Finite Group Databasebeta

← #25269619

Subgroups — #25269619

Order 11008.

2930 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic, complemented
2C2×C4×D4×D43C211yesmaximal, characteristic
3#19142930C212yesmaximal, complemented
4#19142881C212yesmaximal, complemented
5#19140409C211yesmaximal, characteristic, complemented
6#19140407C211yesmaximal, characteristic, complemented
7#19140401C211yesmaximal, characteristic, complemented
8#19140399C211yesmaximal, characteristic, complemented
9#19139946C212yesmaximal, complemented
10#19139940C212yesmaximal, complemented
11#19139777C211yesmaximal, characteristic, complemented
12#19139775C211yesmaximal, characteristic, complemented
13#19139771C211yesmaximal, characteristic, complemented
14#19138907C211yesmaximal, characteristic, complemented
15#19138905C211yesmaximal, characteristic, complemented
16#19138045C212yesmaximal, complemented
17#19138043C212yesmaximal, complemented
18#19137955C211yesmaximal, characteristic, complemented
19#19137953C211yesmaximal, characteristic, complemented
20#19137208C212yesmaximal, complemented
21#19137169C212yesmaximal
22C2×#14582758C211yesmaximal, characteristic, complemented
23C43×#2564C211yesmaximal, characteristic, complemented
24C22×Q8×D43C2211yescharacteristic, complemented
25C22×D4×D43C2211yescharacteristic
26C23×C4×D43C2211yescharacteristic
27C23×C4×D43C2211yescharacteristic
28C2×#13063305C2211yescharacteristic
29C2×#13063304C2211yescharacteristic, complemented
30C2×#13063303C2212yes—
31C2×#13063303C2212yescomplemented
32C2×#13063302C2212yescomplemented
33C2×#13063302C2212yescomplemented
34C2×#13063301C2211yescharacteristic
35C22⋊Q8×D43—28no—
36C2×C4×D172C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×C4×C22⋊D43C2211yescharacteristic
41C2×(C22⋊D43)⋊C4C2211yescharacteristic
42C2×(C22⋊D43)⋊C4C2211yescharacteristic
43C4×D4×D43—28no—
44C22×Dic43⋊C4C2212yescomplemented
45C2×C4⋊C4×D43C2211yescharacteristic
46C2×C4⋊C4×D43C2211yescharacteristic, complemented
47C2×C4⋊C4×D43C2212yescomplemented
48C22×(C2×D43)⋊C4C2212yes—
49C2×C22⋊C4×D43C2212yes—
50C2×C22⋊C4×D43C2211yescharacteristic
51C2×C22⋊C4×D43C2211yescharacteristic
52C2×C42×D43C2211yescharacteristic
53#14582839C2211yescharacteristic, complemented
54#14582838C2211yescharacteristic, complemented
55#14582837C2211yescharacteristic, complemented
56#14582836C2211yescharacteristic, complemented
57#14582835C2211yescharacteristic, complemented
58#14582834C2211yescharacteristic, complemented
59#14582833C2212yescomplemented
60#14582833C2212yescomplemented
61#14582831C2212yescomplemented
62#14582830C2212yescomplemented
63#14582823C2212yescomplemented
64#14582822C2212yescomplemented
65#14582822C2212yescomplemented
66#14582821C2212yescomplemented
67#14582820C2211yescharacteristic, complemented
68#14582819C2211yescharacteristic, complemented
69#14582818C2211yescharacteristic, complemented
70#14582812C2211yescharacteristic, complemented
71#14582811C2211yescharacteristic, complemented
72#14582810C2211yescharacteristic, complemented
73#14582803C2212yescomplemented
74#14582803C2212yescomplemented
75#14582796C2212yescomplemented
76#14582794C2212yescomplemented
77#14582784C2212yescomplemented
78#14582783C2212yescomplemented
79#14582780C2212yescomplemented
80#14582779C2212yes—
81#14582778C2212yes—
82#14582777C2212yes—
83#14582777C2212yes—
84#14582776C2212yes—
85#14582775C2212yes—
86#14582775C2212yes—
87#14582773C2212yes—
