Finite Group Databasebeta

← #34026733

Subgroups — #34026733

Order 18688.

808 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989612C211yesmaximal, characteristic
2C2×#17989605C211yesmaximal, characteristic
3#22626033C211yesmaximal, characteristic, complemented
4#22626029C211yesmaximal, characteristic, complemented
5#22625991C211yesmaximal, characteristic, complemented
6#22625987C211yesmaximal, characteristic, complemented
7#22625986C211yesmaximal, characteristic, complemented
8#22625985C211yesmaximal, characteristic, complemented
9#22625825C211yesmaximal, characteristic
10#22625823C211yesmaximal, characteristic
11#22625790C211yesmaximal, characteristic
12#22625730C211yesmaximal, characteristic, complemented
13#22625723C211yesmaximal, characteristic, complemented
14#22625660C211yesmaximal, characteristic
15#22612412C211yesmaximal, characteristic
16#17989612—24no—
17#17989605—24no—
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×#14556658C2211yescharacteristic
21C2×#14556658C2211yescharacteristic
22C2×C4⋊#10596833C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×#14556648C2211yescharacteristic
25C2×#14556648C2211yescharacteristic
26C2×#14556648C2211yescharacteristic
27C2×#14556648C2211yescharacteristic
28C2×#14556646C2211yescharacteristic
29C2×#14556646C2211yescharacteristic
30C2×C4×#10596833C2211yescharacteristic
31C2×C4×#10596833C2211yescharacteristic
32C2×C4×#10596833C2211yescharacteristic
33C2×C4×#10596833C2211yescharacteristic
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×#14556549C2211yescharacteristic
47C2×#14556549C2211yescharacteristic
48C2×C42×D73C2211yescharacteristic
49#17988486C411yescharacteristic
50#17988485C411yescharacteristic
51#17988483C411yescharacteristic
52#17988461C411yescharacteristic
53#17988461C411yescharacteristic
54#17988458C411yescharacteristic
55#17988458C411yescharacteristic
56C4⋊C4×Dic73C2211yescharacteristic
57C4⋊C4×Dic73C2211yescharacteristic
58#17988438C2211yescharacteristic
59#17988438C2211yescharacteristic
60#389×C73C411yescharacteristic
61C22×#10596833C2311yescharacteristic
62C22×#10596833C2311yescharacteristic
63C22×#10596833C2311yescharacteristic
64C22×#10596833C2311yescharacteristic
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69#14556658—22no—
70#14556658—22no—
71#14556658—22no—
72#14556658—22no—
73C4⋊#10596833—22no—
74C4⋊#10596833—22no—
75#14556648—22no—
76#14556648—22no—
77#14556648—22no—
78#14556648D414yes—
79#14556646—22no—
80#14556646—22no—
81C4×#10596833—22no—
82C4×#10596833—22no—
83C4×#10596833—22no—
84C4×#10596833—22no—
85C22×C4×D73C2×C411yescharacteristic
86C22×C4×D73C2×C411yescharacteristic
87C22×C4×D73C2311yescharacteristic
88#14556549—22no—
89#14556549—22no—
90#14556549—22no—
91#14556549—22no—
92C2×C4⋊Dic73C2×C411yescharacteristic
93C2×C4⋊Dic73C2×C411yescharacteristic
94C2×C4⋊Dic73C2×C411yescharacteristic
95C2×C4⋊Dic73C2×C411yescharacteristic
96C2×#11924007C2×C411yescharacteristic
97C2×#11924007C2×C411yescharacteristic
98C2×#11924007C2×C411yescharacteristic
99C2×#11924007C2×C411yescharacteristic
100C2×#11924005C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×#11924005C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×C4×Dic73C2×C411yescharacteristic
