Finite Group Databasebeta

← #33055115

Subgroups — #33055115

Order 18688.

602 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619045C211yesmaximal, characteristic
2#22619040C211yesmaximal, characteristic
3#22618570C211yesmaximal, characteristic
4#22608722C211yesmaximal, characteristic, complemented
5#22608721C211yesmaximal, characteristic, complemented
6#22608715C211yesmaximal, characteristic, complemented
7#22608714C211yesmaximal, characteristic, complemented
8#22608711C211yesmaximal, characteristic, complemented
9#22608710C211yesmaximal, characteristic, complemented
10#22608704C211yesmaximal, characteristic, complemented
11#22608682C211yesmaximal, characteristic, complemented
12#22608682C211yesmaximal, characteristic, complemented
13#22608678C211yesmaximal, characteristic, complemented
14#335×D73C211yesmaximal, characteristic, complemented
15C73×#1571C211yesmaximal, characteristic, complemented
16C4×#11924028C2211yescharacteristic
17#17988716—21no—
18#17988711—21no—
19#17988663—21no—
20#17988657—21no—
21#17988656—21no—
22#17988652—21no—
23C8×C22⋊D73—21no—
24C8×C22⋊D73—21no—
25#17988647C412yes—
26#17988645C412yes—
27#17988644C2211yescharacteristic
28#17988643C2211yescharacteristic
29#17988640C2211yescharacteristic
30#17988640C2211yescharacteristic
31#17988639C2211yescharacteristic
32#17988639C2211yescharacteristic
33#17988639C2211yescharacteristic
34#17988638C2211yescharacteristic
35#17988638C2211yescharacteristic
36#17988612C412yes—
37#17988609C2211yescharacteristic
38C4⋊C8×D73C2211yescharacteristic
39C4⋊C8×D73C2211yescharacteristic
40C4⋊C8×D73C2211yescharacteristic
41#17988552C412yes—
42C4×#11924011C2211yescharacteristic
43C4×C8×D73C2211yescharacteristic
44#17988340C2211yescharacteristic
45#17988340C2211yescharacteristic
46#17988339C2211yescharacteristic
47#17988339C2211yescharacteristic
48#17988339C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988338C2211yescharacteristic
51#17988338C2211yescharacteristic
52#17988337C2211yescharacteristic
53#17988337C2211yescharacteristic
54#17988337C2211yescharacteristic
55#17988337C2211yescharacteristic
56#431×C73C2211yescharacteristic
57#423×C73C2211yescharacteristic
58C2×C4⋊C8×C73C2211yescharacteristic
59#335×C73C2211yescharacteristic
60#335×C73C2211yescharacteristic
61#335×C73C2211yescharacteristic
62#335×C73C2211yescharacteristic
63C2×#11924028C2×C411yescharacteristic
64C2×#11924011—21no—
65C2×#11924011C2×C412yes—
66C2×C8×D73—21no—
67C2×C8×D73—21no—
68C2×C8×D73—21no—
69C2×C8×D73C2×C412yes—
70C4×Dic146D411yescharacteristic
71C4×Dic146Q811yescharacteristic
72C4×D292D411yescharacteristic
73C4×D292Q811yescharacteristic
74C4×C22⋊D73D411yescharacteristic
75C4×C22⋊D73D411yescharacteristic
76C4×C22⋊D73Q811yescharacteristic
77C4×C22⋊D73Q811yescharacteristic
78#14556550C2×C411yescharacteristic
79#14556548C2×C411yescharacteristic
80#14556548C2×C411yescharacteristic
81C42×D73C2311yescharacteristic
82C42×D73C2311yescharacteristic
83C4⋊#10596831C2×C412yes—
84C4⋊#10596831C2311yescharacteristic
85C4⋊#10596831C2311yescharacteristic
86C4⋊#10596831C2311yescharacteristic
87C4⋊#10596831C2311yescharacteristic
88#14556520—21no—
89#14556520—21no—
90#14556520—21no—
91#14556520—21no—
92#14556520C2×C412yes—
