Finite Group Databasebeta

← #34016180

Subgroups — #34016180

Order 18688.

960 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626607C211yesmaximal, characteristic
2C2×#17989607C211yesmaximal, characteristic
3#22625210C214yesmaximal
4#22625203C214yesmaximal, complemented
5#22625195C212yesmaximal, complemented
6#22625194C212yesmaximal, complemented
7C2×#17989139C211yesmaximal, characteristic
8#17989608—21no—
9#17989607—21no—
10#17989607—21no—
11#17989607C2212yes—
12#17989607C2212yes—
13#17989607C2212yes—
14#17989604—21no—
15#17989603C2212yes—
16#17989590—21no—
17C2×#14556658—21no—
18#17989557C2212yes—
19C2×C22⋊#10596833C2212yes—
20C4×#11924037—21no—
21C2×#14556646—21no—
22#17989433C2218yes—
23#17989432C2218yes—
24#17989139—21no—
25#17989139—21no—
26#17989139—21no—
27#17989139—21no—
28#17989139—21no—
29#17989139—21no—
30#17989139—21no—
31#17989139—21no—
32C2×#14556590C411yescharacteristic
33C2×#14556589C411yescharacteristic
34C2×#14556581C2212yes—
35C2×#14556570C411yescharacteristic
36C2×#14556568C2212yes—
37C2×Q8×Dic73C2211yescharacteristic
38C2×#14556556C412yes—
39C2×#14556556C2211yescharacteristic
40C2×#14556547C412yes—
41C22×C4×Dic73C2211yescharacteristic
42C2×C22⋊Q8×C73C411yescharacteristic
43C2×#11924037—22no—
44C22×#10596833—22no—
45#14556658—22no—
46#14556658—22no—
47#14556658—22no—
48C4⋊#10596833—22no—
49C22⋊#10596833—22no—
50C22⋊#10596833—22no—
51C22⋊#10596833C2314yes—
52C22⋊#10596833C2314yes—
53#14556646—22no—
54#14556646—22no—
55#14556646—22no—
56C4×#10596833—22no—
57C22×Dic146C2×C411yescharacteristic
58C22×Dic146C2×C412yes—
59C23×Dic73C2×C411yescharacteristic
60C23×Dic73C2311yescharacteristic
61#14556590—21no—
62#14556590—21no—
63#14556590—21no—
64#14556590—21no—
65#14556589—21no—
66#14556589—21no—
67#14556589—21no—
68#14556589—21no—
69#14556581—22no—
70#14556581—22no—
71#14556581—22no—
72#14556581—22no—
73#14556570—21no—
74#14556570—21no—
75#14556570—21no—
76#14556570—21no—
77#14556568—22no—
78#14556568—22no—
79#14556568—22no—
80#14556568—22no—
81Q8×Dic73—21no—
82Q8×Dic73—21no—
83Q8×Dic73—21no—
84Q8×Dic73—21no—
85#14556556—22no—
86#14556556—22no—
87#14556556—22no—
88#14556556—22no—
89#14556556—21no—
90#14556556—21no—
91#14556556—21no—
92#14556556—21no—
93#14556547—22no—
94#14556547—22no—
95#14556547—22no—
96#14556547—22no—
97C2×C4⋊Dic73C2×C411yescharacteristic
98C2×C4⋊Dic73C2312yes—
99C2×#11924007C2×C412yes—
100C2×#11924007C2×C412yes—
101C2×#11924007C2×C412yes—
102C2×#11924007C2×C412yes—
103C2×#11924007C2312yes—
104C2×C22⋊Dic73C2×C412yes—
105C2×C4×Dic73C2×C412yes—
106C2×C4×Dic73C2×C412yes—
107C2×C4×Dic73C2×C411yescharacteristic
108C2×C4×Dic73C2×C411yescharacteristic
109C2×C4×Dic73D411yescharacteristic
110C2×C4×Dic73D411yescharacteristic
111C2×C4×Dic73D411yescharacteristic
112C2×C4×Dic73D411yescharacteristic
113C2×C4×Dic73D411yescharacteristic
114C2×C4×Dic73D411yescharacteristic
115C2×C4×Dic73D411yescharacteristic
116C2×C4×Dic73D411yescharacteristic
117C2×C4×Dic73C2311yescharacteristic
118C2×C4×Dic73C2311yescharacteristic
119C22×Q8×C73C2×C411yescharacteristic
120C23×C4×C73C2×C411yescharacteristic
121C22⋊Q8×C73—21no—
122C22⋊Q8×C73—21no—
123C22⋊Q8×C73—21no—
124C22⋊Q8×C73—21no—
125C2×C4⋊C4×C73C2×C411yescharacteristic
126C2×C4⋊C4×C73C2×C412yes—
127C2×C22⋊C4×C73C2×C412yes—