105C2×C4×Dic73C2311yescharacteristic
106C2×C4×Dic73C2311yescharacteristic
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109C2×C4×Dic73C2311yescharacteristic
110C2×C4×Dic73C2311yescharacteristic
111C42×D73—22no—
112C42×D73—22no—
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119C2×C4⋊C4×C73C2×C411yescharacteristic
120C2×C4⋊C4×C73C2×C411yescharacteristic
121C2×C4⋊C4×C73C2×C411yescharacteristic
122C2×C4⋊C4×C73C2×C411yescharacteristic
123C2×C42×C73C2×C411yescharacteristic
124#95×C73C2×C411yescharacteristic
125#95×C73C2×C411yescharacteristic
126C2×#10596833—21no—
127C2×#10596833—21no—
128C2×#10596833—21no—
129C2×#10596833—21no—
130C2×#10596833—21no—
131C2×#10596833—21no—
132C2×#10596833—21no—
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×#10596833C2×D412yes—
149C2×#10596833C2×D412yes—
150C23×D73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C22×C411yescharacteristic
153C22×Dic73C22×C411yescharacteristic
154C22×Dic73C22×C411yescharacteristic
155C22×Dic73C22×C411yescharacteristic
156C22×Dic73C22×C411yescharacteristic
157C22×Dic73C2411yescharacteristic
158C2×C4×D73—22no—
159C2×C4×D73—22no—
160C2×C4×D73—22no—
161C2×C4×D73—21no—
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—22no—
166C2×C4×D73—22no—
167C2×C4×D73—41no—
168C2×C4×D73C2×D412yes—
169C2×C4×D73#4112yes—
170C4⋊Dic73—22no—
171C4⋊Dic73—22no—
172C4⋊Dic73—22no—
173C4⋊Dic73—22no—
174#11924007—22no—
175#11924007—22no—
176#11924007—22no—
177#11924007—22no—
178#11924005—22no—
179#11924005—22no—
180#11924005—22no—
181#11924005—22no—
182C4×Dic73—22no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73#4112yes—
194C4×Dic73#4112yes—
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C22×C411yescharacteristic
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200C22×C4×C73C22×C411yescharacteristic
201C22×C4×C73C22×C411yescharacteristic
202C4⋊C4×C73—22no—
203C4⋊C4×C73—22no—
204C4⋊C4×C73—41no—
205C4⋊C4×C73—41no—
206C42×C73—22no—
207C23×C73C23×C411yescharacteristic
208C22×D73—21no—
209C22×D73—21no—
210C22×D73—21no—
211C22×D73—21no—
212C22×D73—21no—
213C22×D73—21no—
214C22×D73C4×D412yes—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
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#11712yes—
234C2×C4×C73C4×D412yes—
235C2×C4×C73#13112yes—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
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#11712yes—
252C2×Dic73#13112yes—
253C2×Dic73#13112yes—
254C2×Dic73C22×D411yescharacteristic
255C2×Dic73C2×#4111yescharacteristic
256C2×Dic73C2×#4111yescharacteristic
257C2×Dic73C2×#4111yescharacteristic
258C2×Dic732−1+411yescharacteristic
259C2×Dic732−1+411yescharacteristic
260C4×D73—28no—
261C4×D73—22no—
262C4×D73—22no—
263C4×D73—22no—
264C4×D73—22no—
265C4×D73—44no—
266#10596833—22no—
267#10596833—22no—
268#10596833—41no—
269#10596833—41no—
270#10596833—41no—
271#10596833—41no—
272#10596833—41no—
273#10596833—41no—
274C22×C73C2×#11711yescharacteristic
275C22×C73C2×C4×D411yescharacteristic
276C22×C73#51911yescharacteristic
277C22×C73C2×#13111yescharacteristic
278C22×C73C2×#13111yescharacteristic
279C22×C73C2×#13111yescharacteristic
280C22×C73#56811yescharacteristic
