Finite Group Databasebeta

← #34012394

Subgroups — #34012394

Order 18688.

466 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989550C211yesmaximal, characteristic
2#22626159C211yesmaximal, characteristic
3C2×#17989478C211yesmaximal, characteristic, complemented
4C2×#17989477C211yesmaximal, characteristic, complemented
5#22624971C211yesmaximal, characteristic, complemented
6#22624971C211yesmaximal, characteristic, complemented
7#22611540C211yesmaximal, characteristic
8C2×D73⋊M16C411yescharacteristic
9C2×#14556670C411yescharacteristic
10C2×#14556666C2211yescharacteristic
11C2×#14556666C2211yescharacteristic
12#17989550—22no—
13#17989550—22no—
14C2×#14556645C2211yescharacteristic
15C2×#14556645C2211yescharacteristic
16C2×C8×#64408C411yescharacteristic
17C2×C8×#64408C411yescharacteristic
18#17989482C412yescomplemented
19C22⋊#11924031C412yescomplemented
20#17989478—22no—
21#17989477—22no—
22C22×C8×D73C2211yescharacteristic
23C2×#14556530C2211yescharacteristic
24C2×#14556530C2211yescharacteristic
25C22⋊#11924003C411yescharacteristic, complemented
26#17988366C411yescharacteristic, complemented
27#17988366C411yescharacteristic, complemented
28C22⋊C16×C73C411yescharacteristic, complemented
29C2×#11924038—21no—
30D73⋊M16—22no—
31D73⋊M16—22no—
32C2×#11924037—21no—
33C2×#11924036C2×C411yescharacteristic
34C2×#11924036C2×C411yescharacteristic
35#14556670—22no—
36#14556670—22no—
37C2×C4⋊#64408—21no—
38C2×C22⋊#64408—21no—
39C2×C4×#64408C2×C411yescharacteristic
40C2×C4×#64408C2×C411yescharacteristic
41#14556666—21no—
42#14556666—21no—
43#14556666—21no—
44#14556666—21no—
45C2×#11924031C2×C412yes—
46C2×#11924031C2×C412yes—
47#14556645—21no—
48#14556645—21no—
49#14556645D412yes—
50#14556645D412yes—
51C8×#64408—22no—
52C8×#64408—22no—
53C22×C4×D73C2×C411yescharacteristic
54C22×#10596831C2×C411yescharacteristic
55C2×C8×D73—21no—
56C2×C8×D73—21no—
57C2×C8×D73—21no—
58C2×C8×D73—21no—
59C2×C8×D73C2×C411yescharacteristic
60C2×C8×D73C2×C411yescharacteristic
61C2×C8×D73C2×C411yescharacteristic
62C2×C8×D73C2311yescharacteristic
63#14556530—21no—
64#14556530—21no—
65#14556530—21no—
66#14556530—21no—
67C2×#11924003C2×C411yescharacteristic
68C2×#11924003C2×C411yescharacteristic
69C22×C8×C73C2×C411yescharacteristic
70C2×C16×C73C2×C411yescharacteristic
71C2×C16×C73C2×C411yescharacteristic
72C22×#64408—21no—
73C22×#64408—21no—
74#11924038—24no—
75#11924037—24no—
76#11924036—21no—
77#11924036—21no—
78#11924036C22⋊C412yes—
79#11924036M1612yes—
80C2×#10596833—21no—
81C2×#10596833—21no—
82C4⋊#64408—24no—
83C22⋊#64408—24no—
84C4×#64408—21no—
85C4×#64408—21no—
86C4×#64408C22⋊C412yes—
87C4×#64408M1612yes—
88#11924031—22no—
89#11924031—22no—
90C23×D73M1611yescharacteristic
91C22×Dic73M1611yescharacteristic
92C2×C4×D73—21no—
93C2×C4×D73—21no—
94C2×C4×D73—21no—
95C2×C4×D73—21no—
96C2×C4×D73C4211yescharacteristic
97C2×C4×D73M1611yescharacteristic
98C2×C4×D73M1611yescharacteristic
99C2×C4×D73C22×C411yescharacteristic
100C2×#10596831—21no—
101C2×#10596831—21no—
102C2×#10596831C4211yescharacteristic
103C2×#10596831C22×C411yescharacteristic
104C8×D73—21no—
105C8×D73—21no—
106C8×D73—21no—