88#14582773C2212yes—
89#14582773C2212yescomplemented
90#14582773C2212yescomplemented
91#14582773C2212yescomplemented
92#14582772C2212yescomplemented
93#14582770C2212yes—
94#14582770C2212yes—
95#14582770C2212yescomplemented
96#14582770C2212yescomplemented
97#14582770C2212yescomplemented
98#14582761C2212yes—
99#14582761C2212yes—
100#14582759C2212yescomplemented
101#14582758C2212yes—
102#14582758C2211yescharacteristic
103#14582758C2211yescharacteristic
104#14582758C2211yescharacteristic, complemented
105#14582758C2211yescharacteristic, complemented
106#14582758C2212yescomplemented
107#14582758C2212yescomplemented
108#14582757C2212yescomplemented
109#14582757C2212yescomplemented
110#14582757C2212yescomplemented
111#14582754C2212yes—
112#14582754C2212yes—
113C2×C43⋊#95C2211yescharacteristic, complemented
114C2×C22⋊Q8×C43C2211yescharacteristic, complemented
115C2×C4×D4×C43C2211yescharacteristic
116C43×#400C2211yescharacteristic, complemented
117C43×#399C2211yescharacteristic, complemented
118C43×#395C2211yescharacteristic, complemented
119C43×#393C2211yescharacteristic, complemented
120C43×#387C2212yescomplemented
121C43×#386C2212yes—
122C43×#385C2212yescomplemented
123C43×#380C2212yescomplemented
124C2×#95×C43C2211yescharacteristic, complemented
125C24×D43C2311yescharacteristic
126C24×D43C2311yescharacteristic
127C22×Dic86C2312yes—
128C22×Dic86C2311yescharacteristic
129C2×Q8×D43—24no—
130C2×Q8×D43—44no—
131C22×D172C2311yescharacteristic
132C22×C22⋊D43C2311yescharacteristic
133C22×C22⋊D43C2311yescharacteristic
134C2×D4×D43—24no—
135C2×D4×D43—24no—
136C2×D4×D43Q818yescomplemented
137C23×Dic43C2311yescharacteristic
138C23×Dic43C2311yescharacteristic
139C23×Dic43C2312yes—
140C22×C4×D43—24no—
141C22×C4×D43—44no—
142C22×C4×D43—44no—
143C22×C4×D43D418yes—
144C22×C4×D43C2311yescharacteristic
145C22×C4×D43C2311yescharacteristic
146C22×C4×D43C2311yescharacteristic
147C22×C4×D43C2311yescharacteristic
148C22×C4×D43C2311yescharacteristic
149C22×C4×D43C2311yescharacteristic
150C22×C4×D43C2312yes—
151C22×C4×D43C2312yes—
152C22×C4×D43C2311yescharacteristic
153C22×C4×D43C2311yescharacteristic
154C22×C4×D43C2311yescharacteristic
155#13063305—24no—
156#13063304—24no—
157#13063303—28no—
158#13063303—44no—
159#13063302—28no—
160#13063302—44no—
161#13063301—24no—
162C4×D172—24no—
163D4×Dic43—24no—
164#13063287—24no—
165C4×C22⋊D43—24no—
166C4×C22⋊D43—24no—
167(C22⋊D43)⋊C4—24no—
168(C22⋊D43)⋊C4—24no—
169C2×C4⋊Dic43C2312yes—
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2311yescharacteristic
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2312yes—
174C2×Dic43⋊C4—44no—
175C2×Dic43⋊C4C2312yes—
176C2×Dic43⋊C4C2312yes—
177C2×Dic43⋊C4C2312yes—
178C2×Dic43⋊C4C2312yes—
179C2×Dic43⋊C4C2311yescharacteristic
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2311yescharacteristic
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2312yes—
188C4⋊C4×D43—24no—
189C4⋊C4×D43—28no—
190C4⋊C4×D43—24no—
191C2×C22⋊Dic43C2311yescharacteristic
192C2×C22⋊Dic43C2311yescharacteristic
193C2×C22⋊Dic43C2312yes—
194C2×C22⋊Dic43C2312yes—
195C2×C22⋊Dic43C2312yes—
196C2×(C2×D43)⋊C4—28no—
197C2×(C2×D43)⋊C4C2311yescharacteristic
198C2×(C2×D43)⋊C4C2311yescharacteristic
199C2×(C2×D43)⋊C4C2311yescharacteristic
200C2×(C2×D43)⋊C4C2311yescharacteristic
201C2×(C2×D43)⋊C4C2312yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2312yes—
204C2×(C2×D43)⋊C4C2312yes—
205C2×(C2×D43)⋊C4C2312yes—