281C2×D73—22no—
282C2×D73—22no—
283C2×D73—22no—
284C2×D73—41no—
285C2×D73—41no—
286C2×D73—41no—
287C2×D73—41no—
288C4×C73—22no—
289C4×C73—22no—
290C4×C73—22no—
291C4×C73—41no—
292C4×C73—41no—
293C4×C73—41no—
294C4×C73—41no—
295Dic73—22no—
296Dic73—22no—
297Dic73—22no—
298Dic73—41no—
299Dic73—41no—
300Dic73—41no—
301Dic73#54711yescharacteristic
302Dic73#54711yescharacteristic
303Dic73#55211yescharacteristic
304Dic73#55211yescharacteristic
305#22604—731nomaximal, Sylow
306C2×C73#234411yescharacteristic
307C2×C73#292211yescharacteristic
308C2×C73#292511yescharacteristic
309C2×C73#292911yescharacteristic
310C2×C73#293311yescharacteristic
311C2×C73#298511yescharacteristic
312C2×C73#298611yescharacteristic
313D73—42no—
314C2×#433—731no—
315C2×#431—731no—
316#2296—731no—
317#1940—731no—
318#1939—731no—
319#1917—731no—
320#1916—731no—
321#1916—731no—
322#1916—731no—
323#1818—731no—
324#1817—731no—
325#1798—731no—
326#1771—731no—
327C8×C4⋊C4—731no—
328#1750—731no—
329C73#2260411yescharacteristic, complemented, Sylow
330C2×#117—731no—
331C2×#117—731no—
332C22×C42—731no—
333#433—1464no—
334#431—1464no—
335C2×C4⋊C8—731no—
336C2×C4⋊C8—731no—
337C2×C4⋊C8—731no—
338C2×C4⋊C8—731no—
339C2×C4⋊C8—731no—
340C2×C4⋊C8—731no—
341C2×C22⋊C8—731no—
342C2×C22⋊C8—731no—
343C2×C22⋊C8—731no—
344C2×C22⋊C8—731no—
345C2×#97—731no—
346C2×#97—731no—
347C2×C4×C8—731no—
348C2×C4×C8—731no—
349C2×C4×C8—731no—
350C2×C4×C8—731no—
351#389—731no—
352#389—731no—
353#389—731no—
354#389#6440811yescharacteristic
355#385—731no—
356#385—731no—
357#385—731no—
358#385—731no—
359C4×C4⋊C4—731no—
360C4×C4⋊C4—731no—
361C4×C4⋊C4—731no—
362C4×C4⋊C4—731no—
363#336—731no—
364#336—731no—
365#336—731no—
366#336—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—
375C23×C4—731no—
376C23×C4—731no—
377C23×C4—731no—
378C22×C8—731no—
379C22×C8—731no—
380C22×C8—731no—
381C22×C8—731no—
382C22×C8—731no—
383C22×C8—731no—
384C22×C8—731no—
385C22×C8—731no—
386#117—1462no—
387#117—1462no—
388#117—1462no—
389#117—1462no—
390C2×C4⋊C4—731no—
391C2×C4⋊C4—731no—
392C2×C4⋊C4—731no—
393C2×C4⋊C4—731no—
394C2×C4⋊C4—731no—
395C2×C4⋊C4—731no—
396C2×C4⋊C4—731no—
397C2×C4⋊C4—731no—
398C2×C4⋊C4C2×#6440811yescharacteristic
399C2×C4⋊C4C2×#6440811yescharacteristic
400C2×C4⋊C4C2×#6440811yescharacteristic
401C2×C4⋊C4C2×#6440811yescharacteristic
402C2×C22⋊C4—731no—
403C2×C22⋊C4—731no—
404C2×C22⋊C4—731no—
405C2×C22⋊C4—731no—
406C2×C42—731no—
407C2×C42—731no—
408C2×C42—731no—
409C2×C42—731no—
410C2×C42—731no—
411C2×C42—731no—
412C2×C42—731no—
413C2×C42—1462no—
414C2×C42—1462no—
415C2×C42C2×#6440811yescharacteristic
416C4⋊C8—1462no—
417C4⋊C8—1462no—
418C4⋊C8—1462no—
419C4⋊C8—1462no—
420C4⋊C8—1462no—
421C4⋊C8—1462no—
422C22⋊C8—734no—
423C22⋊C8—1462no—
424C22⋊C8—1462no—
425C22⋊C8—1462no—
426#97—1462no—
427#97—1462no—
428C4×C8—1462no—
429C4×C8—1462no—
430C4×C8—1462no—
431C4×C8—1462no—
432#95—731no—
433#95—731no—
434#95—731no—
435#95—731no—
436#95—731no—
437#95—731no—
438#95C2×#6440811yescharacteristic
439#95C2×#6440811yescharacteristic
440C24—731no—
441C22×C4—2921no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—731no—
446C22×C4—732no—
447C22×C4—732no—
448C22×C4—731no—
449C22×C4—731no—
450C22×C4—731no—
451C22×C4—1462no—
