Finite Group Databasebeta

← #25264784

Subgroups — #25264784

Order 11008.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583435C211yesmaximal, characteristic, complemented
2C22×#13063287C211yesmaximal, characteristic, complemented
3#19138846C212yesmaximal, complemented
4#19138662C212yesmaximal, complemented
5#19138503C212yesmaximal, complemented
6#19138465C211yesmaximal, characteristic, complemented
7#19138385C211yesmaximal, characteristic, complemented
8#19138313C211yesmaximal, characteristic, complemented
9#19138247C211yesmaximal, characteristic, complemented
10#19138168C211yesmaximal, characteristic, complemented
11#19138089C211yesmaximal, characteristic, complemented
12#19138055C212yesmaximal, complemented
13#19137951C211yesmaximal, characteristic
14#19137859C212yesmaximal, complemented
15#19137840C212yesmaximal, complemented
16#19137138C211yesmaximal, characteristic, complemented
17C22⋊Q8×Dic43C211yesmaximal, characteristic, complemented
18#19137101C211yesmaximal, characteristic, complemented
19#19137100C212yesmaximal, complemented
20#19137053C211yesmaximal, characteristic, complemented
21#19136977C212yesmaximal, complemented
22C4×D4×Dic43C211yesmaximal, characteristic, complemented
23C43×#2417C211yesmaximal, characteristic, complemented
24C23×D172C2211yescharacteristic
25C23×C4×D43C2212yes—
26#14583435—28no—
27C2×#13063320C2212yescomplemented
28C2×#13063316C2211yescharacteristic, complemented
29C2×#13063314C2211yescharacteristic
30C2×#13063314C2211yescharacteristic
31C2×#13063309C2212yescomplemented
32C2×#13063299C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063293C2212yes—
35C2×Q8×Dic43C2211yescharacteristic, complemented
36C2×D4×Dic43C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×#13063287—28no—
39C2×#13063287C2211yescharacteristic
40C2×#13063287C2212yes—
41C2×#13063287C2211yescharacteristic
42C2×#13063287C2212yes—
43C2×#13063287C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×(C22⋊D43)⋊C4C2212yescomplemented
46C2×(C22⋊D43)⋊C4C2212yescomplemented
47C2×#13063283C2212yescomplemented
48C2×#13063283C2212yescomplemented
49C22×(C2×D43)⋊C4C2212yes—
50C22×C4×Dic43C2211yescharacteristic
51C22×C4×Dic43C2211yescharacteristic, complemented
52#14582838C2212yescomplemented
53#14582836C2212yescomplemented
54#14582832C2212yescomplemented
55#14582828C2212yescomplemented
56#14582826C2212yescomplemented
57#14582826C2212yescomplemented
58#14582825C2212yescomplemented
59#14582821C2212yescomplemented
60#14582816C2212yes—
61#14582816C2212yes—
62#14582816C2212yes—
63#14582815C2212yescomplemented
64#14582815C2212yescomplemented
65#14582808C2212yes—
66#14582806C2211yescharacteristic, complemented
67#14582801C2211yescharacteristic
68#14582801C2211yescharacteristic
69#14582800C2211yescharacteristic
70#14582800C2211yescharacteristic
71#14582798C2211yescharacteristic, complemented
72#14582798C2211yescharacteristic, complemented
73#14582795C2211yescharacteristic, complemented
74#14582791C2212yescomplemented
75#14582791C2212yescomplemented
76#14582791C2212yescomplemented
77#14582789C2212yescomplemented
78#14582788C2212yescomplemented
79#14582785C2212yescomplemented
80#14582776C2212yescomplemented
81#14582775C2212yescomplemented
82#14582775C2212yescomplemented
83#14582774C2212yes—
84#14582773C2212yescomplemented
85#14582773C2212yescomplemented
86#14582772C2212yes—
87#14582764C2211yescharacteristic, complemented
88#14582761C2212yescomplemented
89#14582761C2212yescomplemented
90#14582759C2212yes—
