Finite Group Databasebeta

← #34016181

Subgroups — #34016181

Order 18688.

960 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626607C211yesmaximal, characteristic
2C2×#17989608C211yesmaximal, characteristic
3#22625210C214yesmaximal
4#22625205C212yesmaximal, complemented
5#22625204C212yesmaximal, complemented
6#22625193C214yesmaximal, complemented
7C2×#17989140C211yesmaximal, characteristic
8#17989608—21no—
9#17989608—21no—
10#17989608C2212yes—
11#17989608C2212yes—
12#17989608C2212yes—
13#17989607—21no—
14#17989604C2212yes—
15#17989603—21no—
16#17989590—21no—
17C2×C4⋊#10596833—21no—
18#17989557C2212yes—
19C2×C22⋊#10596833C2212yes—
20C4×#11924037—21no—
21C2×#14556646—21no—
22#17989433C2218yes—
23#17989432C2218yes—
24#17989140—21no—
25#17989140—21no—
26#17989140—21no—
27#17989140—21no—
28#17989140—21no—
29#17989140—21no—
30#17989140—21no—
31#17989140—21no—
32C2×#14556590C411yescharacteristic
33C2×#14556590C411yescharacteristic
34C2×#14556582C2211yescharacteristic
35C2×#14556582C2211yescharacteristic
36C2×#14556568C412yes—
37C2×#14556568C2212yes—
38C2×C4×Dic146C412yes—
39C2×C4×Dic146C2212yes—
40C2×#14556550C411yescharacteristic
41C22×C4×Dic73C2211yescharacteristic
42C2×#117×C73C411yescharacteristic
43C2×#11924037—22no—
44C22×#10596833—22no—
45#14556658—22no—
46C4⋊#10596833—22no—
47C4⋊#10596833—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×C412yes—
58C22×Dic146C2×C412yes—
59C23×Dic73C2×C411yescharacteristic
60C23×Dic73C2311yescharacteristic
61#14556590—21no—
62#14556590—21no—
63#14556590—21no—
64#14556590—21no—
65#14556590—21no—
66#14556590—21no—
67#14556590—21no—
68#14556590—21no—
69#14556582—21no—
70#14556582—21no—
71#14556582—21no—
72#14556582—21no—
73#14556582—21no—
74#14556582—21no—
75#14556582—21no—
76#14556582—21no—
77#14556568—22no—
78#14556568—22no—
79#14556568—22no—
80#14556568—22no—
81#14556568—22no—
82#14556568—22no—
83#14556568—22no—
84#14556568—22no—
85C4×Dic146—22no—
86C4×Dic146—22no—
87C4×Dic146—22no—
88C4×Dic146—22no—
89C4×Dic146—22no—
90C4×Dic146—22no—
91C4×Dic146—22no—
92C4×Dic146—22no—
93#14556550—21no—
94#14556550—21no—
95#14556550—21no—
96#14556550—21no—
97C2×C4⋊Dic73C2×C411yescharacteristic
98C2×C4⋊Dic73C2×C411yescharacteristic
99C2×C4⋊Dic73C2×C412yes—
100C2×C4⋊Dic73C2312yes—
101C2×#11924007C2×C412yes—
102C2×#11924007C2×C412yes—
103C2×#11924007C2×C412yes—
104C2×#11924007C2312yes—
105C2×C22⋊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
119C23×C4×C73C2×C411yescharacteristic
120#117×C73—21no—
121#117×C73—21no—
122#117×C73—21no—
123#117×C73—21no—
124C2×C4⋊C4×C73C2×C411yescharacteristic
125C2×C4⋊C4×C73C2×C411yescharacteristic
126C2×C22⋊C4×C73C2×C412yes—
127C2×C42×C73C2×C412yes—
128#11924037—44no—
129C2×#10596833—24no—
130C2×#10596833—24no—
131C2×#10596833—44no—
132C2×Dic146—22no—
133C2×Dic146—22no—
134C2×Dic146—22no—
135C2×Dic146—22no—
136C2×Dic146—44no—
137C2×Dic146—44no—
138C22×Dic73—42no—
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—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—22no—
159C4⋊Dic73—22no—
160C4⋊Dic73—22no—
161C4⋊Dic73—22no—
162#11924007—22no—
163#11924007—22no—
164#11924007—22no—
165#11924007—22no—
166#11924007—22no—
167#11924007—22no—
168#11924007—22no—
169#11924007—22no—
170C22⋊Dic73—22no—
171C22⋊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
191C22×C4×C73—24no—
192C22×C4×C73C22⋊C411yescharacteristic
193C22×C4×C73C22⋊C411yescharacteristic
194C22×C4×C73C22⋊C411yescharacteristic
195C22×C4×C73C22⋊C411yescharacteristic
196C22×C4×C73C22×C412yes—
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C412yes—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C22⋊C4×C73—22no—