452C22×C4—1462no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4—1461no—
457C22×C4—1462no—
458C22×C4—1462no—
459C22×C4—1462no—
460C22×C4C22×#6440811yescharacteristic
461C22×C4C22×#6440811yescharacteristic
462C22×C4C22×#6440811yescharacteristic
463C22×C4C22×#6440811yescharacteristic
464C22×C4C22×#6440811yescharacteristic
465C22×C4C22×#6440811yescharacteristic
466C22×C4C22×#6440811yescharacteristic
467C2×C8—732no—
468C2×C8—732no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8—1461no—
478C2×C8—1461no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—1462no—
496C4⋊C4—1462no—
497C4⋊C4—1462no—
498C4⋊C4—1462no—
499C4⋊C4—1462no—
500C4⋊C4—1462no—
501C4⋊C4—1462no—
502C4⋊C4—1462no—
503C22⋊C4—1462no—
504C22⋊C4—1462no—
505C22⋊C4—1462no—
506C22⋊C4—1462no—
507C42—22no—
508C42—732no—
509C42—732no—
510C42—1461no—
511C42—1461no—
512C42—1461no—
513C42—1461no—
514C42—1461no—
515C42—1461no—
516C42—1461no—
517C42—1461no—
518C42—1461no—
519C42—1461no—
520C42—1462no—
521C23—732no—
522C23—1461no—
523C23—1461no—
524C23—1461no—
525C23—1461no—
526C23—1461no—
527C23—1461no—
528C23C23×#6440811yescharacteristic
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—2924no—
548C2×C4—731no—
549C2×C4—731no—
550C2×C4—731no—
551C2×C4—731no—
552C2×C4—731no—
553C2×C4—731no—
554C2×C4—732no—
555C2×C4—732no—
556C2×C4—732no—
557C2×C4—1462no—
558C2×C4—1462no—
559C2×C4—1462no—
560C2×C4—1462no—
561C2×C4—1468no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4—1461no—
573C2×C4—1461no—
574C2×C4—1461no—
575C2×C4—1461no—
576C2×C4—1461no—
577C2×C4#1455667012yes—
578C2×C4D4×#6440812yes—
579C2×C4#1455667912yes—
580C8—2921no—
581C8—2921no—
582C8—2921no—
583C8—2921no—
584C8—2921no—
585C8—2921no—
586C8—1462no—
587C8—1462no—
588C22—2921no—
589C22—2921no—
590C22—2921no—
591C22—2921no—
592C22—1462no—
593C22—1462no—
594C22—1462no—
595C22C2×#1455667011yescharacteristic
596C22C2×D4×#6440811yescharacteristic
597C22#1798965511yescharacteristic
598C22D73⋊#13111yescharacteristic
599C22D73⋊#13111yescharacteristic
600C22C2×#1455667911yescharacteristic
601C22#1798966511yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—2921no—
610C4—2921no—
611C4—2921no—
612C4—731no—
613C4—731no—
614C4—731no—
615C4—731no—
616C4—1462no—
617C4—1462no—
618C4—1462no—
619C2—2922no—
620C2#2262643911yescharacteristic
621C2#2262661611yescharacteristic
622C2#2262662911yescharacteristic
623C2#2262664711yescharacteristic
624C2#2262666211yescharacteristic
625C2#2262683911yescharacteristic
626C2#2262684111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#389×C73C4
prime radicalC23×D73C22×C4
cosocleC22×Dic73C24
hypercenter#389#64408
hypocenterC73#22604
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #22626033C2semidirect
4. #22626029C2semidirect
5. #22625991C2semidirect
6. #22625987C2semidirect
7. #22625986C2semidirect
8. #22625985C2semidirect
12. #22625730C2semidirect
13. #22625723C2semidirect
329. C73#22604semidirect

Maximal subgroups

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

subgroupindex
C2×#179896122
C2×#179896052
#226260332
#226260292
#226259912
#226259872
#226259862
#226259852
#226258252
#226258232
#226257902
#226257302
#226257232
#226256602
#226124122
#2260473