93#14556520C2×C412yes—
94C22⋊#10596831—21no—
95C22⋊#10596831—21no—
96C22⋊#10596831C2×C412yes—
97#14556503—21no—
98#14556503—21no—
99#14556503—21no—
100#14556503—21no—
101#14556503C2×C412yes—
102#14556503C2×C412yes—
103#14556502—21no—
104#14556501—21no—
105#14556501C2×C412yes—
106C4×#10596831—21no—
107C4×#10596831C2311yescharacteristic
108C4×#10596831C2311yescharacteristic
109C8×Dic73—21no—
110C8×Dic73—21no—
111C8×Dic73—21no—
112C8×Dic73C2×C412yes—
113C2×M16×C73—21no—
114C22×C8×C73—21no—
115C2×C42×C73C2311yescharacteristic
116C4⋊C8×C73—21no—
117C4⋊C8×C73—21no—
118C4⋊C8×C73C2×C412yes—
119C4⋊C8×C73C2311yescharacteristic
120C4⋊C8×C73C2311yescharacteristic
121C4⋊C8×C73C2311yescharacteristic
122C4⋊C8×C73C2311yescharacteristic
123C22⋊C8×C73C2×C412yes—
124C4×C8×C73C2311yescharacteristic
125C4×C8×C73C2311yescharacteristic
126#11924028—24no—
127C2×Dic146C4⋊C411yescharacteristic
128C2×D292C4⋊C411yescharacteristic
129C2×C22⋊D73C4⋊C411yescharacteristic
130C2×C22⋊D73C4⋊C411yescharacteristic
131C2×C4×D73C22×C411yescharacteristic
132C2×C4×D73C22×C411yescharacteristic
133C2×C4×D73C2×D411yescharacteristic
134C2×C4×D73C2×D411yescharacteristic
135C2×C4×D73C2×Q811yescharacteristic
136C2×C4×D73C2×Q811yescharacteristic
137#11924011—24no—
138#11924011—81no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831C22×C412yes—
144C2×#10596831C22×C412yes—
145C8×D73—24no—
146C8×D73—81no—
147C8×D73—81no—
148C8×D73—81no—
149C4⋊Dic73C4⋊C411yescharacteristic
150C4⋊Dic73C4⋊C411yescharacteristic
151#11924007C4⋊C411yescharacteristic
152#11924007C4⋊C411yescharacteristic
153#11924007C4⋊C411yescharacteristic
154#11924007C4⋊C411yescharacteristic
155C22⋊Dic73C4⋊C411yescharacteristic
156C22⋊Dic73C4⋊C411yescharacteristic
157#11924005C4⋊C411yescharacteristic
158#11924005C4⋊C411yescharacteristic
159#11924005C4⋊C411yescharacteristic
160#11924005C4⋊C411yescharacteristic
161C4×Dic73C22×C411yescharacteristic
162C4×Dic73C22×C411yescharacteristic
163C4×Dic73C2×D411yescharacteristic
164C4×Dic73C2×D411yescharacteristic
165C4×Dic73C2×Q811yescharacteristic
166C4×Dic73C2×Q811yescharacteristic
167C22×C4×C73C22×C411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×Q811yescharacteristic
170M16×C73—81no—
171C2×C8×C73—21no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—81no—
176C2×C8×C73C22×C412yes—
177C2×C8×C73C22×C412yes—
178C42×C73C22×C411yescharacteristic
179C42×C73C2×D411yescharacteristic
180C42×C73C2×Q811yescharacteristic
181C42×C73C2411yescharacteristic
182C23×C73C2×C4⋊C411yescharacteristic
183C22×D73C2×C4⋊C411yescharacteristic
184C22×D73C2×C4⋊C411yescharacteristic
185C2×C4×C73—22no—
186C2×C4×C73—21no—
187C2×C4×C73—21no—
188C2×C4×C73—41no—
189C2×C4×C73C2×C4⋊C411yescharacteristic
190C2×C4×C73C2×C4⋊C411yescharacteristic
191C2×C4×C73C2×C4⋊C411yescharacteristic
192C2×C4×C73C23×C411yescharacteristic
193C2×C4×C73C22×D411yescharacteristic
194C2×C4×C73C22×Q811yescharacteristic
195C22⋊D73—22no—
196C22⋊D73—22no—
197C2×Dic73C2×C4⋊C411yescharacteristic
198C2×Dic73C2×C4⋊C411yescharacteristic
199C2×Dic73C2×C4⋊C411yescharacteristic
200C2×Dic73C2×C4⋊C411yescharacteristic
201C2×Dic73C2×C4⋊C411yescharacteristic
202C2×Dic73C2×C4⋊C411yescharacteristic
203D292—22no—
204C4×D73—22no—
205C4×D73—21no—
206C4×D73—21no—
207C4×D73—21no—