128#11924037—44no—
129C2×#10596833—24no—
130C2×#10596833—24no—
131C2×#10596833—44no—
132C2×Dic146—21no—
133C2×Dic146—21no—
134C2×Dic146—22no—
135C2×Dic146—22no—
136C2×Dic146—42no—
137C2×Dic146—44no—
138C22×Dic73—24no—
139C22×Dic73—42no—
140C22×Dic73C22⋊C411yescharacteristic
141C22×Dic73C22⋊C411yescharacteristic
142C22×Dic73C22⋊C411yescharacteristic
143C22×Dic73C22⋊C411yescharacteristic
144C22×Dic73C22×C412yes—
145C22×Dic73C22×C411yescharacteristic
146C22×Dic73C22×C411yescharacteristic
147C22×Dic73C22×C411yescharacteristic
148C22×Dic73C22×C412yes—
149C22×Dic73C2×D411yescharacteristic
150C22×Dic73C2×D411yescharacteristic
151C22×Dic73C2×D411yescharacteristic
152C22×Dic73C2×D411yescharacteristic
153C22×Dic73C2411yescharacteristic
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73—22no—
157C4⋊Dic73—22no—
158#11924007—22no—
159#11924007—22no—
160#11924007—22no—
161#11924007—22no—
162#11924007—22no—
163#11924007—22no—
164#11924007—22no—
165#11924007—22no—
166#11924007—22no—
167#11924007—22no—
168C22⋊Dic73—22no—
169C22⋊Dic73—22no—
170C4×Dic73—22no—
171C4×Dic73—22no—
172C4×Dic73—22no—
173C4×Dic73—22no—
174C4×Dic73C22⋊C411yescharacteristic
175C4×Dic73C22⋊C411yescharacteristic
176C4×Dic73C22⋊C411yescharacteristic
177C4×Dic73C22⋊C411yescharacteristic
178C4×Dic73C22⋊C411yescharacteristic
179C4×Dic73C22⋊C411yescharacteristic
180C4×Dic73C22⋊C411yescharacteristic
181C4×Dic73C22⋊C411yescharacteristic
182C4×Dic73C2×D411yescharacteristic
183C4×Dic73C2×D411yescharacteristic
184C4×Dic73C2×D411yescharacteristic
185C4×Dic73C2×D411yescharacteristic
186C4×Dic73C2×D411yescharacteristic
187C4×Dic73C2×D411yescharacteristic
188C4×Dic73C2×D411yescharacteristic
189C4×Dic73C2×D411yescharacteristic
190C24×C73C22×C411yescharacteristic
191C2×Q8×C73—21no—
192C2×Q8×C73—21no—
193C2×Q8×C73—42no—
194C22×C4×C73—42no—
195C22×C4×C73C22⋊C411yescharacteristic
196C22×C4×C73C22⋊C411yescharacteristic
197C22×C4×C73C22⋊C411yescharacteristic
198C22×C4×C73C22⋊C411yescharacteristic
199C22×C4×C73C22×C412yes—
200C22×C4×C73C22×C411yescharacteristic
201C22×C4×C73C22×C411yescharacteristic
202C22×C4×C73C22×C412yes—
203C4⋊C4×C73—22no—
204C4⋊C4×C73—22no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C22⋊C4×C73—22no—
208C22⋊C4×C73—22no—
209C23×C73—22no—
210C23×C73—22no—
211C23×C73—41no—
212C23×C73C2×C22⋊C411yescharacteristic
213C23×C73C2×C22⋊C411yescharacteristic
214C23×C73C23×C411yescharacteristic
215Q8×C73—42no—
216Q8×C73—42no—
217C2×C4×C73—22no—
218C2×C4×C73—22no—
219C2×C4×C73—22no—
220C2×C4×C73—22no—
221C2×C4×C73—24no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—42no—
227C2×C4×C73C2×C22⋊C411yescharacteristic
228C2×C4×C73C2×C22⋊C411yescharacteristic
229C2×C4×C73C2×C22⋊C411yescharacteristic
230C2×C4×C73C2×C22⋊C411yescharacteristic
231C2×Dic73—22no—
232C2×Dic73—22no—
233C2×Dic73—22no—
234C2×Dic73—22no—
235C2×Dic73—22no—
236C2×Dic73—22no—
237C2×Dic73—22no—
238C2×Dic73—22no—
239C2×Dic73—22no—
240C2×Dic73—22no—
241C2×Dic73—24no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—42no—
246C2×Dic73#10114yes—
247C2×Dic73C2×C22⋊C411yescharacteristic
248C2×Dic73C2×C22⋊C411yescharacteristic
249C2×Dic73C2×C22⋊C411yescharacteristic
250C2×Dic73C2×C22⋊C411yescharacteristic
251C2×Dic73C2×C22⋊C411yescharacteristic