91#14582759C2211yescharacteristic
92#14582756C2212yescomplemented
93#14582756C2212yescomplemented
94#14582754C2212yes—
95#14582754C2212yes—
96#14582754C2212yes—
97C4⋊C4×Dic43C2211yescharacteristic, complemented
98C4⋊C4×Dic43C2212yescomplemented
99C4⋊C4×Dic43C2211yescharacteristic, complemented
100C4⋊C4×Dic43C2211yescharacteristic, complemented
101C4×C4⋊Dic43C2211yescharacteristic, complemented
102C22⋊C4×Dic43C2211yescharacteristic
103C22⋊C4×Dic43C2212yes—
104C22⋊C4×Dic43C2211yescharacteristic
105C22⋊C4×Dic43C2211yescharacteristic, complemented
106C22⋊C4×Dic43C2211yescharacteristic, complemented
107C4×C22⋊Dic43C2211yescharacteristic
108C4×C22⋊Dic43C2211yescharacteristic, complemented
109#14582746C2212yescomplemented
110#14582746C2212yescomplemented
111#14582746C2212yescomplemented
112#14582746C2212yescomplemented
113C42×Dic43C2211yescharacteristic, complemented
114C2×C22⋊Q8×C43C2211yescharacteristic
115C2×C22⋊Q8×C43C2211yescharacteristic, complemented
116C2×C4×D4×C43C2211yescharacteristic
117C22×C4⋊C4×C43C2211yescharacteristic
118C43×#398C2212yescomplemented
119C43×#396C2212yescomplemented
120C43×#391C2211yescharacteristic, complemented
121C43×#389C2211yescharacteristic, complemented
122C43×#386C2212yes—
123C43×#380C2212yes—
124C43×#380C2211yescharacteristic, complemented
125C24×D43C2312yes—
126C22×D172—24no—
127C22×D172—24no—
128C22×D172—24no—
129C22×D172C2312yes—
130C22×D172C2311yescharacteristic
131C22×D172C2311yescharacteristic
132C22×C22⋊D43C2312yes—
133C22×C22⋊D43C2312yes—
134C23×Dic43C2311yescharacteristic
135C23×Dic43C2311yescharacteristic
136C23×Dic43C2311yescharacteristic
137C23×Dic43C2311yescharacteristic
138C22×C4×D43—28no—
139C22×C4×D43—28no—
140C22×C4×D43—44no—
141C22×C4×D43C2312yes—
142C22×C4×D43C2312yes—
143C22×C4×D43C2312yes—
144C22×C4×D43C2312yes—
145#13063320—28no—
146#13063316—24no—
147#13063314—24no—
148#13063314—24no—
149#13063309—28no—
150#13063299—24no—
151#13063299—24no—
152#13063293—28no—
153Q8×Dic43—24no—
154D4×Dic43—24no—
155D4×Dic43—24no—
156#13063287—24no—
157#13063287—28no—
158#13063287—24no—
159#13063287—28no—
160#13063287—24no—
161#13063287D418yescomplemented
162(C22⋊D43)⋊C4—28no—
163(C22⋊D43)⋊C4—44no—
164#13063283—28no—
165#13063283—44no—
166C2×C4⋊Dic43C2312yes—
167C2×C4⋊Dic43C2311yescharacteristic
168C2×C4⋊Dic43C2311yescharacteristic
169C2×C4⋊Dic43C2311yescharacteristic
170C2×C4⋊Dic43C2312yes—
171C2×C4⋊Dic43C2311yescharacteristic
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2312yes—
174C2×Dic43⋊C4C2312yes—
175C2×Dic43⋊C4C2312yes—
176C2×C22⋊Dic43C2311yescharacteristic
177C2×C22⋊Dic43C2311yescharacteristic
178C2×C22⋊Dic43C2311yescharacteristic
179C2×C22⋊Dic43C2311yescharacteristic
180C2×C22⋊Dic43C2312yes—
181C2×(C2×D43)⋊C4—28no—
182C2×(C2×D43)⋊C4C2312yes—
183C2×(C2×D43)⋊C4C2312yes—
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)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2312yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×C4×Dic43—24no—
201C2×C4×Dic43—24no—
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2311yescharacteristic
206C2×C4×Dic43C2311yescharacteristic
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2311yescharacteristic
211C2×C4×Dic43C2312yes—
212C2×C4×Dic43C2312yes—
213C2×C4×Dic43C2311yescharacteristic
214C2×C4×Dic43C2311yescharacteristic
215C2×C4×Dic43C2311yescharacteristic
216C43⋊#95C2312yes—
217C43⋊#95C2312yes—
218C43⋊#95C2312yes—
219C43⋊#95C2312yes—
220C43⋊#95C2312yes—
221C43⋊#95C2312yes—
222C43⋊#95C2312yes—
223C43⋊#95C2312yes—
224C43⋊#95C2312yes—