208C4×D73—21no—
209C4×D73—41no—
210C4×D73—41no—
211C4×D73#13114yes—
212Dic146—22no—
213C8×C73—22no—
214C8×C73—22no—
215C8×C73—41no—
216C8×C73—41no—
217C8×C73—41no—
218C8×C73—41no—
219#10596831—22no—
220#10596831—22no—
221#10596831—41no—
222#10596831—41no—
223#10596831—41no—
224#10596831—41no—
225C22×C73—21no—
226C22×C73—21no—
227C22×C73—21no—
228C22×C73C22×C4⋊C411yescharacteristic
229C2×D73—21no—
230C2×D73—21no—
231C2×D73—21no—
232C2×D73—21no—
233C2×D73—21no—
234C2×D73#42412yes—
235C4×C73—21no—
236C4×C73—21no—
237C4×C73—21no—
238C4×C73—21no—
239C4×C73C2×#13112yes—
240C4×C73#57611yescharacteristic
241C4×C73#57811yescharacteristic
242Dic73—21no—
243Dic73—21no—
244Dic73—21no—
245Dic73—21no—
246Dic73—21no—
247Dic73#42412yes—
248#17812—731nomaximal, Sylow
249C2×C73—41no—
250C2×C73C2×#42411yescharacteristic
251C2×C73#291311yescharacteristic
252C2×C73#291611yescharacteristic
253D73—22no—
254D73—41no—
255#2989—731no—
256#2988—731no—
257#2922—731no—
258#1574—731no—
259#1574—731no—
260#1573—731no—
261#1573—731no—
262#1572—731no—
263#1572—731no—
264#1571—731no—
265#1571D7311yescharacteristic, complemented
266#1565—731no—
267#1565—731no—
268#1564—731no—
269C2×#335—731no—
270C73#1781211yescharacteristic, complemented, Sylow
271C4×#41—731no—
272#446—1461no—
273C8×Q8—1461no—
274#436—1461no—
275#435—1461no—
276#435—1461no—
277C8×D4—1461no—
278C8×D4—1461no—
279C8×D4—1461no—
280#433—732no—
281#433—732no—
282#432—731no—
283#432—731no—
284#431—731no—
285#431—731no—
286#431—731no—
287#431—731no—
288#431—731no—
289#431—731no—
290#431—731no—
291#431C2×D7311yescharacteristic
292#424—732no—
293#423—731no—
294#423C2×D7311yescharacteristic
295C2×C4⋊C8—731no—
296C2×C4⋊C8—731no—
297C2×C4⋊C8—731no—
298C2×C4⋊C8C2×D7311yescharacteristic
299#408—732no—
300C4×M16—731no—
301C2×C4×C8—731no—
302#335—731no—
303#335—731no—
304#335—731no—
305#335—731no—
306#335—731no—
307#335—731no—
308#335C2×D7311yescharacteristic
309#335C2×D7311yescharacteristic
310#335C2×D7311yescharacteristic
311#335C2×D7311yescharacteristic
312#334—731no—
313#334—731no—
314#334—731no—
315#334—731no—
316#334—731no—
317#334—731no—
318C2×#41—731no—
319C2×M16—21no—
320C2×M16—732no—
321C2×M16—1461no—
322C22×C8—21no—
323C22×C8—732no—
324C22×C8—1461no—
325C22×C8—1461no—
326C22×C8—1461no—
327C4×Q8—731no—
328C4×Q8—731no—
329C4×D4—731no—
330C4×D4—731no—
331C4×D4—731no—
332C4×D4—731no—
333C4×D4—731no—
334C4×D4—731no—
335#117—731no—
336#117—731no—
337#117—731no—
338C2×C42—731no—
339C2×C42—731no—
340C2×C42C22×D7311yescharacteristic
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8—732no—
344C4⋊C8—732no—
345C4⋊C8—732no—
346C4⋊C8—731no—
347C4⋊C8—731no—
348C4⋊C8—731no—
349C4⋊C8—731no—
350C4⋊C8—1461no—
351C4⋊C8—1461no—
352C4⋊C8—1461no—
353C4⋊C8—1461no—
354C4⋊C8C4×D7312yes—
355C4⋊C8C22×D7311yescharacteristic
356C4⋊C8C22×D7311yescharacteristic
357C4⋊C8C22×D7311yescharacteristic
358C4⋊C8C22×D7311yescharacteristic
359C22⋊C8—732no—
360C22⋊C8—732no—
361C22⋊C8—732no—
362C22⋊C8—1461no—
363C22⋊C8—1461no—
364C22⋊C8—1461no—
365C22⋊C8—1461no—
366C22⋊C8—1461no—
367C22⋊C8—1461no—
368C22⋊C8C4×D7312yes—
369#97—732no—
370#97—1461no—
371#97—1461no—
372C4×C8—732no—
373C4×C8—731no—
374C4×C8—731no—
375C4×C8—1461no—
376C4×C8—1461no—
377C4×C8—1461no—