107C8×D73—21no—
108C8×D73—21no—
109C8×D73—21no—
110C8×D73C2×D411yescharacteristic
111C8×D73C2×D411yescharacteristic
112C8×D73#4111yescharacteristic
113C8×D73#4111yescharacteristic
114#11924003—21no—
115#11924003—21no—
116C22×C4×C73C4211yescharacteristic
117C2×C8×C73—21no—
118C2×C8×C73—21no—
119C2×C8×C73C4211yescharacteristic
120C2×C8×C73C22×C411yescharacteristic
121C16×C73—21no—
122C16×C73—21no—
123C23×C73#9711yescharacteristic
124C22×D73—21no—
125C22×D73—21no—
126C22×D73—41no—
127C22×D73—41no—
128C22×D73#9711yescharacteristic
129C22×D73C2×M1611yescharacteristic
130C2×#64408—22no—
131C2×#64408—22no—
132C2×#64408—41no—
133C2×#64408—41no—
134C2×#64408—41no—
135C2×#64408—41no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73#9711yescharacteristic
139C2×C4×C73C2×C4211yescharacteristic
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73#9711yescharacteristic
143C2×Dic73C2×M1611yescharacteristic
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—21no—
149C4×D73—21no—
150C4×D73C2×C22⋊C411yescharacteristic
151C4×D73#11711yescharacteristic
152C4×D73C2×M1611yescharacteristic
153C4×D73C2×M1611yescharacteristic
154#10596833—22no—
155#10596833—22no—
156C8×C73—21no—
157C8×C73C4×D411yescharacteristic
158C8×C73C4×D411yescharacteristic
159#10596831—21no—
160#10596831C4×D411yescharacteristic
161#10596831C4×D411yescharacteristic
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73C2×#9711yescharacteristic
166C2×D73—21no—
167C2×D73—21no—
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—42no—
172C2×D73—42no—
173C2×D73#40711yescharacteristic
174C2×D73#43211yescharacteristic
175#64408—42no—
176#64408—42no—
177C4×C73—21no—
178C4×C73C4×C22⋊C411yescharacteristic
179C4×C73C4×M1611yescharacteristic
180Dic73—21no—
181Dic73#40711yescharacteristic
182Dic73#43211yescharacteristic
183#12606—731nomaximal, Sylow
184C2×C73—41no—
185C2×C73#174911yescharacteristic
186C2×C73#211011yescharacteristic
187C2×C73#211011yescharacteristic
188D73—21no—
189D73—21no—
190D73—41no—
191C2×#405—731no—
192#2112—731no—
193#2112—731no—
194C2×#347—731no—
195C2×#347—731no—
196#1375—731no—
197#1375—731no—
198C73#1260611yescharacteristic, complemented, Sylow
199C22×M16—731no—
200C23×C8—731no—
201C2×#117—731no—
202C2×M32—731no—
203C2×M32—731no—
204C2×M32—731no—
205C2×M32—731no—
206#405—1462no—
207#405—1462no—
208C2×#97—731no—
209C2×#97—731no—
210C2×C4×C8—731no—
211C2×C4×C8—731no—
212C22⋊C16—732no—
213C22⋊C16—732no—
214C22⋊C16—731no—
215C22⋊C16—731no—
216C22⋊C16—731no—
217C22⋊C16#6440811yescharacteristic, complemented
218#347—1462no—
219#347—1462no—
220C23×C4—731no—
221C2×M16—1462no—
222C2×M16—1462no—
223C2×M16—1461no—
224C2×M16—1461no—
225C22×C8—731no—
226C22×C8—731no—
227C22×C8—731no—
228C22×C8—731no—
229C22×C8—731no—
230C22×C8—731no—
231C22×C8—731no—
232C22×C8—1461no—
233C22×C8—1461no—
234C22×C8—1461no—
235C22×C8—1461no—
236C22×C8C2×#6440811yescharacteristic
237#117—1462no—
238#117—1462no—
239C2×C4⋊C4—1461no—
240C2×C22⋊C4—1461no—
241C2×C42—731no—
242C2×C42—731no—
243M32—1461no—
244M32—1461no—
245M32—1461no—
246M32—1461no—
247M32—1461no—
248M32—1461no—
249M32—1461no—
250M32—1461no—