225C43⋊#95C2311yescharacteristic
226C43⋊#95C2311yescharacteristic
227C43⋊#95C2311yescharacteristic
228C43⋊#95C2311yescharacteristic
229C43⋊#95C2311yescharacteristic
230C43⋊#95C2311yescharacteristic
231C22×Q8×C43C2311yescharacteristic
232C22×D4×C43C2311yescharacteristic
233C23×C4×C43C2311yescharacteristic
234C23×C4×C43C2312yes—
235C23×C4×C43C2311yescharacteristic
236C22⋊Q8×C43—24no—
237C22⋊Q8×C43—24no—
238C4×D4×C43—24no—
239C2×C4⋊C4×C43—24no—
240C2×C4⋊C4×C43C2312yes—
241C2×C4⋊C4×C43C2311yescharacteristic
242C2×C4⋊C4×C43C2311yescharacteristic
243C2×C4⋊C4×C43C2312yes—
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C4⋊C4×C43C2312yes—
246C2×C4⋊C4×C43C2312yes—
247C2×C4⋊C4×C43C2311yescharacteristic
248C2×C22⋊C4×C43C2311yescharacteristic
249C2×C22⋊C4×C43C2311yescharacteristic
250C2×C22⋊C4×C43C2312yes—
251C2×C22⋊C4×C43C2312yes—
252C2×C22⋊C4×C43C2312yes—
253C2×C42×C43C2311yescharacteristic
254#95×C43C2312yes—
255#95×C43C2312yes—
256#95×C43C2312yes—
257#95×C43C2312yes—
258C24×C43C2411yescharacteristic
259C24×C43C2411yescharacteristic
260C23×D43—24no—
261C23×D43—24no—
262C23×D43—24no—
263C23×D43—24no—
264C23×D43—24no—
265C23×D43—42no—
266C23×D43—42no—
267C23×D43C2412yes—
268C23×D43C2412yes—
269C2×Q8×C43—22no—
270C2×Q8×C43—22no—
271C2×Q8×C43—22no—
272C2×D4×C43—22no—
273C2×D4×C43—22no—
274C2×D4×C43#4114yes—
275C22×C4×C43—22no—
276C22×C4×C43—22no—
277C22×C4×C43—24no—
278C22×C4×C43—22no—
279C22×C4×C43—22no—
280C22×C4×C43—22no—
281C22×C4×C43—24no—
282C22×C4×C43—42no—
283C22×C4×C43#4114yes—
284C22×C4×C43C2412yes—
285C22×C4×C43C2411yescharacteristic
286C22×C4×C43C2412yes—
287C22×C4×C43C2412yes—
288C22×C4×C43C2411yescharacteristic
289C22×C4×C43C2412yes—
290C22×C4×C43C2411yescharacteristic
291C22×C4×C43C2411yescharacteristic
292C22×C4×C43C2411yescharacteristic
293C2×C22⋊D43—24no—
294C2×C22⋊D43—24no—
295C2×C22⋊D43—24no—
296C2×C22⋊D43—24no—
297C2×C22⋊D43—42no—
298C2×C22⋊D43—42no—
299C22×Dic43—22no—
300C22×Dic43—22no—
301C22×Dic43—22no—
302C22×Dic43—22no—
303C22×Dic43—22no—
304C22×Dic43—22no—
305C22×Dic43—22no—
306C22×Dic43—22no—
307C22×Dic43—22no—
308C22×Dic43—41no—
309C22×Dic43—41no—
310C22×Dic43#4114yes—
311C22×Dic43C2411yescharacteristic
312C22×Dic43C2412yes—
313C22×Dic43C2411yescharacteristic
314C22×Dic43C2411yescharacteristic
315C22×Dic43C2411yescharacteristic
316C22×Dic43C2412yes—
317C22×Dic43C2411yescharacteristic
318C22×Dic43C2411yescharacteristic
319C22×Dic43C2411yescharacteristic
320C22×Dic43C2411yescharacteristic
321C2×D172—232no—
322C2×D172—22no—
323C2×D172—22no—
324C2×D172—24no—
325C2×D172—22no—
326C2×D172—22no—
327C2×D172—24no—
328C2×D172—24no—
329C2×D172C2×D414yes—
330C2×D172#4114yes—
331C2×C4×D43—24no—
332C2×C4×D43—24no—
333C2×C4×D43—24no—
334C2×C4×D43—24no—
335C2×C4×D43—24no—
336C2×C4×D43—24no—
337C2×C4×D43—24no—
338C2×C4×D43—24no—
339C2×C4×D43—24no—
340C2×C4×D43—42no—
341C2×C4×D43—42no—
342C2×C4×D43—432no—
343C2×C4×D43C2×D418yes—
344C4⋊C4×C43—24no—
345C4⋊C4×C43—22no—
346C4⋊C4×C43—24no—
347C4⋊C4×C43—22no—
348C4⋊C4×C43—22no—
349C4⋊C4×C43—24no—
350C4⋊C4×C43—42no—
351C4⋊C4×C43C2×D414yes—
352C22⋊C4×C43—24no—
353C22⋊C4×C43—22no—
354C22⋊C4×C43—22no—
355C22⋊C4×C43—24no—
356C22⋊C4×C43—42no—
357C42×C43—22no—
358C22⋊Dic43—22no—
359C22⋊Dic43—22no—
360C22⋊Dic43—22no—
361C22⋊Dic43—22no—
362C22⋊Dic43—24no—
363(C2×D43)⋊C4—24no—
364(C2×D43)⋊C4—24no—
365(C2×D43)⋊C4—24no—
366(C2×D43)⋊C4—24no—
367(C2×D43)⋊C4—24no—
368(C2×D43)⋊C4—24no—
369(C2×D43)⋊C4—24no—
370(C2×D43)⋊C4—24no—
371(C2×D43)⋊C4—24no—
372(C2×D43)⋊C4—24no—
373(C2×D43)⋊C4—24no—