206C2×(C2×D43)⋊C4C2312yes—
207C2×(C2×D43)⋊C4C2312yes—
208C2×(C2×D43)⋊C4C2312yes—
209C2×(C2×D43)⋊C4C2312yes—
210C2×(C2×D43)⋊C4C2312yes—
211C22⋊C4×D43—24no—
212C22⋊C4×D43—28no—
213C22⋊C4×D43—24no—
214C2×C4×Dic43C2311yescharacteristic
215C2×C4×Dic43C2311yescharacteristic
216C2×C4×Dic43C2311yescharacteristic
217C42×D43—24no—
218C43⋊#95C2312yes—
219C43⋊#95C2312yes—
220C43⋊#95C2312yes—
221C43⋊#95C2312yes—
222C43⋊#95C2312yes—
223C43⋊#95C2312yes—
224C43⋊#95C2312yes—
225C43⋊#95C2312yes—
226C43⋊#95C2312yes—
227C43⋊#95C2311yescharacteristic
228C43⋊#95C2311yescharacteristic
229C43⋊#95C2312yes—
230C43⋊#95C2312yes—
231C43⋊#95C2312yes—
232C43⋊#95C2312yes—
233C22×Q8×C43C2311yescharacteristic
234C22×D4×C43C2311yescharacteristic
235C23×C4×C43C2311yescharacteristic
236C23×C4×C43C2312yes—
237C23×C4×C43C2311yescharacteristic
238C22⋊Q8×C43—24no—
239C4×D4×C43—24no—
240C2×C4⋊C4×C43C2311yescharacteristic
241C2×C4⋊C4×C43C2311yescharacteristic
242C2×C4⋊C4×C43C2312yes—
243C2×C4⋊C4×C43C2312yes—
244C2×C4⋊C4×C43C2312yes—
245C2×C22⋊C4×C43C2311yescharacteristic
246C2×C22⋊C4×C43C2311yescharacteristic
247C2×C22⋊C4×C43C2312yes—
248C2×C22⋊C4×C43C2312yes—
249C2×C22⋊C4×C43C2312yes—
250C2×C42×C43C2311yescharacteristic
251#95×C43C2312yes—
252#95×C43C2312yes—
253#95×C43C2312yes—
254#95×C43C2312yes—
255#95×C43C2311yescharacteristic
256#95×C43C2311yescharacteristic
257#95×C43C2312yes—
258C24×C43C2411yescharacteristic
259C24×C43C2411yescharacteristic
260C23×D43—22no—
261C23×D43—22no—
262C23×D43—42no—
263C23×D43—42no—
264C23×D43—42no—
265C23×D43—42no—
266C23×D43C2×D414yes—
267C23×D43C2×Q814yes—
268C23×D43C2×Q814yescomplemented
269C23×D43#4114yes—
270C23×D43C2411yescharacteristic
271C23×D43C2411yescharacteristic
272C23×D43C2411yescharacteristic
273C2×Q8×C43—22no—
274C2×Q8×C43—42no—
275C2×D4×C43—22no—
276C2×D4×C43—22no—
277C2×D4×C43C2×Q814yescomplemented
278C22×C4×C43—22no—
279C22×C4×C43—24no—
280C22×C4×C43—42no—
281C22×C4×C43—42no—
282C22×C4×C43—42no—
283C22×C4×C43—42no—
284C22×C4×C43C2×D414yes—
285C22×C4×C43C2412yes—
286C22×C4×C43C2412yes—
287C22×C4×C43C2411yescharacteristic
288C22×C4×C43C2412yes—
289C22×C4×C43C2412yes—
290C22×C4×C43C2411yescharacteristic
291C22×C4×C43C2411yescharacteristic
292C22×C4×C43C2411yescharacteristic
293C22×C4×C43C2411yescharacteristic
294C2×C22⋊D43—22no—
295C2×C22⋊D43—22no—
296C2×C22⋊D43—22no—
297C2×C22⋊D43—22no—
298C2×C22⋊D43C2×Q814yes—
299C2×C22⋊D43C2×Q814yescomplemented
300C22×Dic43—24no—
301C22×Dic43—22no—
302C22×Dic43—24no—
303C22×Dic43—24no—
304C22×Dic43—42no—
305C22×Dic43—42no—
306C22×Dic43C2×D414yes—
307C22×Dic43C2412yes—
308C22×Dic43C2412yes—
309C22×Dic43C2411yescharacteristic
310C22×Dic43C2412yes—
311C22×Dic43C2412yes—
312C22×Dic43C2411yescharacteristic
313C22×Dic43C2411yescharacteristic
314C22×Dic43C2411yescharacteristic
315C22×Dic43C2411yescharacteristic
316Q8×D43—416no—
317D4×D43—232no—
318C2×D172—22no—
319C2×D172—22no—
320C2×D172C2×Q814yes—
321C2×C4×D43—24no—
322C2×C4×D43—24no—
323C2×C4×D43—22no—
324C2×C4×D43—22no—
325C2×C4×D43—24no—
326C2×C4×D43—22no—
327C2×C4×D43—22no—
328C2×C4×D43—24no—
329C2×C4×D43—22no—
330C2×C4×D43—24no—
331C2×C4×D43—22no—
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—416no—
342C2×C4×D43—416no—
343C2×C4×D43C2×D414yes—
344C2×C4×D43C2×D414yes—
345C2×C4×D43C2×D414yes—
346C2×C4×D43C2×D414yes—
347C2×C4×D43C2×Q814yescomplemented
348C2×Dic86—22no—
349C2×Dic86—24no—
350C2×Dic86—24no—
351C2×Dic86—24no—
352C2×Dic86—42no—
353C4⋊C4×C43—22no—