251C2×C16—732no—
252C2×C16—732no—
253C2×C16—731no—
254C2×C16—731no—
255C2×C16C2×#6440811yescharacteristic
256C2×C16C2×#6440811yescharacteristic
257#97—732no—
258#97—732no—
259#97—1461no—
260#97—1461no—
261C4×C8—1462no—
262C4×C8—1462no—
263C24—731no—
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—731no—
269C22×C4—1461no—
270C22×C4—1461no—
271C22×C4—1461no—
272C22×C4—1461no—
273C22×C4—1461no—
274C22×C4—1461no—
275C22×C4C4×#6440811yescharacteristic
276M16—1464no—
277M16—1464no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—731no—
281C2×C8—731no—
282C2×C8—731no—
283C2×C8—731no—
284C2×C8—731no—
285C2×C8—732no—
286C2×C8—732no—
287C2×C8—731no—
288C2×C8—1461no—
289C2×C8—1461no—
290C2×C8—1461no—
291C2×C8—1461no—
292C2×C8—1461no—
293C2×C8—1461no—
294C2×C8—1461no—
295C2×C8—1461no—
296C2×C8—1461no—
297C2×C8—1461no—
298C2×C8—1461no—
299C2×C8—1461no—
300C2×C8C4×#6440811yescharacteristic
301C2×C8C22×#6440811yescharacteristic
302C4⋊C4—1464no—
303C22⋊C4—1464no—
304C42—732no—
305C42—732no—
306C42—1461no—
307C42—1461no—
308C16—21no—
309C16—21no—
310C16—1462no—
311C16—1462no—
312C16—1461no—
313C16—1461no—
314C23—2921no—
315C23—2921no—
316C23—731no—
317C23—731no—
318C23—1461no—
319C23—1461no—
320C23#1455664511yescharacteristic
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—2921no—
324C2×C4—2921no—
325C2×C4—2921no—
326C2×C4—2921no—
327C2×C4—731no—
328C2×C4—731no—
329C2×C4—731no—
330C2×C4—731no—
331C2×C4—731no—
332C2×C4—731no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1462no—
338C2×C4—1462no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4#1455664511yescharacteristic
344C2×C4C2×C4×#6440811yescharacteristic
345C8—21no—
346C8—731no—
347C8—731no—
348C8—1462no—
349C8—1462no—
350C8—1461no—
351C8D4×#6440811yescharacteristic
352C8D4×#6440811yescharacteristic
353C22—21no—
354C22—21no—
355C22—21no—
356C22—2922no—
357C22—2922no—
358C22—731no—
359C22—731no—
360C22—1461no—
361C22—1461no—
362C22—1461no—
363C22—1461no—
364C22—1461no—
365C22C2×#1455664511yescharacteristic
366C4—21no—
367C4—2922no—
368C4—2922no—
369C4—731no—
370C4—731no—
371C4—1461no—
372C4C22⋊C4×#6440811yescharacteristic
373C4M16×#6440811yescharacteristic
374C2—41no—
375C2—2921no—
376C2—1461no—
377C2—1461no—
378C2#2262565911yescharacteristic
379C2#2262615011yescharacteristic
380C2#2262615111yescharacteristic
subgroupG/H
centerC2×C4C2×C4×#64408
commutatorC2×C4×C73C2×C42
FrattiniC2×C8C22×#64408
FittingC22⋊C16×C73C4
socleC22×C73C2×#97
prime radicalC23×D73M16
cosocleC2×C8×D73C23
hypercenterC22⋊C16#64408
hypocenterC73#12606
LCSG ▷ C2×C4×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
3. C2×#17989478C2semidirect
4. C2×#17989477C2semidirect
5. #22624971C2semidirect
6. #22624971C2semidirect
18. #17989482C4semidirect
19. C22⋊#11924031C4semidirect
25. C22⋊#11924003C4semidirect
26. #17988366C4semidirect
27. #17988366C4semidirect
28. C22⋊C16×C73C4semidirect
198. C73#12606semidirect
217. C22⋊C16#64408semidirect

Maximal subgroups

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

subgroupindex
C2×#179895502
#226261592
C2×#179894782
C2×#179894772
#226249712
#226115402
#1260673