Finite Group Databasebeta

← #34018171

Subgroups — #34018171

Order 18688.

634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626626C211yesmaximal, characteristic
2#22626576C211yesmaximal, characteristic
3#22625509C211yesmaximal, characteristic, complemented
4#22625507C211yesmaximal, characteristic, complemented
5#22625506C211yesmaximal, characteristic, complemented
6#22625505C211yesmaximal, characteristic, complemented
7#22625500C211yesmaximal, characteristic, complemented
8#22625498C211yesmaximal, characteristic, complemented
9#22625497C211yesmaximal, characteristic, complemented
10#22625495C211yesmaximal, characteristic, complemented
11#22625488C211yesmaximal, characteristic, complemented
12#22625484C211yesmaximal, characteristic, complemented
13#22625483C211yesmaximal, characteristic, complemented
14C2×#17989449C211yesmaximal, characteristic, complemented
15#22618891C211yesmaximal, characteristic
16C2×#14556678—21no—
17#17989612—21no—
18#17989611—21no—
19#17989609C2211yescharacteristic
20#17989608C2211yescharacteristic
21#17989606C2211yescharacteristic
22#17989603C2211yescharacteristic
23#17989594—21no—
24#17989593—21no—
25#17989593—21no—
26#17989591C2211yescharacteristic
27#17989590C2211yescharacteristic
28#17989590C2211yescharacteristic
29#17989590C2211yescharacteristic
30#17989588C2211yescharacteristic
31C2×C4⋊#10596833C2211yescharacteristic
32C2×C4⋊#10596833C2211yescharacteristic
33C2×C4⋊#10596833C2211yescharacteristic
34#17989560—21no—
35#17989551—21no—
36#17989451C2211yescharacteristic
37#17989451C2211yescharacteristic
38#17989451C2211yescharacteristic
39#17989451C2211yescharacteristic
40#17989450C2211yescharacteristic
41#17989450C2211yescharacteristic
42#17989450C2211yescharacteristic
43#17989450C2211yescharacteristic
44#17989449C2211yescharacteristic
45#17989449C2211yescharacteristic
46#17989449C2211yescharacteristic
47#17989449C2211yescharacteristic
48#17989449C2211yescharacteristic
49#17989449C2211yescharacteristic
50#17989448C2211yescharacteristic
51#17989448C2211yescharacteristic
52C4×#11924027C2211yescharacteristic
53#17988716C411yescharacteristic
54#17988715C411yescharacteristic
55#17988663C411yescharacteristic
56#17988662C411yescharacteristic
57#17988659C411yescharacteristic
58#17988658C411yescharacteristic
59#17988655C411yescharacteristic
60#17988639C2211yescharacteristic
61#17988637C2211yescharacteristic
62#17988637C2211yescharacteristic
63#17988539C2211yescharacteristic
64M16×Dic73C2211yescharacteristic
65C2×C8×Dic73C2211yescharacteristic
66#435×C73C411yescharacteristic
67#14556678—44no—
68C2×#11924038—21no—
69C2×#11924037—21no—
70C2×#11924037—21no—
71C2×#11924037—21no—
72C2×#11924036—21no—
73C22×#10596833—21no—
74C22×#10596833—21no—
75C22×#10596833—21no—
76#14556658—21no—
77#14556658—21no—
78#14556658—21no—
79#14556658—21no—
80C4⋊#10596833—21no—
81C4⋊#10596833—21no—
82C4⋊#10596833—21no—
83C4⋊#10596833—21no—
84C4⋊#10596833C2311yescharacteristic