252C2×Dic73C2×C22⋊C411yescharacteristic
253C2×Dic73C22×D411yescharacteristic
254C2×Dic73C22×D411yescharacteristic
255Dic146—44no—
256Dic146—42no—
257Dic146—42no—
258Dic146—44no—
259#10596833—44no—
260#10596833—44no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73—21no—
266C22×C73—21no—
267C22×C73—21no—
268C22×C73—44no—
269C22×C73C2×#10112yes—
270C22×C73C22×C22⋊C411yescharacteristic
271C22×C73#56812yes—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73—21no—
275C4×C73—21no—
276C4×C73—42no—
277C4×C73—42no—
278Dic73—21no—
279Dic73—21no—
280Dic73—21no—
281Dic73—21no—
282Dic73—21no—
283Dic73—42no—
284Dic73—42no—
285Dic73#41012yes—
286Dic73C2×#10112yes—
287Dic73C2×#10112yes—
288#17404—731nomaximal, Sylow
289C2×C73—22no—
290C2×C73—22no—
291C2×C73—41no—
292C2×C73#287911yescharacteristic
293C2×C73C2×#41011yescharacteristic
294C2×C73C22×#10111yescharacteristic
295C2×#533—731no—
296#2920—731no—
297C2×#432—731no—
298#1472—734no—
299#1470—734no—
300#1467—732no—
301#1467—732no—
302C73#1740411yescharacteristic, complemented, Sylow
303#533—1461no—
304#533—1461no—
305#533—1461no—
306#533—1461no—
307#533—1461no—
308#533—1461no—
309#533—1461no—
310#533—1461no—
311C2×C4⋊Q8—731no—
312C2×C4⋊Q8—731no—
313C2×#125—732no—
314C2×C22⋊Q8—731no—
315C2×C22⋊Q8—732no—
316C2×C22⋊Q8#6440811yescharacteristic
317C2×C4×Q8—731no—
318C2×C4×Q8—731no—
319C2×C4×Q8—732no—
320C2×#117—732no—
321C22×C42—731no—
322#432—732no—
323#432—732no—
324#432—732no—
325#432—1461no—
326#432—1461no—
327#432—1461no—
328#431—732no—
329#431—1461no—
330#423—1461no—
331C2×C4⋊C8—1461no—
332#407—732no—
333C2×C22⋊C8—732no—
334C4×M16—1461no—
335C2×#97—1461no—
336#324—738no—
337#324—738no—
338C22×Q8—732no—
339C22×Q8—731no—
340C22×Q8C2×#6440811yescharacteristic
341C23×C4—731no—
342C23×C4—731no—
343C23×C4C2×#6440811yescharacteristic
344C2×M16—1462no—
345C22×C8—1462no—
346C4⋊Q8—1461no—
347C4⋊Q8—1461no—
348C4⋊Q8—1461no—
349C4⋊Q8—1461no—
350C4⋊Q8—1461no—
351C4⋊Q8—1461no—
352C4⋊Q8—1461no—
353C4⋊Q8—1461no—
354#125—1462no—
355#125—1462no—
356#125—1462no—
357#125—1462no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—1462no—
363C22⋊Q8—1462no—
364C22⋊Q8—1462no—
365C22⋊Q8—1462no—
366C22⋊Q8—1461no—
367C22⋊Q8—1461no—
368C22⋊Q8—1461no—
369C22⋊Q8—1461no—
370C4×Q8—1462no—
371C4×Q8—1462no—
372C4×Q8—1462no—
373C4×Q8—1462no—
374C4×Q8—1461no—
375C4×Q8—1461no—
376C4×Q8—1461no—
377C4×Q8—1461no—
378C4×Q8—1461no—
379C4×Q8—1461no—
380C4×Q8—1461no—
381C4×Q8—1461no—
382#117—1462no—
383#117—1462no—
384#117—1462no—
385#117—1462no—
386C2×C4⋊C4—732no—
387C2×C4⋊C4—732no—
388C2×C4⋊C4—732no—
389C2×C4⋊C4—732no—
390C2×C4⋊C4—732no—
391C2×C4⋊C4—732no—
392C2×C4⋊C4—731no—
393C2×C4⋊C4C2×#6440812yes—
394C2×C4⋊C4C2×#6440811yescharacteristic
395C2×C22⋊C4—732no—
396C2×C22⋊C4C2×#6440812yes—
397C2×C42—731no—
398C2×C42—731no—
399C2×C42—731no—
400C2×C42—731no—
401C2×C42—731no—
402C2×C42—731no—
403C2×C42—731no—
404C2×C42—731no—
405C2×C42—731no—
406C2×C42—731no—
407C2×C42—731no—
408C2×C42—731no—
409C2×C42—732no—
410C2×C42—732no—
411C4⋊C8—1462no—
412C4⋊C8—1462no—
413C4⋊C8—1462no—
414C4⋊C8—1462no—
415C22⋊C8—734no—
416C22⋊C8—734no—
417C22⋊C8—1462no—
418C22⋊C8—1462no—
419#97—1462no—
420#97—1462no—
421#97—1462no—
422C4×C8—1462no—
423C24C22×#6440811yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—42no—
