Finite Group Databasebeta

← #34021808

Subgroups — #34021808

Order 18688.

906 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989593C211yesmaximal, characteristic
2C2×#17989551C211yesmaximal, characteristic
3#22625991C211yesmaximal, characteristic, complemented
4#22625990C211yesmaximal, characteristic, complemented
5#22625989C211yesmaximal, characteristic, complemented
6#22625988C211yesmaximal, characteristic, complemented
7#22625987C211yesmaximal, characteristic, complemented
8#22625986C211yesmaximal, characteristic, complemented
9#22625985C211yesmaximal, characteristic, complemented
10#22625984C211yesmaximal, characteristic, complemented
11#22625597C211yesmaximal, characteristic
12#22625597C211yesmaximal, characteristic
13#22625594C211yesmaximal, characteristic
14C2×#17989453C211yesmaximal, characteristic
15#22612333C211yesmaximal, characteristic
16C22×#11924037C2211yescharacteristic
17C22×#11924037C2211yescharacteristic
18C23×#10596833C2211yescharacteristic
19C23×#10596833C2211yescharacteristic
20#17989593—24no—
21C2×#14556658C2211yescharacteristic
22C2×#14556658C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×C4⋊#10596833C2211yescharacteristic
25#17989551—24no—
26C2×#14556646C2211yescharacteristic
27C2×#14556646C2211yescharacteristic
28C2×C4×#10596833C2211yescharacteristic
29C2×C4×#10596833C2211yescharacteristic
30#17989453C2211yescharacteristic
31#17989453C2211yescharacteristic
32#17989453C2211yescharacteristic
33#17989453C2211yescharacteristic
34#17989453C2211yescharacteristic
35#17989453C2211yescharacteristic
36#17989453C2211yescharacteristic
37#17989453C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44#17989453C2211yescharacteristic
45#17989453C2211yescharacteristic
46C2×#14556547C2211yescharacteristic
47C2×#14556547C2211yescharacteristic
48C22×C4×Dic73C2211yescharacteristic
49#17988456C411yescharacteristic
50#17988456C411yescharacteristic
51#17988451C411yescharacteristic
52#17988451C411yescharacteristic
53#17988447C411yescharacteristic
54#17988445C411yescharacteristic
55#17988445C411yescharacteristic
56C4⋊C4×Dic73C2211yescharacteristic
57C4⋊C4×Dic73C2211yescharacteristic
58#17988438C2211yescharacteristic
59#17988438C2211yescharacteristic
60#380×C73C411yescharacteristic
61C2×#11924037—22no—
62C2×#11924037—22no—
63C2×#11924037—22no—
64C2×#11924037—22no—
65C2×#11924037—22no—
66C2×#11924037D414yes—
67C22×#10596833—22no—
68C22×#10596833—22no—
69C22×#10596833—22no—
70C22×#10596833—22no—
71C22×#10596833—22no—
72C22×#10596833Q814yes—
73C22×#10596833C2311yescharacteristic
74C22×#10596833C2311yescharacteristic
75C22×#10596833C2311yescharacteristic
76C22×#10596833C2311yescharacteristic
77C22×#10596833C2311yescharacteristic
78C22×#10596833C2311yescharacteristic
79C22×#10596833C2311yescharacteristic
80C22×#10596833C2311yescharacteristic
81#14556658—22no—
82#14556658—22no—
83C4⋊#10596833—22no—
84C4⋊#10596833—22no—
85#14556646—22no—
86#14556646—22no—
87C4×#10596833—22no—
88C4×#10596833—22no—
89C23×Dic73C2×C411yescharacteristic
90C23×Dic73C2311yescharacteristic
91#14556547—22no—
92#14556547—22no—
93#14556547—22no—
94#14556547—22no—
95C2×C4⋊Dic73C2×C411yescharacteristic
96C2×C4⋊Dic73C2×C411yescharacteristic
97C2×#11924007C2×C411yescharacteristic
98C2×#11924007C2×C411yescharacteristic
99C2×#11924007C2×C411yescharacteristic
100C2×#11924007C2×C411yescharacteristic
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×#11924007C2×C411yescharacteristic