374(C2×D43)⋊C4—42no—
375(C2×D43)⋊C4—42no—
376(C2×D43)⋊C4—42no—
377(C2×D43)⋊C4—42no—
378(C2×D43)⋊C4—42no—
379(C2×D43)⋊C4—42no—
380(C2×D43)⋊C4C2×D418yes—
381C4⋊Dic43—24no—
382C4⋊Dic43—22no—
383C4⋊Dic43—22no—
384C4⋊Dic43—22no—
385C4⋊Dic43—24no—
386C4⋊Dic43—22no—
387C4⋊Dic43—42no—
388C4⋊Dic43—42no—
389Dic43⋊C4—24no—
390Dic43⋊C4—42no—
391C4×Dic43—22no—
392C4×Dic43—22no—
393C4×Dic43—22no—
394C4×Dic43—22no—
395C4×Dic43—22no—
396C4×Dic43—22no—
397C4×Dic43—22no—
398C4×Dic43—22no—
399C4×Dic43—24no—
400C4×Dic43—22no—
401C4×Dic43—22no—
402C4×Dic43—24no—
403C4×Dic43—41no—
404C4×Dic43C2×D414yes—
405C23×C43—21no—
406C23×C43—21no—
407C23×C43—21no—
408C23×C43—21no—
409C23×C43—21no—
410C23×C43—21no—
411C23×C43—21no—
412C23×C43—21no—
413C23×C43—21no—
414C23×C43—21no—
415C23×C43C2×#4112yes—
416C23×C43C2×#4112yes—
417C23×C43C2×#4112yes—
418C23×C43C2×#4112yes—
419C23×C43C2511yescharacteristic
420C22×D43—216no—
421C22×D43—22no—
422C22×D43—22no—
423C22×D43—22no—
424C22×D43—22no—
425C22×D43—22no—
426C22×D43—22no—
427C22×D43—22no—
428C22×D43—22no—
429C22×D43—22no—
430C22×D43—22no—
431C22×D43—22no—
432C22×D43—22no—
433C22×D43—48no—
434C22×D43—48no—
435C22×D43—48no—
436C22×D43—48no—
437C22×D43—48no—
438C22×D43—48no—
439C22×D43C22×D414yes—
440C22×D43C2×#4114yes—
441Q8×C43—44no—
442D4×C43—28no—
443C2×C4×C43—21no—
444C2×C4×C43—21no—
445C2×C4×C43—21no—
446C2×C4×C43—22no—
447C2×C4×C43—21no—
448C2×C4×C43—22no—
449C2×C4×C43—28no—
450C2×C4×C43—21no—
451C2×C4×C43—22no—
452C2×C4×C43—22no—
453C2×C4×C43—21no—
454C2×C4×C43—22no—
455C2×C4×C43—21no—
456C2×C4×C43—22no—
457C2×C4×C43—21no—
458C2×C4×C43—22no—
459C2×C4×C43—22no—
460C2×C4×C43—22no—
461C2×C4×C43—21no—
462C2×C4×C43—22no—
463C2×C4×C43—21no—
464C2×C4×C43—22no—
465C2×C4×C43—48no—
466C2×C4×C43—44no—
467C2×C4×C43C22×D414yes—
468C2×C4×C43C22×D412yes—
469C2×C4×C43C2×#4112yes—
470C2×C4×C43C2×#4112yes—
471C2×C4×C43C2×#4112yes—
472C2×C4×C43C2×#4112yes—
473C22⋊D43—48no—
474C22⋊D43—48no—
475C2×Dic43—21no—
476C2×Dic43—21no—
477C2×Dic43—21no—
478C2×Dic43—21no—
479C2×Dic43—28no—
480C2×Dic43—21no—
481C2×Dic43—21no—
482C2×Dic43—21no—
483C2×Dic43—22no—
484C2×Dic43—21no—
485C2×Dic43—21no—
486C2×Dic43—21no—
487C2×Dic43—21no—
488C2×Dic43—22no—
489C2×Dic43—21no—
490C2×Dic43—21no—
491C2×Dic43—21no—
492C2×Dic43—22no—
493C2×Dic43—22no—
494C2×Dic43—22no—
495C2×Dic43—21no—
496C2×Dic43—21no—
497C2×Dic43—21no—
498C2×Dic43—21no—
499C2×Dic43—22no—
500C2×Dic43—21no—
501C2×Dic43—44no—
502C2×Dic43—44no—
503C2×Dic43—44no—
504C2×Dic43C22×D412yes—
505C2×Dic43C22×D412yes—
506C2×Dic43C2×#4112yes—
507C2×Dic43C2×#4112yes—
508C2×Dic43H(5,𝔽2)12yes—
509D172—216no—
510D172—28no—
511D172—28no—
512C4×D43—216no—
513C4×D43—48no—
514C4×D43—48no—
515C4×D43—48no—
516#34700—431nomaximal, Sylow
517C22×C43—22no—
518C22×C43—22no—
519C22×C43—22no—
520C22×C43—22no—
521C22×C43—22no—
522C22×C43—22no—
523C22×C43—22no—
524C22×C43—22no—
525C22×C43—22no—
526C22×C43—41no—
527C22×C43—41no—
528C22×C43—41no—
529C22×C43—41no—
530C22×C43#52914yescomplemented
531C22×C43C23×D411yescharacteristic
532C22×C43C22×#4111yescharacteristic
533C22×C43C22×#4111yescharacteristic
534C22×C43C22×#4111yescharacteristic
535C22×C43C22×#4111yescharacteristic
536C22×C43C2×H(5,𝔽2)11yescharacteristic
537C22×C43#58511yescharacteristic
538C2×D43—24no—
539C2×D43—24no—
540C2×D43—24no—
541C2×D43—24no—
542C2×D43—24no—
543C2×D43—24no—
544C2×D43—432no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—42no—
553C4×C43—22no—
554C4×C43—22no—
555C4×C43—24no—
556C4×C43—41no—
557C4×C43—42no—