85C4⋊#10596833C2311yescharacteristic
86C4⋊#10596833C2311yescharacteristic
87C4⋊#10596833C2311yescharacteristic
88C4⋊#10596833C2311yescharacteristic
89C4⋊#10596833C2311yescharacteristic
90C4⋊#10596833C2311yescharacteristic
91C4⋊#10596833C2311yescharacteristic
92#14556648—21no—
93#14556648—21no—
94C22⋊#10596833—21no—
95C22⋊#10596833—21no—
96#14556646—21no—
97#14556646—21no—
98C4×#10596833—21no—
99C4×#10596833—21no—
100C2×#11924027D411yescharacteristic
101C2×#11924012C2×C411yescharacteristic
102C2×#11924011C2×C411yescharacteristic
103C2×#11924011C2×C411yescharacteristic
104C22×#10596831C2×C411yescharacteristic
105C4×Dic146C2×C411yescharacteristic
106#14556556Q811yescharacteristic
107D4×Dic73Q811yescharacteristic
108C4×C22⋊D73C2×C411yescharacteristic
109C4×C22⋊D73C2×C411yescharacteristic
110#14556551Q811yescharacteristic
111#14556551Q811yescharacteristic
112#14556549D411yescharacteristic
113#14556547D411yescharacteristic
114#14556547D411yescharacteristic
115C2×C4×Dic73C2311yescharacteristic
116C2×C4×Dic73C2311yescharacteristic
117C42×D73C2311yescharacteristic
118C4⋊#10596831C2×C411yescharacteristic
119#14556520C2×C411yescharacteristic
120#14556520C2×C411yescharacteristic
121#14556520C2×C411yescharacteristic
122#14556520C2×C411yescharacteristic
123C22⋊#10596831C2×C411yescharacteristic
124C22⋊#10596831C2×C411yescharacteristic
125#14556503C2×C411yescharacteristic
126#14556503C2×C411yescharacteristic
127#14556502C2×C411yescharacteristic
128#14556501C2×C411yescharacteristic
129#14556501C2×C411yescharacteristic
130C8×Dic73C2×C411yescharacteristic
131C8×Dic73C2×C411yescharacteristic
132C8×Dic73C2311yescharacteristic
133C8×Dic73C2311yescharacteristic
134C8×Dic73C2311yescharacteristic
135C8×Dic73C2311yescharacteristic
136C2×M16×C73C2×C411yescharacteristic
137C22×C8×C73C2×C411yescharacteristic
138C4×D4×C73C2×C411yescharacteristic
139C4⋊C8×C73C2×C411yescharacteristic
140C22⋊C8×C73C2×C411yescharacteristic
141C22⋊C8×C73C2×C411yescharacteristic
142#97×C73C2×C411yescharacteristic
143#11924038—42no—
144#11924037—42no—
145#11924037—42no—
146#11924037—42no—
147#11924036—42no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—21no—
154C2×#10596833—21no—
155C2×#10596833—21no—
156C2×#10596833—42no—
157C2×#10596833—42no—
158C2×#10596833—42no—
159#11924027—22no—
160#11924027—22no—
161C2×Dic146C4⋊C411yescharacteristic
162C2×C22⋊D73C4⋊C411yescharacteristic
163C2×C22⋊D73C4⋊C411yescharacteristic
164C22×Dic73C2×D411yescharacteristic
165C22×Dic73C2×D411yescharacteristic
166C22×Dic73C2×Q811yescharacteristic
167C22×Dic73C2×Q811yescharacteristic
168C2×C4×D73C22×C411yescharacteristic
169C2×C4×D73C2×D411yescharacteristic
170C2×C4×D73C2×Q811yescharacteristic
171#11924012—22no—
172#11924011—22no—
173#11924011—41no—
174C2×#10596831—22no—
175C2×#10596831C22×C411yescharacteristic
176C2×#10596831C22×C411yescharacteristic
177C2×#10596831C22×C411yescharacteristic