104C2×#11924007C2×C411yescharacteristic
105C2×C22⋊Dic73C2×C411yescharacteristic
106C2×C22⋊Dic73C2×C411yescharacteristic
107C2×C4×Dic73—22no—
108C2×C4×Dic73—22no—
109C2×C4×Dic73C2×C411yescharacteristic
110C2×C4×Dic73C2×C411yescharacteristic
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C2×C4×Dic73C2311yescharacteristic
114C2×C4×Dic73C2311yescharacteristic
115C2×C4×Dic73C2311yescharacteristic
116C2×C4×Dic73C2311yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123C23×C4×C73C2×C411yescharacteristic
124C2×C4⋊C4×C73C2×C411yescharacteristic
125C2×C4⋊C4×C73C2×C411yescharacteristic
126C2×C22⋊C4×C73C2×C411yescharacteristic
127C2×C22⋊C4×C73C2×C411yescharacteristic
128#95×C73C2×C411yescharacteristic
129#95×C73C2×C411yescharacteristic
130#11924037—28no—
131#11924037—44no—
132C2×#10596833—28no—
133C2×#10596833—21no—
134C2×#10596833—21no—
135C2×#10596833—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—44no—
154C2×#10596833C2×D412yes—
155C2×#10596833C2×D412yes—
156C2×#10596833C2×Q812yes—
157C2×#10596833C2×Q812yes—
158C22×Dic73—22no—
159C22×Dic73—22no—
160C22×Dic73—41no—
161C22×Dic73C22×C411yescharacteristic
162C22×Dic73C22×C411yescharacteristic
163C22×Dic73C22×C411yescharacteristic
164C22×Dic73C22×C411yescharacteristic
165C22×Dic73C22×C411yescharacteristic
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C2×D412yes—
169C22×Dic73C2×Q812yes—
170C22×Dic73#4112yes—
171C22×Dic73#4112yes—
172C22×Dic73#4112yes—
173C22×Dic73#4112yes—
174C22×Dic73C2411yescharacteristic
175C4⋊Dic73—22no—
176C4⋊Dic73—41no—
177#11924007—22no—
178#11924007—22no—
179#11924007—22no—
180#11924007—22no—
181#11924007—22no—
182#11924007—22no—
183#11924007—41no—
184#11924007—41no—
185C22⋊Dic73—22no—
186C22⋊Dic73—22no—
187C4×Dic73—22no—
188C4×Dic73—22no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C24×C73C22×C411yescharacteristic
202C22×C4×C73—22no—
203C22×C4×C73—22no—
204C22×C4×C73—41no—
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C22×C411yescharacteristic
208C22×C4×C73C22×C411yescharacteristic
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C4⋊C4×C73—22no—
212C4⋊C4×C73—41no—
213C22⋊C4×C73—22no—
214C22⋊C4×C73—22no—
215C23×C73—21no—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73#11712yes—
220C23×C73C4×D412yes—
221C23×C73C4×Q812yes—
222C23×C73C23×C411yescharacteristic
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—44no—
241C2×C4×C73#13112yes—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—44no—
260C2×Dic73#11712yes—
261C2×Dic73C4×D412yes—
262C2×Dic73C4×Q812yes—
263C2×Dic73C22⋊Q814yes—
264C2×Dic73#12314yes—
265C2×Dic73#12514yes—
266C2×Dic73#12614yes—
267C2×Dic73#13112yes—
268C2×Dic73C22×D411yescharacteristic
269C2×Dic73C22×Q811yescharacteristic
270C2×Dic73C2×#4111yescharacteristic
271C2×Dic73C2×#4111yescharacteristic
272C2×Dic73C2×#4111yescharacteristic
273C2×Dic73C2×#4111yescharacteristic
274#10596833—22no—
275#10596833—22no—
276#10596833—22no—
277#10596833—22no—
278#10596833—41no—
279#10596833—41no—
280#10596833—41no—
281#10596833—41no—
282C22×C73—22no—
283C22×C73—22no—
284C22×C73—22no—
285C22×C73—22no—
286C22×C73—22no—
287C22×C73—22no—
288C22×C73#38714yes—
289C22×C73C2×#11711yescharacteristic
290C22×C73C2×C4×D411yescharacteristic
291C22×C73C2×C4×Q811yescharacteristic
292C22×C73C2×#13111yescharacteristic
293C22×C73C2×#13111yescharacteristic
294C22×C73#56811yescharacteristic
295C22×C73#56811yescharacteristic
296C4×C73—22no—