558C4×C43—41no—
559C4×C43—42no—
560C4×C43—42no—
561C4×C43#52514yes—
562Dic43—22no—
563Dic43—22no—
564Dic43—41no—
565Dic43—41no—
566Dic43—41no—
567Dic43—42no—
568Dic43—41no—
569Dic43—41no—
570Dic43—42no—
571Dic43#54614yes—
572C2×#529—431no—
573C22×C4×D4—431no—
574#2480—432no—
575#2468—432no—
576#2457—432no—
577#2454—431no—
578#2447—431no—
579#2442—431no—
580#2435—431no—
581#2427—431no—
582#2420—431no—
583#2418—432no—
584#2417D4311yescharacteristic, complemented
585#2408—431no—
586#2395—432no—
587#2392—432no—
588C4×#124—431no—
589C4×C22⋊Q8—431no—
590C4×#121—431no—
591C4×#120—432no—
592#2293—431no—
593#2280—432no—
594C42×D4—431no—
595C2×C43—24no—
596C2×C43—42no—
597C2×C43C2×#52511yescharacteristic
598C2×C43C2×#52911yescharacteristic
599C2×C43#346011yescharacteristic
600C2×C43C2×#54611yescharacteristic
601C2×C43D4×#4111yescharacteristic
602C2×C43#347511yescharacteristic
603C2×C43#348111yescharacteristic
604D43—44no—
605D43—44no—
606C23×D4—431no—
607C24×C4—432no—
608#529—868no—
609C2×#126—432no—
610C2×#125—431no—
611C2×#124—431no—
612C2×#124—431no—
613C2×#123—432no—
614C2×C22⋊Q8C2×D4311yescharacteristic
615C2×C22⋊Q8C2×D4311yescharacteristic, complemented
616C2×#121—431no—
617C2×#121—431no—
618C2×#120—432no—
619C2×C4×Q8—431no—
620C2×C4×D4—431no—
621C2×C4×D4—431no—
622C2×C4×D4—431no—
623C2×C4×D4—432no—
624C2×C4×D4—431no—
625C2×C4×D4—431no—
626C2×C4×D4—432no—
627C2×C4×D4—431no—
628C2×C4×D4—432no—
629C2×C4×D4—432no—
630C2×C4×D4—868no—
631C2×C4×D4C2×D4311yescharacteristic
632C2×#117—432no—
633C2×#117—432no—
634C22×C4⋊C4C2×D4311yescharacteristic
635C22×C22⋊C4—432no—
636C22×C42—431no—
637C22×C42—431no—
638#400—432no—
639#399—432no—
640#398—432no—
641#398C2×D4312yescomplemented
642#397—432no—
643#397—432no—
644#397—432no—
645#397—432no—
646#396—432no—
647#396C2×D4312yescomplemented
648#394—432no—
649#394—432no—
650#394—432no—
651#394—432no—
652#394—432no—
653#392—432no—
654#391—431no—
655#391C2×D4311yescharacteristic, complemented
656#390—431no—
657#390—431no—
658#390—431no—
659#390—431no—
660#389—431no—
661#389—431no—
662#389—431no—
663#389C2×D4311yescharacteristic, complemented
664#388—432no—
665#388—432no—
666#388—432no—
667#388—432no—
668#388—432no—
669#387—432no—
670#386—432no—
671#386—432no—
672#386—432no—
673#386C2×D4312yes—
674#385—432no—
675#385—432no—
676#385—432no—
677#385—432no—
678#382—431no—
679#381—432no—
680#381—432no—
681#380—431no—
682#380—432no—
683#380—432no—
684#380—432no—
685#380C2×D4312yes—
686#380C2×D4311yescharacteristic, complemented
687#379—432no—
688#379—432no—
689#379—432no—
690C4×C4⋊C4—432no—
691C4×C4⋊C4—431no—
692C4×C4⋊C4—431no—
693C4×C4⋊C4—431no—
694C4×C4⋊C4—431no—
695C4×C22⋊C4—431no—
696C4×C22⋊C4—431no—
697C4×C22⋊C4—431no—
698C4×C22⋊C4—431no—
699C4×C22⋊C4—431no—
700C4×C22⋊C4—431no—
701C4×C22⋊C4—432no—
702C4×C22⋊C4—432no—
703C4×C22⋊C4—432no—
704C4×C22⋊C4—432no—
705C4×C22⋊C4—432no—
706C43—431no—
707C43#3470011yescharacteristic, complemented, Sylow
708C25—432no—
709C22×Q8C22×D4311yescharacteristic
710C22×D4—432no—
711C22×D4—432no—
712C22×D4—431no—
713C22×D4—431no—
714C22×D4—432no—
715C22×D4—864no—
716C22×D4—864no—
717C22×D4—864no—
718C22×D4C22×D4311yescharacteristic
719C23×C4—431no—
720C23×C4—432no—
721C23×C4—431no—
722C23×C4—431no—
723C23×C4—431no—
724C23×C4—432no—
725C23×C4—432no—
726C23×C4—432no—
727C23×C4—868no—
728C23×C4—868no—
729C23×C4—1724no—
730C23×C4C22×D4311yescharacteristic
731C23×C4C22×D4312yes—
732C23×C4C22×D4311yescharacteristic
733#126—868no—
734#125—864no—
735#124—864no—
736#124—864no—
