C22—1722no—
1148C22—1722no—
1149C22—1721no—
1150C22—1722no—
1151C22—1722no—
1152C22—1721no—
1153C22—1721no—
1154C22C23×C4×D4311yescharacteristic
1155C22H(5,𝔽2)×D4311yescharacteristic
1156C22C2×#1306337111yescharacteristic
1157C22C2×#1306337111yescharacteristic
1158C22C2×#1306337111yescharacteristic
1159C22#1458373511yescharacteristic
1160C22#1458373611yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—24no—
1164C4—22no—
1165C4—42no—
1166C4—41no—
1167C4—42no—
1168C4—41no—
1169C4—41no—
1170C4—862no—
1171C4—862no—
1172C4—862no—
1173C4—1722no—
1174C4—1721no—
1175C4—1722no—
1176C4—1721no—
1177C4—1721no—
1178C4#1458337314yes—
1179C2—42no—
1180C2—1724no—
1181C2—1724no—
1182C2—1722no—
1183C2—1722no—
1184C2C2×#1458337311yescharacteristic
1185C2#1914780111yescharacteristic
1186C2C4×#1306337111yescharacteristic
1187C2#1914890511yescharacteristic
1188C2#1914891811yescharacteristic
1189C2#1914899611yescharacteristic
1190C2#1914902311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2346C2
socle, cosocleC23×C43C25
prime radicalC2×#14583468C2
hypercenter#2346D43
hypocenterC43#34415
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2346

Complements

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

NH ≅ G/Ntype
2. #19137766C2semidirect
3. #19137735C2semidirect
4. #19137705C2semidirect
5. #19137635C2semidirect
6. #19137632C2semidirect
7. #19137613C2semidirect
8. #19137610C2semidirect
9. #19137573C2semidirect
10. #19137480C2semidirect
11. C22⋊C4×D172C2semidirect
12. #19137415C2semidirect
13. #19137320C2semidirect
14. #19137318C2semidirect
15. #19137289C2semidirect
16. #19137286C2semidirect
17. #19137257C2semidirect
18. #19137248C2semidirect
19. #19137184C2semidirect
20. C4×#13063300C2semidirect
21. #19137103C2semidirect
22. #19137081C2semidirect
23. C43×#2346C2semidirect
26. #14583468C4semidirect
37. C2×C4×D172C22semidirect
38. C2×C4×D172C22semidirect
41. C2×#13063287C22semidirect
42. C2×#13063287C22semidirect
43. C2×#13063283C22semidirect
44. C2×#13063282C22semidirect
45. C2×C4⋊C4×D43C22semidirect
48. C2×C42×D43C22semidirect
49. #14582803C22semidirect
50. #14582803C22semidirect
51. #14582803C22semidirect
54. #14582801C22semidirect
55. #14582801C22semidirect
58. #14582800C22semidirect
59. #14582800C22semidirect
63. #14582798C22semidirect
64. #14582798C22semidirect
67. #14582791C22semidirect
68. #14582791C22semidirect
69. #14582790C22semidirect
70. #14582790C22semidirect
71. #14582789C22semidirect
72. #14582789C22semidirect
73. #14582788C22semidirect
74. #14582788C22semidirect
79. #14582777C22semidirect
80. #14582777C22semidirect
81. #14582777C22semidirect
82. #14582777C22semidirect
83. #14582777C22semidirect
84. #14582777C22semidirect
85. #14582777C22semidirect
86. #14582777C22semidirect
87. #14582777C22semidirect
88. #14582777C22semidirect
89. #14582777C22semidirect
93. #14582773C22semidirect
94. #14582773C22semidirect
95. #14582770C22semidirect
96. #14582770C22semidirect
97. #14582765C22semidirect
99. #14582756C22semidirect
100. #14582756C22semidirect
103. C4⋊C4×Dic43C22semidirect
104. C4⋊C4×Dic43C22semidirect
105. C4×(C2×D43)⋊C4C22semidirect
106. C4×(C2×D43)⋊C4C22semidirect
107. C4×(C2×D43)⋊C4C22semidirect
108. C4×(C2×D43)⋊C4C22semidirect
110. #14582746C22semidirect
111. #14582746C22semidirect
112. #14582745C22semidirect
114. C43×#389C22semidirect
115. C43×#389C22semidirect
118. C43×#382C22semidirect
120. C4×C4⋊C4×C43C22semidirect
121. C4×C4⋊C4×C43C22semidirect
123. C43×#376C22semidirect
127. C2×#10621898C2×C4semidirect
131. C22×D172C2×C4semidirect
151. #13063322C2×C4semidirect
152. #13063313C2×C4semidirect
153. #13063300C2×C4semidirect
154. #13063300C2×C4semidirect
155. #13063300C2×C4semidirect
156. #13063300C2×C4semidirect
157. #13063295C2×C4semidirect
158. #13063295C2×C4semidirect
229. #117×C43C2×C4semidirect
594. #2346D43semidirect
661. #389C2×D43semidirect
662. #389C2×D43semidirect
698. #382C2×D43semidirect
707. C4×C4⋊C4C2×D43semidirect
708. C4×C4⋊C4C2×D43semidirect
718. #376C2×D43semidirect
719. C43#34415semidirect
766. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834682
#191377662
#191377352
#191377052
#191376352
#191376322
#191376132
#191376102
#191375732
#191374802
C22⋊C4×D1722
#191374152
#191373202
#191373182
#191372892
#191372862
#191372572
#191372482
#191371842
C4×#130633002
#191371032
#191370812
C43×#23462
#3441543