427C2×Q8—2922no—
428C2×Q8—2924no—
429C2×Q8—1462no—
430C2×Q8—1462no—
431C2×Q8—1461no—
432C2×Q8—1461no—
433C22×C4—42no—
434C22×C4—2922no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—731no—
438C22×C4—732no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—731no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—732no—
449C22×C4—1464no—
450C22×C4C22⋊#6440811yescharacteristic
451C22×C4C22⋊#6440811yescharacteristic
452C22×C4C22⋊#6440811yescharacteristic
453C22×C4C22⋊#6440811yescharacteristic
454C22×C4C22×#6440812yes—
455C22×C4C22×#6440811yescharacteristic
456C22×C4C22×#6440811yescharacteristic
457C22×C4C22×#6440812yes—
458M16—2924no—
459C2×C8—2924no—
460C2×C8—1464no—
461C2×C8—1464no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—1462no—
467C4⋊C4—1462no—
468C4⋊C4—1462no—
469C4⋊C4—1462no—
470C4⋊C4—1462no—
471C4⋊C4—1462no—
472C4⋊C4—1462no—
473C4⋊C4—1462no—
474C4⋊C4—1462no—
475C4⋊C4—1462no—
476C4⋊C4—1462no—
477C4⋊C4—1462no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—1462no—
483C22⋊C4—1462no—
484C42—731no—
485C42—731no—
486C42—731no—
487C42—731no—
488C42—731no—
489C42—731no—
490C42—731no—
491C42—731no—
492C42—731no—
493C42—731no—
494C42—731no—
495C42—731no—
496C42—731no—
497C42—731no—
498C42—731no—
499C42—731no—
500C42—1462no—
501C42—1462no—
502C42—1462no—
503C42—1462no—
504C23—22no—
505C23—22no—
506C23—41no—
507C23C2×C22⋊#6440811yescharacteristic
508C23C2×C22⋊#6440811yescharacteristic
509C23C23×#6440811yescharacteristic
510Q8—42no—
511Q8—42no—
512Q8—2922no—
513Q8—2922no—
514Q8—2924no—
515Q8—2924no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—2922no—
527C2×C4—2921no—
528C2×C4—2921no—
529C2×C4—2921no—
530C2×C4—731no—
531C2×C4—731no—
532C2×C4—731no—
533C2×C4—734no—
534C2×C4—731no—
535C2×C4—731no—
536C2×C4—731no—
537C2×C4—731no—
538C2×C4—731no—
539C2×C4—1462no—
540C2×C4—1462no—
541C2×C4—1464no—
542C2×C4—1462no—
543C2×C4—1462no—
544C2×C4—1462no—
545C2×C4—1462no—
546C2×C4—1462no—
547C2×C4—1462no—
548C2×C4—1462no—
549C2×C4—1462no—
550C2×C4C2×C22⋊#6440811yescharacteristic
551C2×C4C2×C22⋊#6440811yescharacteristic
552C2×C4C2×C22⋊#6440811yescharacteristic
553C2×C4C2×C22⋊#6440811yescharacteristic
554C8—2924no—
555C8—2924no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—44no—
564C22D73⋊#10112yes—
565C22C22×C22⋊#6440811yescharacteristic
566C22#1798966512yes—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—42no—
572C4—42no—
573C4—2922no—
574C4—2922no—
575C4—732no—
576C4—732no—
577C4—732no—
578C4—1461no—
579C4—1461no—
580C4—1461no—
581C4—1461no—
582C4—1461no—
583C2—22no—
584C2—22no—
585C2—41no—
586C2#2262651511yescharacteristic
587C2D73⋊#41011yescharacteristic
588C2C2×D73⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#64408
commutatorC23×C73C23×C4
FrattiniC23C23×#64408
FittingC2×C22⋊Q8×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC22×Dic73C24
hypercenterC2×C22⋊Q8#64408
hypocenterC73#17404
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #22625203C2semidirect
5. #22625195C2semidirect
6. #22625194C2semidirect
302. C73#17404semidirect

Maximal subgroups

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

subgroupindex
#226266072
C2×#179896072
#226252102
#226252032
#226251952
#226251942
C2×#179891392
#1740473