178C2×#10596831C22×C411yescharacteristic
179C4⋊Dic73C4⋊C411yescharacteristic
180#11924007C4⋊C411yescharacteristic
181#11924007C4⋊C411yescharacteristic
182#11924007C4⋊C411yescharacteristic
183#11924007C4⋊C411yescharacteristic
184C22⋊Dic73C4⋊C411yescharacteristic
185C22⋊Dic73C4⋊C411yescharacteristic
186#11924005C4⋊C411yescharacteristic
187#11924005C4⋊C411yescharacteristic
188C4×Dic73C22×C411yescharacteristic
189C4×Dic73C22×C411yescharacteristic
190C4×Dic73C2×D411yescharacteristic
191C4×Dic73C2×D411yescharacteristic
192C4×Dic73C2×D411yescharacteristic
193C4×Dic73C2×Q811yescharacteristic
194C4×Dic73C2×Q811yescharacteristic
195C4×Dic73C2×Q811yescharacteristic
196C4×Dic73C2411yescharacteristic
197C2×D4×C73C4⋊C411yescharacteristic
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200M16×C73—41no—
201C2×C8×C73—41no—
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C4⋊C4×C73C4⋊C411yescharacteristic
207C22⋊C4×C73C4⋊C411yescharacteristic
208C22⋊C4×C73C4⋊C411yescharacteristic
209C42×C73C22×C411yescharacteristic
210C23×C73C2×C4⋊C411yescharacteristic
211C23×C73C2×C4⋊C411yescharacteristic
212C22×D73C2×C4⋊C411yescharacteristic
213D4×C73—22no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73C2×C4⋊C411yescharacteristic
219C2×C4×C73C2×C4⋊C411yescharacteristic
220C2×C4×C73C2×C4⋊C411yescharacteristic
221C2×C4×C73C2×C4⋊C411yescharacteristic
222C2×C4×C73C23×C411yescharacteristic
223C22⋊D73—22no—
224C22⋊D73—22no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—41no—
228C2×Dic73—41no—
229C2×Dic73C2×C4⋊C411yescharacteristic
230C2×Dic73C2×C4⋊C411yescharacteristic
231C2×Dic73C2×C4⋊C411yescharacteristic
232C2×Dic73C2×C4⋊C411yescharacteristic
233C2×Dic73C2×C4⋊C411yescharacteristic
234C2×Dic73AGL(1,ℤ/8)12yes—
235C2×Dic73#13712yes—
236C2×Dic73C22×D411yescharacteristic
237C2×Dic73C22×Q811yescharacteristic
238C4×D73—21no—
239C4×D73—21no—
240C4×D73—21no—
241C4×D73—21no—
242C4×D73—41no—
243Dic146—22no—
244#10596833—41no—
245#10596833—41no—
246#10596833—41no—
247#10596833—41no—
248#10596833—41no—
249#10596833—41no—
250#10596833—41no—
251#10596833—41no—
252C8×C73—21no—
253C8×C73—21no—
254C8×C73—21no—
255C8×C73—21no—
256#10596831—21no—
257#10596831—21no—
258#10596831—21no—
259#10596831#13112yescomplemented
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73#42812yes—
266C22×C73C22×C4⋊C411yescharacteristic
267C2×D73—21no—
268C2×D73—21no—
269C2×D73—21no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73C2×#13111yescharacteristic
275C4×C73#56811yescharacteristic
276Dic73—21no—
277Dic73—21no—
278Dic73—21no—
279Dic73—21no—
280Dic73—21no—
281Dic73#42812yes—
282Dic73C2×AGL(1,ℤ/8)11yescharacteristic
283Dic73C2×#13711yescharacteristic
284#17830—731nomaximal, Sylow
285C2×C73—22no—
286C2×C73—41no—
287C2×C73#290611yescharacteristic
288C2×C73C2×#42811yescharacteristic
289C2×C73#291611yescharacteristic
290D73—41no—
291#2965—731no—
292#2925—731no—
293#2906—731no—
294#1574—731no—
295#1574—731no—
296#1573—731no—