354C4⋊C4×C43—24no—
355C4⋊C4×C43—22no—
356C4⋊C4×C43—42no—
357C4⋊C4×C43—42no—
358C22⋊C4×C43—22no—
359C22⋊C4×C43—22no—
360C22⋊C4×C43—24no—
361C22⋊C4×C43—42no—
362C22⋊C4×C43—42no—
363C42×C43—22no—
364C22⋊Dic43—22no—
365C22⋊Dic43—22no—
366C22⋊Dic43—24no—
367C22⋊Dic43—42no—
368C22⋊Dic43—42no—
369(C2×D43)⋊C4—22no—
370(C2×D43)⋊C4—22no—
371(C2×D43)⋊C4—22no—
372(C2×D43)⋊C4—22no—
373(C2×D43)⋊C4—24no—
374(C2×D43)⋊C4—24no—
375(C2×D43)⋊C4—24no—
376(C2×D43)⋊C4—24no—
377(C2×D43)⋊C4—24no—
378(C2×D43)⋊C4—24no—
379(C2×D43)⋊C4—42no—
380(C2×D43)⋊C4—42no—
381(C2×D43)⋊C4—42no—
382(C2×D43)⋊C4—42no—
383C4⋊Dic43—22no—
384C4⋊Dic43—22no—
385C4⋊Dic43—24no—
386C4⋊Dic43—42no—
387C4⋊Dic43—42no—
388Dic43⋊C4—22no—
389Dic43⋊C4—24no—
390Dic43⋊C4—22no—
391Dic43⋊C4—24no—
392Dic43⋊C4—24no—
393Dic43⋊C4—24no—
394Dic43⋊C4—24no—
395Dic43⋊C4—42no—
396Dic43⋊C4—42no—
397Dic43⋊C4—42no—
398Dic43⋊C4—42no—
399Dic43⋊C4—42no—
400Dic43⋊C4—42no—
401C4×Dic43—22no—
402C4×Dic43—22no—
403C4×Dic43—22no—
404C23×C43—22no—
405C23×C43—22no—
406C23×C43—21no—
407C23×C43—21no—
408C23×C43—22no—
409C23×C43—22no—
410C23×C43C22×D412yes—
411C23×C43C22×Q812yes—
412C23×C43C22×Q812yes—
413C23×C43C2×#4112yes—
414C23×C43C2511yescharacteristic
415C22×D43—22no—
416C22×D43—22no—
417C22×D43—22no—
418C22×D43—22no—
419C22×D43—21no—
420C22×D43—21no—
421C22×D43—22no—
422C22×D43—22no—
423C22×D43—28no—
424C22×D43—44no—
425C22×D43—44no—
426C22×D43—48no—
427C22×D43—48no—
428C22×D43—48no—
429C22×D43—44no—
430C22×D43—44no—
431C22×D43—48no—
432C22×D43C22⋊Q8116yescomplemented
433C22×D43C22×D412yes—
434C22×D43C22×D412yes—
435C22×D43C22×Q812yes—
436C22×D43C22×Q812yes—
437C22×D43C22×Q812yes—
438C22×D43C2×#4112yes—
439C22×D43C2×#4112yes—
440Q8×C43—44no—
441D4×C43—28no—
442C2×C4×C43—21no—
443C2×C4×C43—21no—
444C2×C4×C43—22no—
445C2×C4×C43—22no—
446C2×C4×C43—21no—
447C2×C4×C43—22no—
448C2×C4×C43—22no—
449C2×C4×C43—21no—
450C2×C4×C43—22no—
451C2×C4×C43—22no—
452C2×C4×C43—22no—
453C2×C4×C43—22no—
454C2×C4×C43—22no—
455C2×C4×C43—22no—
456C2×C4×C43—22no—
457C2×C4×C43—22no—
458C2×C4×C43—22no—
459C2×C4×C43—22no—
460C2×C4×C43—22no—
461C2×C4×C43—22no—
462C2×C4×C43—44no—
463C2×C4×C43—44no—
464C2×C4×C43—84no—
465C2×C4×C43C22×D412yes—
466C2×C4×C43C22×D412yes—
467C2×C4×C43C22×Q812yes—
468C22⋊D43—28no—
469C22⋊D43—28no—
470C2×Dic43—21no—
471C2×Dic43—21no—
472C2×Dic43—22no—
473C2×Dic43—28no—
474C2×Dic43—21no—
475C2×Dic43—22no—
476C2×Dic43—22no—
477C2×Dic43—21no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—22no—
486C2×Dic43—22no—
487C2×Dic43—22no—
488C2×Dic43—22no—
489C2×Dic43—22no—
490C2×Dic43—44no—
491C2×Dic43—84no—
492C2×Dic43C22×D412yes—
493C2×Dic43C22×D412yes—
494C2×Dic43C22×Q812yes—
495C2×Dic43H(5,𝔽2)14yes—
496D172—28no—
497C4×D43—28no—
498C4×D43—28no—
499C4×D43—28no—
500C4×D43—44no—
501C4×D43—44no—
502C4×D43—44no—
503C4×D43—44no—
504C4×D43—48no—
505C4×D43—44no—
506C4×D43—48no—
507C4×D43—44no—
508Dic86—44no—
509Dic86—48no—
510#35010—431nomaximal, Sylow
511C22×C43—22no—
512C22×C43—22no—
513C22×C43—24no—
514C22×C43—24no—
515C22×C43—22no—
516C22×C43—24no—
517C22×C43—41no—
518C22×C43—41no—
519C22×C43—42no—
520C22×C43C2×C22⋊Q814yes—
521C22×C43C23×D411yescharacteristic
522C22×C43C23×Q811yescharacteristic
523C22×C43C22×#4111yescharacteristic
524C22×C43C2×H(5,𝔽2)12yes—
525C22×C43#58512yes—
526C2×D43—22no—
527C2×D43—22no—
528C2×D43—22no—
529C2×D43—22no—
530C2×D43—24no—
531C2×D43—24no—
532C2×D43—24no—
533C2×D43—24no—
534C2×D43—22no—