737#123—868no—
738C22⋊Q8—24no—
739C22⋊Q8—24no—
740#121—864no—
741#121—864no—
742#120—868no—
743C4×Q8—864no—
744C4×D4—24no—
745C4×D4—438no—
746C4×D4—864no—
747C4×D4—868no—
748C4×D4—868no—
749C4×D4—868no—
750C4×D4—864no—
751C4×D4—864no—
752C4×D4—864no—
753C4×D4—864no—
754C4×D4—1724no—
755#117—868no—
756#117—1724no—
757C2×C4⋊C4—24no—
758C2×C4⋊C4—432no—
759C2×C4⋊C4—432no—
760C2×C4⋊C4—431no—
761C2×C4⋊C4—431no—
762C2×C4⋊C4—431no—
763C2×C4⋊C4—432no—
764C2×C4⋊C4—431no—
765C2×C4⋊C4—432no—
766C2×C4⋊C4—432no—
767C2×C4⋊C4—432no—
768C2×C4⋊C4C22×D4311yescharacteristic
769C2×C4⋊C4C22×D4312yes—
770C2×C4⋊C4C22×D4312yes—
771C2×C4⋊C4C22×D4311yescharacteristic
772C2×C4⋊C4C22×D4311yescharacteristic
773C2×C4⋊C4C22×D4312yes—
774C2×C4⋊C4C22×D4312yes—
775C2×C4⋊C4C22×D4311yescharacteristic
776C2×C22⋊C4—432no—
777C2×C22⋊C4—431no—
778C2×C22⋊C4—431no—
779C2×C22⋊C4—431no—
780C2×C22⋊C4—431no—
781C2×C22⋊C4—432no—
782C2×C22⋊C4—432no—
783C2×C22⋊C4—432no—
784C2×C22⋊C4—432no—
785C2×C22⋊C4—432no—
786C2×C22⋊C4—432no—
787C2×C22⋊C4—432no—
788C2×C22⋊C4—432no—
789C2×C22⋊C4—432no—
790C2×C22⋊C4—432no—
791C2×C22⋊C4—432no—
792C2×C22⋊C4—432no—
793C2×C22⋊C4—432no—
794C2×C22⋊C4—432no—
795C2×C22⋊C4—432no—
796C2×C22⋊C4—432no—
797C2×C22⋊C4—432no—
798C2×C22⋊C4—432no—
799C2×C22⋊C4—868no—
800C2×C22⋊C4C22×D4312yes—
801C2×C22⋊C4C22×D4311yescharacteristic
802C2×C22⋊C4C22×D4311yescharacteristic
803C2×C22⋊C4C22×D4312yes—
804C2×C22⋊C4C22×D4312yes—
805C2×C42—431no—
806C2×C42—431no—
807C2×C42—431no—
808C2×C42—432no—
809C2×C42—432no—
810C2×C42—431no—
811C2×C42—431no—
812C2×C42—431no—
813C2×C42—431no—
814C2×C42—431no—
815C2×C42—431no—
816C2×C42—431no—
817C2×C42—431no—
818C2×C42—431no—
819C2×C42—864no—
820C2×C42—864no—
821C2×C42C22×D4311yescharacteristic
822#95—431no—
823#95—431no—
824#95—431no—
825#95—431no—
826#95—431no—
827#95—431no—
828#95—432no—
829#95—432no—
830#95—432no—
831#95—432no—
832#95—432no—
833#95—432no—
834#95—432no—
835#95—432no—
836#95—432no—
837#95C22×D4312yes—
838#95C22×D4312yes—
839#95C22×D4312yes—
840#95C22×D4312yes—
841C24—432no—
842C24—432no—
843C24—864no—
844C24—864no—
845C24—864no—
846C24—864no—
847C24—864no—
848C24—1722no—
849C24—1722no—
850C24C23×D4311yescharacteristic
851C24C23×D4311yescharacteristic
852C2×Q8—22no—
853C2×Q8—22no—
854C2×Q8—22no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—434no—
858C2×D4—434no—
859C2×D4—864no—
860C2×D4—864no—
861C2×D4—8632no—
862C2×D4—864no—
863C2×D4—864no—
864C2×D4—864no—
865C2×D4—864no—
866C2×D4—862no—
867C2×D4—862no—
868C2×D4—864no—
869C2×D4—862no—
870C2×D4—862no—
871C2×D4—1722no—
872C2×D4—1722no—
873C2×D4#1062190214yes—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—24no—
877C22×C4—22no—
878C22×C4—24no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—42no—
882C22×C4—431no—
883C22×C4—434no—
884C22×C4—431no—
885C22×C4—431no—
886C22×C4—438no—
887C22×C4—431no—
888C22×C4—432no—
889C22×C4—431no—
890C22×C4—431no—
891C22×C4—431no—
892C22×C4—432no—
893C22×C4—431no—
894C22×C4—864no—
895C22×C4—864no—
896C22×C4—864no—
897C22×C4—864no—
898C22×C4—864no—
899C22×C4—864no—
900C22×C4—864no—
901C22×C4—864no—
902C22×C4—862no—
903C22×C4—862no—
904C22×C4—862no—
905C22×C4—862no—
906C22×C4—862no—
907C22×C4—862no—
908C22×C4—862no—
909C22×C4—862no—
910C22×C4—862no—
911C22×C4—864no—
912C22×C4—1722no—
913C22×C4—1722no—
914C22×C4—17232no—
915C22×C4—1721no—
916C22×C4—1721no—
917C22×C4#1062190014yes—
918C22×C4C23×D4312yes—
919C22×C4C23×D4311yescharacteristic
920C22×C4C23×D4311yescharacteristic
921C22×C4C23×D4312yes—
