Finite Group Databasebeta

← #33055809

Subgroups — #33055809

Order 18688.

710 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618972C211yesmaximal, characteristic, complemented
2#22618971C211yesmaximal, characteristic, complemented
3C2×C4×#11924013C211yesmaximal, characteristic
4#22608842C214yesmaximal, complemented
5#22608813C214yesmaximal, complemented
6#22608677C211yesmaximal, characteristic, complemented
7#22608323C211yesmaximal, characteristic, complemented
8#22608215C211yesmaximal, characteristic, complemented
9C73×#1478C211yesmaximal, characteristic, complemented
10C22×#11924013C411yescharacteristic
11C2×C4×D292C2211yescharacteristic
12C4×#11924013C412yes—
13C4×#11924013C412yes—
14C4×#11924013C2212yes—
15C4×#11924013C2212yes—
16#17988666—22no—
17#17988665—22no—
18#17988665C2214yescomplemented
19#17988664C2214yescomplemented
20#17988640C2211yescharacteristic
21#17988640C2211yescharacteristic
22C2×#14556524C411yescharacteristic
23C2×#14556512C411yescharacteristic
24C2×#14556511C411yescharacteristic
25#17988551—22no—
26#17988549—22no—
27C2×C4×#10596831C2211yescharacteristic
28#17988339C2212yescomplemented
29#17988337C2212yescomplemented
30#17988316C2214yescomplemented
31#17988309C2212yescomplemented
32C8×#10596831C2212yescomplemented
33C2×C4×D4×C73C2211yescharacteristic
34#431×C73C2211yescharacteristic
35#431×C73C2211yescharacteristic
36D4⋊C8×C73C2214yescomplemented
37C22×D292C2×C411yescharacteristic
38C22×C4×D73—21no—
39C2×#11924013—24no—
40C2×#11924013C2×C412yes—
41C2×#11924013C2×C412yes—
42C2×#11924012—24no—
43C2×#11924011—24no—
44C22×#10596831C2×C411yescharacteristic
45C22×#10596831C2×C411yescharacteristic
46C4×D292—21no—
47C4×D292—21no—
48C4×D292C2×C412yes—
49C4×D292C2312yes—
50C2×C4⋊Dic73C2×C411yescharacteristic
51C2×#11924005—21no—
52#14556524C2×C412yes—
53#14556524C2×C412yes—
54C4⋊#10596831D412yes—
55C4⋊#10596831C2312yes—
56#14556512C2×C412yes—
57#14556512C2×C412yes—
58#14556511C2×C412yes—
59#14556511C2×C412yes—
60C22⋊#10596831—24no—
61C22⋊#10596831—21no—
62C22⋊#10596831D412yes—
63#14556503—24no—
64C4×#10596831—21no—
65C4×#10596831C2×C411yescharacteristic
66C4×#10596831C2×C411yescharacteristic
67C4×#10596831C2311yescharacteristic
68C4×#10596831C2311yescharacteristic
69C4×#10596831C2312yes—
70C22×D4×C73C2×C411yescharacteristic
71C23×C4×C73—21no—
72C4×D4×C73—21no—
73C4×D4×C73—21no—
74C4×D4×C73C2×C412yes—
75C4×D4×C73C2312yes—
76C2×C4⋊C4×C73C2×C411yescharacteristic
77C2×C22⋊C4×C73—21no—
78C2×C42×C73C2311yescharacteristic
79C4⋊C8×C73—21no—
80C4⋊C8×C73C2312yes—
81C22⋊C8×C73—21no—
82C22⋊C8×C73—21no—
83C4×C8×C73—21no—
84C4×C8×C73C2312yes—
85C23×D73—21no—
86C2×D292—22no—
87C2×D292—22no—
88C2×D292—21no—
89C2×D292C22×C412yes—
90C22×Dic73—21no—
91C2×C4×D73—22no—
92C2×C4×D73—22no—
93C2×C4×D73—82no—
94#11924013—24no—
95#11924013—24no—
96#11924012—84no—
97#11924011—84no—
98C2×#10596831—22no—
99C2×#10596831—22no—
100C2×#10596831M1614yescomplemented
101C2×#10596831C22×C411yescharacteristic
102C2×#10596831C22×C411yescharacteristic
103C2×#10596831C22×C411yescharacteristic
104C2×#10596831C22×C411yescharacteristic
105C2×#10596831C2×D414yes—
106C4⋊Dic73—21no—
107C4⋊Dic73C22×C412yes—
108#11924005—22no—
109#11924005—22no—
110C24×C73—21no—
111C2×D4×C73—21no—
112C2×D4×C73—22no—
113C2×D4×C73—22no—
114C2×D4×C73C22×C412yes—
115C22×C4×C73—21no—