535C2×D43—24no—
536C2×D43—416no—
537C2×D43—416no—
538C2×D43—41no—
539C2×D43—41no—
540C2×D43—42no—
541C2×D43C2×C22⋊Q814yes—
542C2×D43C2×C22⋊Q814yes—
543C4×C43—22no—
544C4×C43—22no—
545C4×C43—22no—
546C4×C43—42no—
547C4×C43—41no—
548C4×C43—41no—
549C4×C43—42no—
550C4×C43—42no—
551C4×C43—42no—
552Dic43—22no—
553Dic43—22no—
554Dic43—42no—
555Dic43—41no—
556Dic43—41no—
557Dic43—42no—
558Dic43—42no—
559Dic43—42no—
560Dic43#53414yes—
561C22×C22⋊Q8—431no—
562C22×C4×D4—431no—
563#2855—432no—
564#2848—432no—
565#2627—431no—
566#2627—431no—
567#2626—431no—
568#2626—431no—
569#2579—432no—
570#2579—432no—
571#2564—431no—
572#2564—431no—
573#2564—431no—
574#2564D4311yescharacteristic, complemented
575#2487—431no—
576#2487—431no—
577#2417—432no—
578#2417—432no—
579#2409—431no—
580#2409—431no—
581#2315—432no—
582#2308—432no—
583C2×#380—431no—
584C2×C43—24no—
585C2×C43—42no—
586C2×C43C22×C22⋊Q811yescharacteristic
587C2×C43C2×#53411yescharacteristic
588C2×C43#344911yescharacteristic
589C2×C43#350112yes—
590C2×C43#350512yes—
591D43—24no—
592D43—24no—
593D43—42no—
594C23×Q8—431no—
595C23×D4—431no—
596C24×C4—431no—
597C24×C4—431no—
598C2×C22⋊Q8—431no—
599C2×C22⋊Q8—431no—
600C2×C22⋊Q8—432no—
601C2×C22⋊Q8—431no—
602C2×C22⋊Q8—432no—
603C2×C22⋊Q8—432no—
604C2×C22⋊Q8—432no—
605C2×C22⋊Q8—868no—
606C2×C22⋊Q8C2×D4311yescharacteristic, complemented
607C2×C4×D4—431no—
608C2×C4×D4—431no—
609C2×C4×D4—431no—
610C2×C4×D4—431no—
611C2×C4×D4—431no—
612C2×C4×D4—431no—
613C2×C4×D4—431no—
614C2×C4×D4—868no—
615C2×C4×D4C2×D4311yescharacteristic
616C22×C4⋊C4—432no—
617C22×C4⋊C4—432no—
618C22×C4⋊C4—431no—
619C22×C4⋊C4—431no—
620C22×C22⋊C4—432no—
621C22×C22⋊C4—432no—
622C22×C22⋊C4—431no—
623C22×C22⋊C4—431no—
624C22×C42—431no—
625#400—431no—
626#400—431no—
627#400—431no—
628#400C2×D4311yescharacteristic, complemented
629#399—431no—
630#399—431no—
631#399—431no—
632#399C2×D4311yescharacteristic, complemented
633#398—432no—
634#398—432no—
635#398—432no—
636#398—432no—
637#396—432no—
638#396—432no—
639#396—432no—
640#396—432no—
641#395—431no—
642#395—431no—
643#395—431no—
644#395C2×D4311yescharacteristic, complemented
645#393—431no—
646#393—431no—
647#393—431no—
648#393C2×D4311yescharacteristic, complemented
649#391—432no—
650#391—432no—
651#389—432no—
652#389—432no—
653#387—432no—
654#387—432no—
655#387—432no—
656#387C2×D4312yescomplemented
657#386—432no—
658#386—432no—
659#386—432no—
660#386—432no—
661#386—432no—
662#386—432no—
663#386—432no—
664#386C2×D4312yes—
665#385—432no—
666#385—432no—
667#385—432no—
668#385—432no—
669#385—432no—
670#385—432no—
671#385—432no—
672#385—432no—
673#385—432no—
674#385—432no—
675#385—432no—
676#385C2×D4312yescomplemented
677#381—432no—
678#381—432no—
679#380—432no—
680#380—432no—
681#380—432no—
682#380—432no—
683#380—432no—
684#380—432no—
685#380—432no—
686#380—431no—
687#380—431no—
688#380—431no—
689#380—431no—
690#380C2×D4312yescomplemented
691#379—432no—
692#379—432no—
693C2×#95—431no—
694C2×#95C2×D4311yescharacteristic, complemented
695C43#3501011yescharacteristic, complemented, Sylow
696C25—431no—
697C25—431no—
698C22×Q8—432no—
699C22×Q8—431no—
700C22×Q8—864no—
701C22×Q8—1724no—
702C22×Q8C22×D4311yescharacteristic
703C22×D4—431no—
704C22×D4—431no—
705C22×D4—438no—
706C22×D4—431no—
707C22×D4—864no—
708C22×D4—864no—
709C22×D4C22×D4311yescharacteristic
710C23×C4—431no—
711C23×C4—431no—
712C23×C4—431no—
713C23×C4—431no—
714C23×C4—438no—
715C23×C4—431no—