922C22×C4C23×D4312yes—
923C22×C4C23×D4312yes—
924C22×C4C23×D4311yescharacteristic
925C22×C4C23×D4311yescharacteristic
926C22×C4C23×D4311yescharacteristic
927C4⋊C4—24no—
928C4⋊C4—22no—
929C4⋊C4—24no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—24no—
933C4⋊C4—42no—
934C4⋊C4—862no—
935C4⋊C4—864no—
936C4⋊C4—864no—
937C4⋊C4—864no—
938C4⋊C4—862no—
939C4⋊C4—862no—
940C4⋊C4—862no—
941C4⋊C4—1722no—
942C4⋊C4—1722no—
943C4⋊C4—1722no—
944C4⋊C4D4×D4314yes—
945C22⋊C4—22no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—22no—
949C22⋊C4—42no—
950C22⋊C4—438no—
951C22⋊C4—864no—
952C22⋊C4—864no—
953C22⋊C4—864no—
954C22⋊C4—864no—
955C22⋊C4—864no—
956C22⋊C4—864no—
957C22⋊C4—864no—
958C22⋊C4—864no—
959C22⋊C4—862no—
960C22⋊C4—862no—
961C22⋊C4—862no—
962C22⋊C4—862no—
963C22⋊C4—864no—
964C22⋊C4—864no—
965C22⋊C4—864no—
966C22⋊C4—864no—
967C22⋊C4—1722no—
968C22⋊C4—1722no—
969C22⋊C4—1722no—
970C22⋊C4—1722no—
971C22⋊C4—1722no—
972C22⋊C4—1722no—
973C42—22no—
974C42—434no—
975C42—862no—
976C42—862no—
977C42—862no—
978C42—862no—
979C42—864no—
980C42—862no—
981C42—864no—
982C42—862no—
983C42—862no—
984C42—862no—
985C42—862no—
986C42—862no—
987C42—1721no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—434no—
999C23—434no—
1000C23—8616no—
1001C23—862no—
1002C23—862no—
1003C23—862no—
1004C23—862no—
1005C23—862no—
1006C23—862no—
1007C23—862no—
1008C23—862no—
1009C23—862no—
1010C23—862no—
1011C23—862no—
1012C23—862no—
1013C23—1728no—
1014C23—1728no—
1015C23—1728no—
1016C23—1728no—
1017C23—1728no—
1018C23—1728no—
1019C23#41×D4312yes—
1020C23C2×#1062190012yes—
1021C23C2×#1062190212yes—
1022C23C2×#1062190212yes—
1023C23C24×D4311yescharacteristic
1024Q8—44no—
1025D4—28no—
1026D4—8616no—
1027D4—868no—
1028D4—868no—
1029D4—1728no—
1030D4—1728no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—28no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—48no—
1054C2×C4—44no—
1055C2×C4—432no—
1056C2×C4—432no—
1057C2×C4—432no—
1058C2×C4—432no—
1059C2×C4—432no—
1060C2×C4—8616no—
1061C2×C4—868no—
1062C2×C4—861no—
1063C2×C4—861no—
1064C2×C4—861no—
1065C2×C4—861no—
1066C2×C4—861no—
1067C2×C4—861no—
1068C2×C4—861no—
1069C2×C4—862no—
1070C2×C4—861no—
1071C2×C4—861no—
1072C2×C4—861no—
1073C2×C4—861no—
1074C2×C4—862no—
1075C2×C4—861no—
1076C2×C4—862no—
1077C2×C4—862no—
1078C2×C4—861no—
1079C2×C4—861no—
1080C2×C4—861no—
1081C2×C4—862no—
1082C2×C4—861no—
1083C2×C4—861no—
1084C2×C4—861no—
1085C2×C4—862no—
1086C2×C4—861no—
1087C2×C4—1728no—
1088C2×C4—1728no—
1089C2×C4—1728no—
1090C2×C4—1724no—
1091C2×C4—1724no—
1092C2×C4—1724no—
1093C2×C4C2×D4×D4314yes—
1094C2×C4C2×D4×D4312yes—
1095C2×C4#41×D4312yes—
1096C2×C4C2×#1062190012yes—
1097C2×C4C2×#1062190012yes—
1098C2×C4C2×#1062190212yes—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—864no—
1113C22—864no—
1114C22—864no—
1115C22—864no—
1116C22—864no—
1117C22—864no—
1118C22—17232no—
1119C22—1722no—
1120C22—1722no—
1121C22—1722no—
1122C22—1722no—
1123C22—1722no—
1124C22—1722no—
1125C22—1722no—
1126C22—1722no—
1127C22#1458343514yescomplemented
1128C22C22×D4×D4311yescharacteristic
1129C22C2×#41×D4311yescharacteristic
1130C22C2×#41×D4311yescharacteristic
1131C22C22×#1062190011yescharacteristic
1132C22C22×#1062190211yescharacteristic
1133C22H(5,𝔽2)×D4311yescharacteristic
1134C22#1458373611yescharacteristic
1135C4—24no—
1136C4—22no—
1137C4—22no—
1138C4—42no—
1139C4—41no—
1140C4—42no—
1141C4—41no—
1142C4—42no—
1143C4—434no—
1144C4—862no—
1145C4—862no—
1146C4—1721no—
1147C4—1721no—
1148C4—1721no—
1149C4—1722no—