205C22⋊C4×C73—22no—
206C42×C73—22no—
207C42×C73—22no—
208C23×C73—22no—
209C23×C73—22no—
210C23×C73—41no—
211C23×C73C2×C22⋊C411yescharacteristic
212C23×C73C2×C22⋊C411yescharacteristic
213C23×C73C23×C411yescharacteristic
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—22no—
217C2×C4×C73—22no—
218C2×C4×C73—22no—
219C2×C4×C73—22no—
220C2×C4×C73—22no—
221C2×C4×C73—24no—
222C2×C4×C73—42no—
223C2×C4×C73#10114yes—
224C2×C4×C73C2×C22⋊C411yescharacteristic
225C2×C4×C73C2×C22⋊C411yescharacteristic
226C2×C4×C73C2×C22⋊C411yescharacteristic
227C2×C4×C73C2×C22⋊C411yescharacteristic
228C2×Dic73—22no—
229C2×Dic73—22no—
230C2×Dic73—22no—
231C2×Dic73—22no—
232C2×Dic73—22no—
233C2×Dic73—22no—
234C2×Dic73—22no—
235C2×Dic73—24no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—42no—
244C2×Dic73C2×C22⋊C411yescharacteristic
245C2×Dic73C2×C22⋊C411yescharacteristic
246C2×Dic73C2×C22⋊C411yescharacteristic
247C2×Dic73C2×C22⋊C411yescharacteristic
248C2×Dic73C2×C22⋊C411yescharacteristic
249C2×Dic73C2×C22⋊C411yescharacteristic
250C2×Dic73C22×D411yescharacteristic
251C2×Dic73C22×D411yescharacteristic
252Dic146—44no—
253Dic146—44no—
254Dic146—44no—
255Dic146—44no—
256#10596833—44no—
257#10596833—44no—
258C22×C73—21no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73—44no—
266C22×C73C2×#10112yes—
267C22×C73C22×C22⋊C411yescharacteristic
268C22×C73#56812yes—
269C4×C73—21no—
270C4×C73—21no—
271C4×C73—42no—
272C4×C73—42no—
273C4×C73C2×#10112yes—
274C4×C73C2×#10112yes—
275Dic73—21no—
276Dic73—21no—
277Dic73—21no—
278Dic73—21no—
279Dic73—21no—
280Dic73—21no—
281Dic73—21no—
282Dic73—42no—
283Dic73—42no—
284Dic73#41012yes—
285#17404—731nomaximal, Sylow
286C2×C73—22no—
287C2×C73—22no—
288C2×C73—41no—
289C2×C73#287911yescharacteristic
290C2×C73C2×#41011yescharacteristic
291C2×C73C22×#10111yescharacteristic
292C2×#533—731no—
293#2920—731no—
294C2×#432—731no—
295#1472—734no—
296#1470—732no—
297#1470—732no—
298#1467—734no—
299C73#1740411yescharacteristic, complemented, Sylow
300#533—1461no—
301#533—1461no—
302#533—1461no—
303#533—1461no—
304#533—1461no—
305#533—1461no—
306#533—1461no—
307#533—1461no—
308C2×C4⋊Q8—731no—
309C2×C4⋊Q8—731no—
310C2×#125—731no—
311C2×#125—731no—
312C2×C22⋊Q8—732no—
313C2×C22⋊Q8—732no—
314C2×C4×Q8—732no—
315C2×C4×Q8—732no—
316C2×#117—731no—
317C2×#117#6440811yescharacteristic
318C22×C42—731no—
319#432—732no—
320#432—732no—
321#432—732no—
322#432—1461no—
323#432—1461no—
324#432—1461no—
325#431—732no—
326#431—1461no—
327#423—1461no—
328C2×C4⋊C8—1461no—
329#407—732no—
330C2×C22⋊C8—732no—
331C4×M16—1461no—
332C2×#97—1461no—
333#324—738no—
334#324—738no—
335C22×Q8—732no—
336C22×Q8—732no—
337C23×C4—731no—
338C23×C4—731no—
339C23×C4C2×#6440811yescharacteristic
340C2×M16—1462no—
341C22×C8—1462no—
342C4⋊Q8—1461no—
343C4⋊Q8—1461no—
344C4⋊Q8—1461no—
345C4⋊Q8—1461no—
346C4⋊Q8—1461no—
347C4⋊Q8—1461no—
348C4⋊Q8—1461no—
349C4⋊Q8—1461no—
350#125—1461no—
351#125—1461no—
352#125—1461no—
353#125—1461no—
354#125—1461no—
355#125—1461no—
356#125—1461no—
357#125—1461no—
358C22⋊Q8—1462no—
359C22⋊Q8—1462no—
360C22⋊Q8—1462no—
361C22⋊Q8—1462no—
362C22⋊Q8—1462no—
363C22⋊Q8—1462no—
364C22⋊Q8—1462no—
365C22⋊Q8—1462no—
366C4×Q8—1462no—
367C4×Q8—1462no—
368C4×Q8—1462no—
369C4×Q8—1462no—
370C4×Q8—1462no—
371C4×Q8—1462no—
372C4×Q8—1462no—
373C4×Q8—1462no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—1461no—
379#117—1461no—
380#117—1461no—
381#117—1461no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—731no—
384C2×C4⋊C4—732no—
385C2×C4⋊C4—732no—
386C2×C4⋊C4—732no—
387C2×C4⋊C4—732no—
388C2×C4⋊C4—732no—
389C2×C4⋊C4—732no—