716C23×C4—431no—
717C23×C4—431no—
718C23×C4—432no—
719C23×C4—431no—
720C23×C4—431no—
721C23×C4—432no—
722C23×C4—431no—
723C23×C4—432no—
724C23×C4—431no—
725C23×C4—864no—
726C23×C4—1724no—
727C23×C4—1724no—
728C23×C4C22×D4312yes—
729C23×C4C22×D4311yescharacteristic
730C23×C4C22×D4311yescharacteristic
731C22⋊Q8—24no—
732C22⋊Q8—868no—
733C22⋊Q8—868no—
734C22⋊Q8—864no—
735C22⋊Q8—864no—
736C22⋊Q8—864no—
737C22⋊Q8—1724no—
738C22⋊Q8—1724no—
739C4×D4—24no—
740C4×D4—864no—
741C4×D4—864no—
742C4×D4—864no—
743C4×D4—864no—
744C4×D4—864no—
745C4×D4—864no—
746C4×D4—864no—
747C2×C4⋊C4—431no—
748C2×C4⋊C4—431no—
749C2×C4⋊C4—431no—
750C2×C4⋊C4—432no—
751C2×C4⋊C4—432no—
752C2×C4⋊C4—432no—
753C2×C4⋊C4—432no—
754C2×C4⋊C4—431no—
755C2×C4⋊C4—432no—
756C2×C4⋊C4—432no—
757C2×C4⋊C4—432no—
758C2×C4⋊C4—432no—
759C2×C4⋊C4—432no—
760C2×C4⋊C4—432no—
761C2×C4⋊C4—432no—
762C2×C4⋊C4—432no—
763C2×C4⋊C4—432no—
764C2×C4⋊C4—432no—
765C2×C4⋊C4—864no—
766C2×C4⋊C4—864no—
767C2×C4⋊C4—868no—
768C2×C4⋊C4—1724no—
769C2×C4⋊C4C22×D4311yescharacteristic
770C2×C4⋊C4C22×D4312yes—
771C2×C4⋊C4C22×D4311yescharacteristic
772C2×C4⋊C4C22×D4312yes—
773C2×C4⋊C4C22×D4312yes—
774C2×C22⋊C4—431no—
775C2×C22⋊C4—431no—
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—864no—
794C2×C22⋊C4—864no—
795C2×C22⋊C4—868no—
796C2×C22⋊C4—868no—
797C2×C22⋊C4C22×D4311yescharacteristic
798C2×C22⋊C4C22×D4311yescharacteristic
799C2×C22⋊C4C22×D4312yes—
800C2×C22⋊C4C22×D4312yes—
801C2×C22⋊C4C22×D4312yes—
802C2×C42—431no—
803C2×C42—431no—
804C2×C42—431no—
805C2×C42—864no—
806C2×C42C22×D4311yescharacteristic
807#95—432no—
808#95—431no—
809#95—431no—
810#95—432no—
811#95—432no—
812#95—432no—
813#95—432no—
814#95—432no—
815#95—432no—
816#95—432no—
817#95—432no—
818#95—432no—
819#95—432no—
820#95—432no—
821#95—432no—
822#95C22×D4312yes—
823#95C22×D4311yescharacteristic
824#95C22×D4311yescharacteristic
825#95C22×D4312yes—
826#95C22×D4312yes—
827#95C22×D4312yes—
828#95C22×D4312yes—
829C24—431no—
830C24—431no—
831C24—434no—
832C24—434no—
833C24—434no—
834C24—431no—
835C24—434no—
836C24—862no—
837C24—862no—
838C24—1722no—
839C24—1722no—
840C24—1722no—
841C24—1722no—
842C24C23×D4311yescharacteristic
843C24C23×D4311yescharacteristic
844C2×Q8—22no—
845C2×Q8—42no—
846C2×Q8—864no—
847C2×Q8—864no—
848C2×Q8—864no—
849C2×Q8—862no—
850C2×Q8—1722no—
851C2×Q8—17216no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—434no—
855C2×D4—434no—
856C2×D4—434no—
857C2×D4—862no—
858C2×D4—862no—
859C2×D4—8632no—
860C2×D4—862no—
861C2×D4—862no—
862C2×D4—862no—
863C2×D4—862no—
864C2×D4Q8×D4314yescomplemented
865C22×C4—24no—
866C22×C4—22no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—431no—
872C22×C4—434no—
873C22×C4—431no—
874C22×C4—431no—
875C22×C4—434no—
876C22×C4—434no—
877C22×C4—434no—
878C22×C4—434no—
879C22×C4—434no—
880C22×C4—432no—
881C22×C4—432no—
882C22×C4—431no—
883C22×C4—432no—
884C22×C4—432no—
885C22×C4—431no—
886C22×C4—864no—
887C22×C4—864no—
888C22×C4—862no—
889C22×C4—864no—
890C22×C4—862no—
891C22×C4—862no—
892C22×C4—862no—
893C22×C4—864no—
894C22×C4—862no—
895C22×C4—864no—
896C22×C4—864no—
897C22×C4—862no—
898C22×C4—864no—
899C22×C4—864no—
900C22×C4—862no—
901C22×C4—1722no—
902C22×C4—1722no—
903C22×C4—1722no—
904C22×C4—1722no—
905C22×C4—1722no—
906C22×C4—1722no—
907C22×C4—1722no—
908C22×C4—1722no—
909C22×C4—1722no—
910C22×C4—17216no—
911C22×C4—17216no—
912C22×C4—1722no—
913C22×C4—1722no—
914C22×C4D4×D4314yes—
915C22×C4C23×D4312yes—