1150C4—1721no—
1151C4—1722no—
1152C4—1721no—
1153C4#1458340914yes—
1154C2—24no—
1155C2—42no—
1156C2—1724no—
1157C2—1724no—
1158C2C2×#1458340911yescharacteristic
1159C2C2×#1458343511yescharacteristic
1160C2#1914801211yescharacteristic
1161C2#546×D4311yescharacteristic
1162C2D4×#1062190211yescharacteristic
1163C2#1914816011yescharacteristic
1164C2#1914820611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2417C2
prime radical#19137951C2
hypercenter#2417D43
hypocenterC43#34700
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2417

Complements

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

NH ≅ G/Ntype
1. C2×#14583435C2semidirect
2. C22×#13063287C2semidirect
3. #19138846C2semidirect
4. #19138662C2semidirect
5. #19138503C2semidirect
6. #19138465C2semidirect
7. #19138385C2semidirect
8. #19138313C2semidirect
9. #19138247C2semidirect
10. #19138168C2semidirect
11. #19138089C2semidirect
12. #19138055C2semidirect
14. #19137859C2semidirect
15. #19137840C2semidirect
16. #19137138C2semidirect
17. C22⋊Q8×Dic43C2semidirect
18. #19137101C2semidirect
19. #19137100C2semidirect
20. #19137053C2semidirect
21. #19136977C2semidirect
22. C4×D4×Dic43C2semidirect
23. C43×#2417C2semidirect
27. C2×#13063320C22semidirect
28. C2×#13063316C22semidirect
31. C2×#13063309C22semidirect
35. C2×Q8×Dic43C22semidirect
45. C2×(C22⋊D43)⋊C4C22semidirect
46. C2×(C22⋊D43)⋊C4C22semidirect
47. C2×#13063283C22semidirect
48. C2×#13063283C22semidirect
51. C22×C4×Dic43C22semidirect
52. #14582838C22semidirect
53. #14582836C22semidirect
54. #14582832C22semidirect
55. #14582828C22semidirect
56. #14582826C22semidirect
57. #14582826C22semidirect
58. #14582825C22semidirect
59. #14582821C22semidirect
63. #14582815C22semidirect
64. #14582815C22semidirect
66. #14582806C22semidirect
71. #14582798C22semidirect
72. #14582798C22semidirect
73. #14582795C22semidirect
74. #14582791C22semidirect
75. #14582791C22semidirect
76. #14582791C22semidirect
77. #14582789C22semidirect
78. #14582788C22semidirect
79. #14582785C22semidirect
80. #14582776C22semidirect
81. #14582775C22semidirect
82. #14582775C22semidirect
84. #14582773C22semidirect
85. #14582773C22semidirect
87. #14582764C22semidirect
88. #14582761C22semidirect
89. #14582761C22semidirect
92. #14582756C22semidirect
93. #14582756C22semidirect
97. C4⋊C4×Dic43C22semidirect
98. C4⋊C4×Dic43C22semidirect
99. C4⋊C4×Dic43C22semidirect
100. C4⋊C4×Dic43C22semidirect
101. C4×C4⋊Dic43C22semidirect
105. C22⋊C4×Dic43C22semidirect
106. C22⋊C4×Dic43C22semidirect
108. C4×C22⋊Dic43C22semidirect
109. #14582746C22semidirect
110. #14582746C22semidirect
111. #14582746C22semidirect
112. #14582746C22semidirect
113. C42×Dic43C22semidirect
115. C2×C22⋊Q8×C43C22semidirect
118. C43×#398C22semidirect
119. C43×#396C22semidirect
120. C43×#391C22semidirect
121. C43×#389C22semidirect
124. C43×#380C22semidirect
161. #13063287D4semidirect
530. C22×C43#529semidirect
584. #2417D43semidirect
615. C2×C22⋊Q8C2×D43semidirect
641. #398C2×D43semidirect
647. #396C2×D43semidirect
655. #391C2×D43semidirect
663. #389C2×D43semidirect
686. #380C2×D43semidirect
707. C43#34700semidirect
1127. C22#14583435semidirect

Maximal subgroups

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

subgroupindex
C2×#145834352
C22×#130632872
#191388462
#191386622
#191385032
#191384652
#191383852
#191383132
#191382472
#191381682
#191380892
#191380552
#191379512
#191378592
#191378402
#191371382
C22⋊Q8×Dic432
#191371012
#191371002
#191370532
#191369772
C4×D4×Dic432
C43×#24172
#3470043