297#1573—731no—
298#1571—731no—
299#1570—731no—
300#1569—731no—
301#1569—731no—
302#1567—731no—
303#1565—731no—
304#1565—731no—
305C2×#334—731no—
306C73#1783011yescharacteristic, complemented, Sylow
307C2×#131—1461no—
308C4×#41—731no—
309#446—731no—
310#446—731no—
311#436—731no—
312#436—731no—
313#435—731no—
314#435—731no—
315#435—731no—
316#435#6440811yescharacteristic
317#433—1461no—
318#433—1461no—
319#432—731no—
320#432—731no—
321#431—731no—
322#431—731no—
323#431—731no—
324#431—731no—
325#431—731no—
326#424—1461no—
327#424—1461no—
328#424—1461no—
329#423—731no—
330#423—731no—
331#423—731no—
332#423—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C2×C4⋊C8—731no—
336C2×C4⋊C8—731no—
337#408—1461no—
338#405—1461no—
339C4×M16—731no—
340C4×M16—731no—
341C2×C4×C8—731no—
342#335—731no—
343#335—731no—
344#335—731no—
345#335—731no—
346#335—731no—
347#335—731no—
348#335—731no—
349#335—731no—
350#334—731no—
351#334—731no—
352#334—731no—
353#334—731no—
354#334—731no—
355#334—731no—
356#334—731no—
357#334—731no—
358C2×#41—731no—
359#131—2924no—
360C2×M16—731no—
361C2×M16—731no—
362C2×M16—731no—
363C2×M16—1461no—
364C2×M16—1461no—
365C2×M16—1461no—
366C2×M16—1461no—
367C2×M16C2×#6440811yescharacteristic
368C22×C8—731no—
369C22×C8—1461no—
370C22×C8—1461no—
371C22×C8—1461no—
372C22×C8—1461no—
373C22×C8C2×#6440811yescharacteristic
374C4×Q8—731no—
375C4×Q8—731no—
376C4×D4—731no—
377C4×D4—731no—
378C4×D4—731no—
379C4×D4—731no—
380C4×D4—731no—
381C4×D4C2×#6440811yescharacteristic
382#117—731no—
383#117—731no—
384#117—731no—
385C2×C42—731no—
386C2×C42—731no—
387C2×C42—731no—
388C4⋊C8—731no—
389C4⋊C8—731no—
390C4⋊C8—731no—
391C4⋊C8—731no—
392C4⋊C8—731no—
393C4⋊C8—731no—
394C4⋊C8—731no—
395C4⋊C8—731no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—731no—
400C4⋊C8—731no—
401C4⋊C8—1461no—
402C4⋊C8—1461no—
403C4⋊C8—1461no—
404C4⋊C8—1461no—
405C4⋊C8—1461no—
406C4⋊C8—1461no—
407C4⋊C8—1461no—
408C4⋊C8—1461no—
409C4⋊C8C2×#6440811yescharacteristic
410C22⋊C8—731no—
411C22⋊C8—731no—
412C22⋊C8—731no—
413C22⋊C8—731no—
414C22⋊C8—1461no—
415C22⋊C8—1461no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8C2×#6440811yescharacteristic
419C22⋊C8C2×#6440811yescharacteristic
420#97—731no—
421#97—731no—
422#97—731no—
423#97—1461no—
424#97—1461no—
425#97C2×#6440811yescharacteristic
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—731no—
430C4×C8—731no—
431C4×C8—731no—
432C4×C8—1461no—
433C4×C8—1461no—
434#41—1462no—
435#41—1462no—
436C2×Q8—731no—
437C2×D4—731no—
438C2×D4—731no—
439C2×D4C4⋊#6440811yescharacteristic
440C22×C4—731no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—731no—
446C22×C4—731no—
447C22×C4C22×#6440811yescharacteristic
448C22×C4C22×#6440811yescharacteristic
449M16—41no—
450M16—2921no—
451M16—2922no—
452M16—2922no—
453M16—2922no—
454M16—2922no—
455M16—1462no—
456M16—1462no—
457C2×C8—41no—
458C2×C8—2922no—
459C2×C8—2922no—
460C2×C8—2922no—
461C2×C8—2922no—