116C22×C4×C73—22no—
117C22×C4×C73—22no—
118C22×C4×C73—82no—
119C22×C4×C73C22×C411yescharacteristic
120C22×C4×C73C2×D411yescharacteristic
121C22×C4×C73#4111yescharacteristic
122C2×C8×C73—22no—
123C2×C8×C73—22no—
124C4⋊C4×C73—21no—
125C4⋊C4×C73C22×C412yes—
126C22⋊C4×C73—22no—
127C22⋊C4×C73—22no—
128C42×C73C22×C411yescharacteristic
129C42×C73C2×D411yescharacteristic
130C42×C73#4111yescharacteristic
131C42×C73C2411yescharacteristic
132C23×C73—22no—
133C23×C73—42no—
134C23×C73—81no—
135C23×C73—81no—
136C23×C73C4×D411yescharacteristic
137C22×D73—22no—
138C22×D73—42no—
139C22×D73—81no—
140C22×D73—81no—
141D4×C73—22no—
142D4×C73—22no—
143D4×C73—42no—
144C2×C4×C73—22no—
145C2×C4×C73—22no—
146C2×C4×C73—41no—
147C2×C4×C73—44no—
148C2×C4×C73—82no—
149C2×C4×C73—81no—
150C2×C4×C73C4×D411yescharacteristic
151C2×C4×C73C4×D411yescharacteristic
152C2×C4×C73C4×D411yescharacteristic
153C2×C4×C73C2×M1612yes—
154C2×C4×C73#13112yes—
155C2×C4×C73C23×C411yescharacteristic
156C2×C4×C73C22×D411yescharacteristic
157C2×C4×C73C2×#4111yescharacteristic
158C2×Dic73—22no—
159C2×Dic73—81no—
160D292—22no—
161D292—22no—
162D292—42no—
163C4×D73—44no—
164C4×D73—82no—
165C8×C73—42no—
166C8×C73—42no—
167#10596831—21no—
168#10596831—21no—
169#10596831—24no—
170#10596831—42no—
171#10596831C2×M1612yes—
172#10596831C2×M1612yes—
173C22×C73—21no—
174C22×C73—21no—
175C22×C73—42no—
176C22×C73—42no—
177C22×C73—42no—
178C22×C73—84no—
179C22×C73#43612yes—
180C22×C73C2×C4×D411yescharacteristic
181C2×D73—42no—
182C2×D73—42no—
183C2×D73—42no—
184C2×D73—84no—
185C4×C73—21no—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73—42no—
189C4×C73#43612yes—
190C4×C73C22×M1611yescharacteristic
191C4×C73C2×#13111yescharacteristic
192C4×C73#57612yes—
193Dic73—42no—
194#17895—731nomaximal, Sylow
195C2×C73—22no—
196C2×C73—82no—
197C2×C73C2×#43611yescharacteristic
198C2×C73#294811yescharacteristic
199C2×C73#295711yescharacteristic
200D73—82no—
201#2975—731no—
202#2975—731no—
203C2×C4×D8—731no—
204#1594—734no—
205#1589—734no—
206#1564—731no—
207#1478—731no—
208#1478D7311yescharacteristic, complemented
209#1450—731no—
210C73#1789511yescharacteristic, complemented, Sylow
211C22×D8—731no—
212C2×C4×D4—731no—
213C2×C4×D4C2×D7311yescharacteristic
214C4×D8—732no—
215C4×D8—732no—
216C4×D8—732no—
217C4×D8—732no—
218#436—734no—
219#436—734no—
220#436—1462no—
221#436—1462no—
222#431—731no—
223#431—731no—
224#431C2×D7311yescharacteristic
225#431C2×D7311yescharacteristic
226C2×#107—731no—
227C2×#102—731no—
228C2×#102—731no—
229#407—1462no—
230#407—1462no—
231C2×C4×C8—731no—
232#335—732no—
233#334—732no—
234D4⋊C8—734no—
235D4⋊C8C2×D7314yescomplemented
236#322—732no—
237C82—732no—
238C22×D4—731no—
239C22×D4C4×D7311yescharacteristic
240C23×C4—21no—
241C23×C4—1461no—
242C2×D8—732no—
243C2×D8—732no—
244C2×D8—1464no—
245C2×M16—1464no—
246C2×M16—1464no—
247C22×C8—731no—
248C22×C8—731no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—732no—
252C4×D4—732no—
253C4×D4—1461no—
254C4×D4—1461no—
255C4×D4C4×D7312yes—
256C4×D4C22×D7312yes—
257C2×C4⋊C4—731no—
258C2×C4⋊C4C4×D7311yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—1461no—
261C2×C42C22×D7311yescharacteristic
262#107—732no—
263#107—732no—
264C4⋊C8—21no—
265C4⋊C8—732no—
266C4⋊C8—732no—
267C4⋊C8C22×D7312yes—
268#102—732no—
269#102—732no—
270#102—732no—