297C4×C73—41no—
298C4×C73—41no—
299C4×C73—41no—
300C4×C73—41no—
301C4×C73—41no—
302Dic73—22no—
303Dic73—41no—
304Dic73—41no—
305Dic73—41no—
306Dic73—41no—
307Dic73—41no—
308Dic73#38714yes—
309Dic73C2×C22⋊Q811yescharacteristic
310Dic73C2×#12311yescharacteristic
311Dic73C2×#12511yescharacteristic
312Dic73C2×#12611yescharacteristic
313#21026—731nomaximal, Sylow
314C2×C73—24no—
315C2×C73C2×#38711yescharacteristic
316C2×C73#292411yescharacteristic
317C2×C73#292411yescharacteristic
318C2×C73#293511yescharacteristic
319C2×C73#293511yescharacteristic
320C2×C73#296011yescharacteristic
321C2×C73#296111yescharacteristic
322C2×#424—731no—
323C2×#405—731no—
324#2285—731no—
325#1917—731no—
326#1917—731no—
327#1917—731no—
328#1917—731no—
329#1916—731no—
330#1916—731no—
331#1916—731no—
332#1916—731no—
333#1729—731no—
334#1729—731no—
335#1728—731no—
336C2×#336—731no—
337C73#2102611yescharacteristic, complemented, Sylow
338C22×M16—731no—
339C22×M16—731no—
340C23×C8—731no—
341C23×C8—731no—
342C2×#117—731no—
343C2×#117—731no—
344C22×C42—731no—
345#424—1464no—
346C2×C4⋊C8—731no—
347C2×C4⋊C8—731no—
348C2×C4⋊C8—731no—
349C2×C4⋊C8—731no—
350#405—1464no—
351C2×#97—731no—
352C2×#97—731no—
353C2×C4×C8—731no—
354C2×C4×C8—731no—
355#384—731no—
356#384—731no—
357#382—731no—
358#382—731no—
359#380—731no—
360#380—731no—
361#380—731no—
362#380#6440811yescharacteristic
363C4×C4⋊C4—731no—
364C4×C4⋊C4—731no—
365C4×C4⋊C4—731no—
366C4×C4⋊C4—731no—
367#336—731no—
368#336—731no—
369#336—731no—
370#336—731no—
371#336—731no—
372#336—731no—
373#336—731no—
374#336—731no—
375#336—731no—
376#336—731no—
377#336—731no—
378#336—731no—
379#336—731no—
380#336—731no—
381#336—731no—
382#336—731no—
383C23×C4—731no—
384C23×C4—731no—
385C23×C4C2×#6440811yescharacteristic
386C2×M16—734no—
387C2×M16—1462no—
388C2×M16—1462no—
389C2×M16—1462no—
390C2×M16—1462no—
391C2×M16—1462no—
392C22×C8—734no—
393C22×C8—731no—
394C22×C8—731no—
395C22×C8—731no—
396C22×C8—731no—
397C22×C8—731no—
398C22×C8—731no—
399C22×C8—731no—
400C22×C8—731no—
401C22×C8—1462no—
402C22×C8—1462no—
403C22×C8—1462no—
404C22×C8—1462no—
405C22×C8—1462no—
406#117—1462no—
407#117—1462no—
408#117—1462no—
409#117—1462no—
410C2×C4⋊C4—731no—
411C2×C4⋊C4—731no—
412C2×C4⋊C4—731no—
413C2×C4⋊C4—731no—
414C2×C4⋊C4—731no—
415C2×C4⋊C4—731no—
416C2×C4⋊C4—731no—
417C2×C4⋊C4—731no—
418C2×C4⋊C4—731no—
419C2×C4⋊C4—731no—
420C2×C4⋊C4C2×#6440811yescharacteristic
421C2×C4⋊C4C2×#6440811yescharacteristic
422C2×C22⋊C4—731no—
423C2×C22⋊C4—731no—
424C2×C22⋊C4C2×#6440811yescharacteristic
425C2×C22⋊C4C2×#6440811yescharacteristic
426C2×C42—731no—
427C2×C42—731no—
428C2×C42—731no—
429C2×C42—731no—
430C2×C42—731no—
431C2×C42—731no—
432C2×C42—731no—
433C2×C42—731no—
434C2×C42—1462no—
435C2×C42—1462no—
436C4⋊C8—1462no—
437C4⋊C8—1462no—
438C4⋊C8—1462no—
439C4⋊C8—1462no—
440#97—1462no—
441#97—1462no—
442C4×C8—1462no—
443C4×C8—1462no—
444#95—731no—
445#95—731no—
446#95—731no—
447#95—731no—
448#95—731no—
449#95—731no—
450#95C2×#6440811yescharacteristic
451#95C2×#6440811yescharacteristic
452C24C22×#6440811yescharacteristic
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—41no—
456C22×C4—2921no—
457C22×C4—732no—
458C22×C4—732no—
459C22×C4—731no—
460C22×C4—731no—
461C22×C4—732no—
462C22×C4—732no—
463C22×C4—732no—
464C22×C4—732no—
465C22×C4—731no—
466C22×C4—731no—
467C22×C4—731no—
468C22×C4—731no—
469C22×C4—731no—
470C22×C4—731no—
471C22×C4—1462no—
472C22×C4—1462no—