462C2×C8—731no—
463C2×C8—731no—
464C2×C8—731no—
465C2×C8—731no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1462no—
475C2×C8C22×#6440811yescharacteristic
476C2×C8C22×#6440811yescharacteristic
477C2×C8C22×#6440811yescharacteristic
478C2×C8C22×#6440811yescharacteristic
479C4⋊C4—731no—
480C4⋊C4—731no—
481C4⋊C4—731no—
482C4⋊C4—731no—
483C4⋊C4—731no—
484C4⋊C4C4⋊#6440811yescharacteristic
485C22⋊C4—731no—
486C22⋊C4—731no—
487C22⋊C4—731no—
488C22⋊C4—731no—
489C22⋊C4C4⋊#6440811yescharacteristic
490C22⋊C4C4⋊#6440811yescharacteristic
491C42—731no—
492C42—731no—
493C42—731no—
494C42—731no—
495C42—731no—
496C42—731no—
497C42—731no—
498C42—731no—
499C42—731no—
500C42C22×#6440811yescharacteristic
501C23—731no—
502C23C2×C4⋊#6440811yescharacteristic
503C23C2×C4⋊#6440811yescharacteristic
504Q8—1462no—
505D4—22no—
506D4—1462no—
507D4—1462no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—2921no—
513C2×C4—2921no—
514C2×C4—2921no—
515C2×C4—731no—
516C2×C4—731no—
517C2×C4—732no—
518C2×C4—732no—
519C2×C4—731no—
520C2×C4—731no—
521C2×C4—731no—
522C2×C4—731no—
523C2×C4—731no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4C2×C4⋊#6440811yescharacteristic
531C2×C4C2×C4⋊#6440811yescharacteristic
532C2×C4C2×C4⋊#6440811yescharacteristic
533C2×C4C2×C4⋊#6440811yescharacteristic
534C2×C4C23×#6440811yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—2921no—
540C8—2921no—
541C8—2921no—
542C8—2921no—
543C8—2921no—
544C8—2921no—
545C8—2921no—
546C8—2921no—
547C8—732no—
548C8—1461no—
549C8—1461no—
550C8—1461no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—1461no—
557C22—1461no—
558C22—1461no—
559C22#1798959812yes—
560C22C22×C4⋊#6440811yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—731no—
566C4—731no—
567C4—732no—
568C4—1461no—
569C4—1461no—
570C4—1461no—
571C4—1461no—
572C4—1461no—
573C4D73⋊#13111yescharacteristic
574C4#1798966511yescharacteristic
575C2—22no—
576C2—41no—
577C2—2921no—
578C2#2262657811yescharacteristic
579C2C2×#1798959811yescharacteristic
580C2#2262659311yescharacteristic
subgroupG/H
centerC22C22×C4⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#435×C73C4
socleC22×C73C22×C4⋊C4
prime radicalC2×#11924027D4
cosocleC4×Dic73C24
hypercenter#435#64408
hypocenterC73#17830
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #22625509C2semidirect
4. #22625507C2semidirect
5. #22625506C2semidirect
6. #22625505C2semidirect
7. #22625500C2semidirect
8. #22625498C2semidirect
9. #22625497C2semidirect
10. #22625495C2semidirect
11. #22625488C2semidirect
12. #22625484C2semidirect
13. #22625483C2semidirect
14. C2×#17989449C2semidirect
259. #10596831#131semidirect
306. C73#17830semidirect

Maximal subgroups

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

subgroupindex
#226266262
#226265762
#226255092
#226255072
#226255062
#226255052
#226255002
#226254982
#226254972
#226254952
#226254882
#226254842
#226254832
C2×#179894492
#226188912
#1783073