916C22×C4C23×D4311yescharacteristic
917C22×C4C23×D4312yes—
918C22×C4C23×D4312yes—
919C22×C4C23×D4311yescharacteristic
920C22×C4C23×D4312yes—
921C22×C4C23×D4311yescharacteristic
922C22×C4C23×D4311yescharacteristic
923C22×C4C23×D4311yescharacteristic
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—24no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—862no—
930C4⋊C4—862no—
931C4⋊C4—864no—
932C4⋊C4—864no—
933C4⋊C4—864no—
934C4⋊C4—864no—
935C4⋊C4—864no—
936C4⋊C4—862no—
937C4⋊C4—864no—
938C4⋊C4—862no—
939C4⋊C4—1722no—
940C4⋊C4—1722no—
941C4⋊C4—1722no—
942C4⋊C4—1722no—
943C4⋊C4—1722no—
944C4⋊C4—1722no—
945C4⋊C4—1722no—
946C4⋊C4—1722no—
947C22⋊C4—22no—
948C22⋊C4—24no—
949C22⋊C4—22no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—862no—
953C22⋊C4—862no—
954C22⋊C4—862no—
955C22⋊C4—864no—
956C22⋊C4—864no—
957C22⋊C4—864no—
958C22⋊C4—864no—
959C22⋊C4—864no—
960C22⋊C4—864no—
961C22⋊C4—862no—
962C22⋊C4—862no—
963C22⋊C4—864no—
964C22⋊C4—862no—
965C22⋊C4—1722no—
966C22⋊C4—1722no—
967C22⋊C4—1722no—
968C22⋊C4—1722no—
969C22⋊C4—1722no—
970C22⋊C4—1722no—
971C42—22no—
972C42—862no—
973C42—862no—
974C42—862no—
975C23—22no—
976C23—22no—
977C23—21no—
978C23—21no—
979C23—22no—
980C23—22no—
981C23—432no—
982C23—432no—
983C23—432no—
984C23—432no—
985C23—432no—
986C23—432no—
987C23—4316no—
988C23—432no—
989C23—868no—
990C23—862no—
991C23—862no—
992C23—862no—
993C23—862no—
994C23—861no—
995C23—861no—
996C23—862no—
997C23—862no—
998C23—1724no—
999C23—1728no—
1000C23—1728no—
1001C23—1724no—
1002C23—1728no—
1003C23—1724no—
1004C23—1728no—
1005C23—1724no—
1006C23C2×D4×D4312yes—
1007C23C2×Q8×D4312yes—
1008C23C2×Q8×D4312yes—
1009C23#41×D4312yes—
1010C23C24×D4311yescharacteristic
1011Q8—44no—
1012Q8—1724no—
1013Q8—1728no—
1014D4—28no—
1015D4—868no—
1016D4—868no—
1017D4—868no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—44no—
1039C2×C4—44no—
1040C2×C4—84no—
1041C2×C4—432no—
1042C2×C4—434no—
1043C2×C4—432no—
1044C2×C4—432no—
1045C2×C4—868no—
1046C2×C4—868no—
1047C2×C4—868no—
1048C2×C4—868no—
1049C2×C4—861no—
1050C2×C4—861no—
1051C2×C4—862no—
1052C2×C4—861no—
1053C2×C4—862no—
1054C2×C4—861no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—862no—
1062C2×C4—862no—
1063C2×C4—862no—
1064C2×C4—862no—
1065C2×C4—862no—
1066C2×C4—862no—
1067C2×C4—862no—
1068C2×C4—3444no—
1069C2×C4—1724no—
1070C2×C4—1724no—
1071C2×C4—1724no—
1072C2×C4—1724no—
1073C2×C4—1724no—
1074C2×C4—1728no—
1075C2×C4—1728no—
1076C2×C4—1724no—
1077C2×C4—1724no—
1078C2×C4C2×D4×D4312yes—
1079C2×C4C2×D4×D4312yes—
1080C2×C4C2×Q8×D4312yes—
1081C22—24no—
1082C22—22no—
1083C22—24no—
1084C22—22no—
1085C22—22no—
1086C22—24no—
1087C22—41no—
1088C22—42no—
1089C22—41no—
1090C22—434no—
1091C22—434no—
1092C22—864no—
1093C22—864no—
1094C22—862no—
1095C22—862no—
1096C22—864no—
1097C22—864no—
1098C22—862no—
1099C22—862no—
1100C22—862no—
1101C22—864no—
1102C22—17216no—
1103C22—17216no—
1104C22—1721no—
1105C22—1722no—
1106C22—1721no—
1107C22C22⋊Q8×D4314yes—
1108C22C22×D4×D4311yescharacteristic
1109C22C22×Q8×D4311yescharacteristic
1110C22C2×#41×D4311yescharacteristic
1111C22H(5,𝔽2)×D4312yes—
1112C22#1458373512yes—
1113C4—22no—
1114C4—22no—
1115C4—22no—
1116C4—41no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—41no—
1121C4—42no—
1122C4—434no—
1123C4—862no—
1124C4—862no—
1125C4—1721no—
1126C4—1722no—
1127C4—1722no—
1128C4—1722no—
1129C4—1721no—
1130C4—1722no—
1131C2—24no—
1132C2—42no—
1133C2—864no—