473C22×C4C22×#6440811yescharacteristic
474C22×C4C22×#6440811yescharacteristic
475C22×C4C22×#6440811yescharacteristic
476C22×C4C22×#6440811yescharacteristic
477C22×C4C22×#6440811yescharacteristic
478C22×C4C22×#6440811yescharacteristic
479M16—2924no—
480M16—1468no—
481C2×C8—2924no—
482C2×C8—732no—
483C2×C8—732no—
484C2×C8—732no—
485C2×C8—732no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8—1461no—
494C2×C8—1461no—
495C2×C8—1461no—
496C2×C8—1461no—
497C2×C8—1461no—
498C2×C8—1461no—
499C2×C8—1461no—
500C2×C8—1461no—
501C2×C8—1461no—
502C2×C8—1468no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C4⋊C4—22no—
508C4⋊C4—41no—
509C4⋊C4—2921no—
510C4⋊C4—2921no—
511C4⋊C4—2921no—
512C4⋊C4—1462no—
513C4⋊C4—1462no—
514C4⋊C4—1462no—
515C4⋊C4—1462no—
516C4⋊C4—1462no—
517C4⋊C4—1462no—
518C4⋊C4—1462no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—1462no—
522C22⋊C4—1462no—
523C42—1461no—
524C42—1461no—
525C42—1461no—
526C42—1461no—
527C42—1461no—
528C42—1461no—
529C42—1462no—
530C42—1461no—
531C42—1461no—
532C42—1462no—
533C42—1461no—
534C42—1461no—
535C42—1461no—
536C42—1461no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23#1455667012yes—
542C23D4×#6440812yes—
543C23Q8×#6440812yes—
544C23C23×#6440811yescharacteristic
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—44no—
563C2×C4—2924no—
564C2×C4—731no—
565C2×C4—731no—
566C2×C4—732no—
567C2×C4—731no—
568C2×C4—731no—
569C2×C4—732no—
570C2×C4—731no—
571C2×C4—731no—
572C2×C4—732no—
573C2×C4—734no—
574C2×C4—734no—
575C2×C4—734no—
576C2×C4—734no—
577C2×C4—732no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4—1461no—
581C2×C4—1461no—
582C2×C4—1461no—
583C2×C4—1461no—
584C2×C4—1461no—
585C2×C4—1461no—
586C2×C4—1461no—
587C2×C4—1461no—
588C2×C4—1461no—
589C2×C4—1461no—
590C2×C4—1461no—
591C2×C4—1461no—
592C2×C4—1461no—
593C2×C4—1461no—
594C2×C4—1461no—
595C2×C4#1455667812yes—
596C8—2921no—
597C8—2921no—
598C8—2921no—
599C8—2921no—
600C8—1462no—
601C8—1462no—
602C8—1462no—
603C8—1462no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22#1798953614yes—
611C22C2×#1455667011yescharacteristic
612C22C2×D4×#6440811yescharacteristic
613C22C2×Q8×#6440811yescharacteristic
614C22C2×#1455667811yescharacteristic
615C22D73⋊#13111yescharacteristic
616C22#1798966511yescharacteristic
617C22#1798966611yescharacteristic
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—2921no—
625C4—2921no—
626C4—2921no—
627C4—2921no—
628C4—2921no—
629C4—731no—
630C4—731no—
631C4—731no—
632C4—731no—
633C4—734no—
634C4—1462no—
635C2—24no—
636C2C2×#1798953611yescharacteristic
637C2#2262662011yescharacteristic
638C2#2262662311yescharacteristic
639C2#2262667311yescharacteristic
640C2#2262667511yescharacteristic
641C2#2262671911yescharacteristic
642C2#2262672211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#380×C73C4
prime radicalC24×C73C22×C4
cosocleC22×Dic73C24
hypercenter#380#64408
hypocenterC73#21026
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #22625991C2semidirect
4. #22625990C2semidirect
5. #22625989C2semidirect
6. #22625988C2semidirect
7. #22625987C2semidirect
8. #22625986C2semidirect
9. #22625985C2semidirect
10. #22625984C2semidirect
337. C73#21026semidirect

Maximal subgroups

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

subgroupindex
C2×#179895932
C2×#179895512
#226259912
#226259902
#226259892
#226259882
#226259872
#226259862
#226259852
#226259842
#226255972
#226255942
C2×#179894532
#226123332
#2102673