390C2×C4⋊C4C2×#6440811yescharacteristic
391C2×C4⋊C4C2×#6440811yescharacteristic
392C2×C22⋊C4—732no—
393C2×C22⋊C4C2×#6440812yes—
394C2×C42—731no—
395C2×C42—731no—
396C2×C42—731no—
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—732no—
407C2×C42C2×#6440812yes—
408C4⋊C8—1462no—
409C4⋊C8—1462no—
410C4⋊C8—1462no—
411C4⋊C8—1462no—
412C22⋊C8—734no—
413C22⋊C8—734no—
414C22⋊C8—1462no—
415C22⋊C8—1462no—
416#97—1462no—
417#97—1462no—
418#97—1462no—
419C4×C8—1462no—
420C24C22×#6440811yescharacteristic
421C2×Q8—2924no—
422C2×Q8—2924no—
423C2×Q8—1462no—
424C2×Q8—1462no—
425C2×Q8—1462no—
426C2×Q8—1462no—
427C22×C4—24no—
428C22×C4—2922no—
429C22×C4—2922no—
430C22×C4—731no—
431C22×C4—731no—
432C22×C4—731no—
433C22×C4—731no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—732no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—732no—
444C22×C4C22⋊#6440811yescharacteristic
445C22×C4C22⋊#6440811yescharacteristic
446C22×C4C22⋊#6440811yescharacteristic
447C22×C4C22⋊#6440811yescharacteristic
448C22×C4C22×#6440812yes—
449C22×C4C22×#6440811yescharacteristic
450C22×C4C22×#6440811yescharacteristic
451C22×C4C22×#6440812yes—
452M16—2924no—
453C2×C8—2924no—
454C2×C8—1464no—
455C2×C8—1464no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—1462no—
461C4⋊C4—1462no—
462C4⋊C4—1462no—
463C4⋊C4—1462no—
464C4⋊C4—1462no—
465C4⋊C4—1462no—
466C4⋊C4—1462no—
467C4⋊C4—1462no—
468C4⋊C4—1462no—
469C4⋊C4—1462no—
470C4⋊C4—1462no—
471C4⋊C4—1462no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—1462no—
479C22⋊C4—1462no—
480C42—22no—
481C42—22no—
482C42—731no—
483C42—731no—
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—1462no—
499C42—1462no—
500C23—22no—
501C23—22no—
502C23—41no—
503C23C2×C22⋊#6440811yescharacteristic
504C23C2×C22⋊#6440811yescharacteristic
505C23C23×#6440811yescharacteristic
506Q8—2924no—
507Q8—2924no—
508Q8—2924no—
509Q8—2924no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—42no—
519C2×C4—2922no—
520C2×C4—2921no—
521C2×C4—2921no—
522C2×C4—2921no—
523C2×C4—2921no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—2921no—
527C2×C4—731no—
528C2×C4—731no—
529C2×C4—731no—
530C2×C4—731no—
531C2×C4—731no—
532C2×C4—731no—
533C2×C4—731no—
534C2×C4—731no—
535C2×C4—1462no—
536C2×C4—1462no—
537C2×C4—1464no—
538C2×C4—1462no—
539C2×C4—1462no—
540C2×C4—1462no—
541C2×C4—1462no—
542C2×C4—1462no—
543C2×C4#1455665214yes—
544C2×C4C2×C22⋊#6440811yescharacteristic
545C2×C4C2×C22⋊#6440811yescharacteristic
546C2×C4C2×C22⋊#6440811yescharacteristic
547C2×C4C2×C22⋊#6440811yescharacteristic
548C8—2924no—
549C8—2924no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—44no—
558C22C2×#1455665212yes—
559C22C22×C22⋊#6440811yescharacteristic
560C22#1798966612yes—
561C4—21no—
562C4—21no—
563C4—42no—
564C4—42no—
565C4—2922no—
566C4—2922no—
567C4—732no—
568C4—1461no—
569C4—1461no—
570C4—1461no—
571C4—1461no—
572C4—1461no—
573C4—1461no—
574C4—1461no—
575C4C2×#1455665212yes—
576C4C2×#1455665212yes—
577C2—22no—
578C2—22no—
579C2—41no—
580C2#2262651611yescharacteristic
581C2D73⋊#41011yescharacteristic
582C2C22×#1455665211yescharacteristic
subgroupG/H
centerC22C22×C22⋊#64408
commutatorC23×C73C23×C4
FrattiniC23C23×#64408
FittingC2×#117×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC22×Dic73C24
hypercenterC2×#117#64408
hypocenterC73#17404
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
4. #22625205C2semidirect
5. #22625204C2semidirect
6. #22625193C2semidirect
299. C73#17404semidirect

Maximal subgroups

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

subgroupindex
#226266072
C2×#179896082
#226252102
#226252052
#226252042
#226251932
C2×#179891402
#1740473