1134C2—864no—
1135C2—1722no—
1136C2C2×C22⋊Q8×D4311yescharacteristic
1137C2#534×D4311yescharacteristic
1138C2#1914792211yescharacteristic
1139C2#1914839412yes—
1140C2#1914842612yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2564C2
prime radicalC22×D4×D43C22
hypercenter#2564D43
hypocenterC43#35010
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2564

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊Q8×D43C2semidirect
3. #19142930C2semidirect
4. #19142881C2semidirect
5. #19140409C2semidirect
6. #19140407C2semidirect
7. #19140401C2semidirect
8. #19140399C2semidirect
9. #19139946C2semidirect
10. #19139940C2semidirect
11. #19139777C2semidirect
12. #19139775C2semidirect
13. #19139771C2semidirect
14. #19138907C2semidirect
15. #19138905C2semidirect
16. #19138045C2semidirect
17. #19138043C2semidirect
18. #19137955C2semidirect
19. #19137953C2semidirect
20. #19137208C2semidirect
22. C2×#14582758C2semidirect
23. C43×#2564C2semidirect
24. C22×Q8×D43C22semidirect
29. C2×#13063304C22semidirect
31. C2×#13063303C22semidirect
32. C2×#13063302C22semidirect
33. C2×#13063302C22semidirect
44. C22×Dic43⋊C4C22semidirect
46. C2×C4⋊C4×D43C22semidirect
47. C2×C4⋊C4×D43C22semidirect
53. #14582839C22semidirect
54. #14582838C22semidirect
55. #14582837C22semidirect
56. #14582836C22semidirect
57. #14582835C22semidirect
58. #14582834C22semidirect
59. #14582833C22semidirect
60. #14582833C22semidirect
61. #14582831C22semidirect
62. #14582830C22semidirect
63. #14582823C22semidirect
64. #14582822C22semidirect
65. #14582822C22semidirect
66. #14582821C22semidirect
67. #14582820C22semidirect
68. #14582819C22semidirect
69. #14582818C22semidirect
70. #14582812C22semidirect
71. #14582811C22semidirect
72. #14582810C22semidirect
73. #14582803C22semidirect
74. #14582803C22semidirect
75. #14582796C22semidirect
76. #14582794C22semidirect
77. #14582784C22semidirect
78. #14582783C22semidirect
79. #14582780C22semidirect
89. #14582773C22semidirect
90. #14582773C22semidirect
91. #14582773C22semidirect
92. #14582772C22semidirect
95. #14582770C22semidirect
96. #14582770C22semidirect
97. #14582770C22semidirect
100. #14582759C22semidirect
104. #14582758C22semidirect
105. #14582758C22semidirect
106. #14582758C22semidirect
107. #14582758C22semidirect
108. #14582757C22semidirect
109. #14582757C22semidirect
110. #14582757C22semidirect
113. C2×C43⋊#95C22semidirect
114. C2×C22⋊Q8×C43C22semidirect
116. C43×#400C22semidirect
117. C43×#399C22semidirect
118. C43×#395C22semidirect
119. C43×#393C22semidirect
120. C43×#387C22semidirect
122. C43×#385C22semidirect
123. C43×#380C22semidirect
124. C2×#95×C43C22semidirect
136. C2×D4×D43Q8semidirect
268. C23×D43C2×Q8semidirect
277. C2×D4×C43C2×Q8semidirect
299. C2×C22⋊D43C2×Q8semidirect
347. C2×C4×D43C2×Q8semidirect
432. C22×D43C22⋊Q8semidirect
574. #2564D43semidirect
606. C2×C22⋊Q8C2×D43semidirect
628. #400C2×D43semidirect
632. #399C2×D43semidirect
644. #395C2×D43semidirect
648. #393C2×D43semidirect
656. #387C2×D43semidirect
676. #385C2×D43semidirect
690. #380C2×D43semidirect
694. C2×#95C2×D43semidirect
695. C43#35010semidirect
864. C2×D4Q8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×C4×D4×D432
#191429302
#191428812
#191404092
#191404072
#191404012
#191403992
#191399462
#191399402
#191397772
#191397752
#191397712
#191389072
#191389052
#191380452
#191380432
#191379552
#191379532
#191372082
#191371692
C2×#145827582
C43×#25642
#3501043