378C4×C8—1461no—
379C4×C8C22×D7311yescharacteristic
380C4×C8C22×D7311yescharacteristic
381#41—1464no—
382C2×Q8—731no—
383C2×D4—731no—
384C2×D4—731no—
385C2×D4—731no—
386C22×C4—731no—
387C22×C4—731no—
388C22×C4—731no—
389C22×C4—731no—
390C22×C4—731no—
391C22×C4—731no—
392C22×C4C2×C4×D7311yescharacteristic
393C22×C4D4×D7311yescharacteristic
394C22×C4Q8×D7311yescharacteristic
395M16—81no—
396M16—5841no—
397M16—1464no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—81no—
403C2×C8—5841no—
404C2×C8—5841no—
405C2×C8—5841no—
406C2×C8—732no—
407C2×C8—732no—
408C2×C8—1464no—
409C2×C8—1461no—
410C2×C8—1461no—
411C2×C8—1461no—
412C2×C8—1461no—
413C2×C8C2×C4×D7312yes—
414C2×C8C2×C4×D7312yes—
415C4⋊C4—731no—
416C4⋊C4—731no—
417C4⋊C4—731no—
418C4⋊C4—731no—
419C4⋊C4—731no—
420C4⋊C4—731no—
421C22⋊C4—731no—
422C22⋊C4—731no—
423C22⋊C4—731no—
424C22⋊C4—731no—
425C22⋊C4—731no—
426C22⋊C4—731no—
427C42—731no—
428C42—731no—
429C42—731no—
430C42—731no—
431C42—731no—
432C42—731no—
433C42C2×C4×D7311yescharacteristic
434C42D4×D7311yescharacteristic
435C42Q8×D7311yescharacteristic
436C42C23×D7311yescharacteristic
437C23—731no—
438C23—731no—
439C23C4⋊C4×D7311yescharacteristic
440Q8—1462no—
441D4—1462no—
442D4—1462no—
443D4—1462no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—2921no—
449C2×C4—2921no—
450C2×C4—731no—
451C2×C4—734no—
452C2×C4—731no—
453C2×C4—731no—
454C2×C4—731no—
455C2×C4—731no—
456C2×C4—731no—
457C2×C4—1461no—
458C2×C4—1461no—
459C2×C4—1461no—
460C2×C4—1461no—
461C2×C4—1462no—
462C2×C4C4⋊C4×D7311yescharacteristic
463C2×C4C4⋊C4×D7311yescharacteristic
464C2×C4C4⋊C4×D7311yescharacteristic
465C2×C4C22×C4×D7311yescharacteristic
466C2×C4C2×D4×D7311yescharacteristic
467C2×C4C2×Q8×D7311yescharacteristic
468C8—22no—
469C8—22no—
470C8—41no—
471C8—41no—
472C8—41no—
473C8—41no—
474C8—2921no—
475C8—2921no—
476C8—2921no—
477C8—2921no—
478C8—1462no—
479C8—1462no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—732no—
484C22—1461no—
485C22—1461no—
486C22—1461no—
487C22—1461no—
488C22—1461no—
489C22C2×C4⋊C4×D7311yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—732no—
495C4—1461no—
496C4—1461no—
497C4—1461no—
498C4—1461no—
499C4—1461no—
500C4#131×D7312yes—
501C4#1798938811yescharacteristic
502C4#1798940011yescharacteristic
503C2—41no—
504C2—2921no—
505C2—1462no—
506C2#424×D7311yescharacteristic
507C2#2261852711yescharacteristic
508C2#2261854111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1571C2
socleC22×C73C22×C4⋊C4
prime radicalC2×#11924028C2×C4
cosocleC42×C73C24
hypercenter#1571D73
hypocenterC73#17812
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
4. #22608722C2semidirect
5. #22608721C2semidirect
6. #22608715C2semidirect
7. #22608714C2semidirect
8. #22608711C2semidirect
9. #22608710C2semidirect
10. #22608704C2semidirect
11. #22608682C2semidirect
12. #22608682C2semidirect
13. #22608678C2semidirect
14. #335×D73C2semidirect
15. C73×#1571C2semidirect
265. #1571D73semidirect
270. C73#17812semidirect

Maximal subgroups

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

subgroupindex
#226190452
#226190402
#226185702
#226087222
#226087212
#226087152
#226087142
#226087112
#226087102
#226087042
#226086822
#226086782
#335×D732
C73×#15712
#1781273