271#102—732no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—732no—
275C22⋊C8—1464no—
276C22⋊C8—1464no—
277C22⋊C8—1461no—
278C4×C8—21no—
279C4×C8—731no—
280C4×C8—731no—
281C4×C8—731no—
282C4×C8—732no—
283C4×C8—731no—
284C4×C8—1461no—
285C4×C8C22×D7312yes—
286C24—21no—
287C24—1461no—
288C2×D4—21no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—732no—
292C2×D4—1461no—
293C2×D4—1462no—
294C2×D4—1462no—
295C2×D4C2×C4×D7312yes—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—82no—
300C22×C4—5842no—
301C22×C4—1462no—
302C22×C4—1461no—
303C22×C4—1462no—
304C22×C4C2×C4×D7311yescharacteristic
305C22×C4D4×D7311yescharacteristic
306C22×C4#1192402711yescharacteristic
307D8—1464no—
308D8—1464no—
309M16—5844no—
310M16—5844no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—734no—
314C2×C8—731no—
315C2×C8—731no—
316C2×C8—731no—
317C2×C8—731no—
318C2×C8—734no—
319C2×C8—1462no—
320C2×C8—1462no—
321C4⋊C4—21no—
322C4⋊C4—732no—
323C4⋊C4—1461no—
324C4⋊C4C2×C4×D7312yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—1462no—
328C22⋊C4—1462no—
329C42C2×C4×D7311yescharacteristic
330C42D4×D7311yescharacteristic
331C42#1192402711yescharacteristic
332C42C23×D7311yescharacteristic
333C23—22no—
334C23—42no—
335C23—81no—
336C23—81no—
337C23—2922no—
338C23—5841no—
339C23—5841no—
340C23—1462no—
341C23#1455655111yescharacteristic
342D4—22no—
343D4—22no—
344D4—42no—
345D4—2922no—
346D4—1462no—
347D4—1462no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—44no—
352C2×C4—82no—
353C2×C4—81no—
354C2×C4—2924no—
355C2×C4—5842no—
356C2×C4—5841no—
357C2×C4—1462no—
358C2×C4#1455655111yescharacteristic
359C2×C4#1455655111yescharacteristic
360C2×C4#1455655111yescharacteristic
361C2×C4M16×D7312yes—
362C2×C4#1455659712yes—
363C2×C4C22×C4×D7311yescharacteristic
364C2×C4C2×D4×D7311yescharacteristic
365C2×C4C2×#1192402711yescharacteristic
366C8—42no—
367C8—42no—
368C8—2922no—
369C8—732no—
370C8—732no—
371C8—1464no—
372C8—1461no—
373C8—1461no—
374C22—21no—
375C22—21no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—84no—
380C22—2922no—
381C22—2922no—
382C22—2922no—
383C22—5844no—
384C22#1798866212yes—
385C22C2×#1455655111yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—2922no—
391C4#1798866212yes—
392C4C2×M16×D7311yescharacteristic
393C4C2×#1455659711yescharacteristic
394C4#1798939112yes—
395C2—22no—
396C2—82no—
397C2—5842no—
398C2C2×#1798866211yescharacteristic
399C2#2261877911yescharacteristic
400C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1478C2
socleC22×C73C2×C4×D4
prime radicalC22×#11924013C4
cosocleC42×C73C24
hypercenter#1478D73
hypocenterC73#17895
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
1. #22618972C2semidirect
2. #22618971C2semidirect
4. #22608842C2semidirect
5. #22608813C2semidirect
6. #22608677C2semidirect
7. #22608323C2semidirect
8. #22608215C2semidirect
9. C73×#1478C2semidirect
18. #17988665C22semidirect
19. #17988664C22semidirect
28. #17988339C22semidirect
29. #17988337C22semidirect
30. #17988316C22semidirect
31. #17988309C22semidirect
32. C8×#10596831C22semidirect
36. D4⋊C8×C73C22semidirect
100. C2×#10596831M16semidirect
208. #1478D73semidirect
210. C73#17895semidirect
235. D4⋊C8C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226189722
#226189712
C2×C4×#119240132
#226088422
#226088132
#226086772
#226083232
#226082152
C73×#14782
#1789573