Finite Group Databasebeta

← #34012451

Subgroups — #34012451

Order 18688.

420 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626159C211yesmaximal, characteristic
2C2×#17989478C211yesmaximal, characteristic, complemented
3C2×#17989477C211yesmaximal, characteristic, complemented
4#22625667C211yesmaximal, characteristic
5#22624971C211yesmaximal, characteristic, complemented
6#22624971C211yesmaximal, characteristic, complemented
7C2×M32×D73C211yesmaximal, characteristic
8C2×#14556666C2211yescharacteristic
9C2×#14556666C2211yescharacteristic
10#17989555C411yescharacteristic
11C2×#14556645C2211yescharacteristic
12C2×#14556645C2211yescharacteristic
13C4×C22⋊#64408C411yescharacteristic
14#17989482C412yescomplemented
15C22⋊#11924031C412yescomplemented
16#17989478—22no—
17#17989477—22no—
18#17989452C411yescharacteristic
19#17989452C411yescharacteristic
20C22×C8×D73C2211yescharacteristic
21C2×#14556531C411yescharacteristic, complemented
22C2×#14556530C2211yescharacteristic
23C2×#14556530C2211yescharacteristic
24M32×D73—22no—
25M32×D73—22no—
26C2×C16×D73C411yescharacteristic, complemented
27C2×C16×D73C411yescharacteristic, complemented
28C2×M32×C73C411yescharacteristic, complemented
29C2×#11924036C2×C411yescharacteristic
30C2×#11924036C2×C411yescharacteristic
31C2×C22⋊#64408—21no—
32C2×C4×#64408C2×C411yescharacteristic
33C2×C4×#64408C2×C411yescharacteristic
34#14556666—21no—
35#14556666—21no—
36#14556666—21no—
37#14556666—21no—
38C2×#11924031C2×C412yes—
39C2×#11924031C2×C412yes—
40#14556648—21no—
41C22⋊#10596833—21no—
42#14556645—21no—
43#14556645—21no—
44#14556645—21no—
45#14556645—21no—
46(C2×#64408)⋊C4—21no—
47C22×C4×D73C2×C411yescharacteristic
48C22×#10596831C2×C411yescharacteristic
49C2×C8×D73—21no—
50C2×C8×D73—21no—
51C2×C8×D73—21no—
52C2×C8×D73—21no—
53C2×C8×D73C2×C411yescharacteristic
54C2×C8×D73C2×C411yescharacteristic
55C2×C8×D73C2×C411yescharacteristic
56C2×C8×D73C2311yescharacteristic
57#14556531—22no—
58#14556530—21no—
59#14556530—21no—
60#14556530D412yes—
61#14556530D412yes—
62C2×#11924003C2×C411yescharacteristic
63C2×#11924003C2×C411yescharacteristic
64C16×D73—22no—
65C16×D73—22no—
66C22×C8×C73C2×C411yescharacteristic
67M32×C73—22no—
68C2×C16×C73C2×C411yescharacteristic
69C2×C16×C73C2×C411yescharacteristic
70C22×#64408—21no—
71C22×#64408—21no—
72#11924036—21no—
73#11924036—21no—
74#11924036—21no—
75#11924036—21no—
76C2×#10596833—21no—
77C2×#10596833—21no—
78C22⋊#64408—42no—
79C4×#64408—21no—
80C4×#64408—21no—
81C4×#64408—21no—
82C4×#64408—21no—
83#11924031—22no—
84#11924031—22no—
85C23×D73M1611yescharacteristic
86C22×Dic73M1611yescharacteristic
87C2×C4×D73—21no—
88C2×C4×D73—21no—
89C2×C4×D73—21no—
90C2×C4×D73—21no—
91C2×C4×D73C4211yescharacteristic
92C2×C4×D73M1611yescharacteristic
93C2×C4×D73M1611yescharacteristic
94C2×C4×D73C22×C411yescharacteristic
95C2×#10596831—21no—
96C2×#10596831—21no—
97C2×#10596831C4211yescharacteristic
98C2×#10596831C22×C411yescharacteristic
99C8×D73—21no—
100C8×D73—21no—
101C8×D73—21no—
102C8×D73—21no—
103C8×D73—21no—
104C8×D73—21no—
105C8×D73C2×D411yescharacteristic
106C8×D73C2×D411yescharacteristic
107C8×D73#4111yescharacteristic
108C8×D73#4111yescharacteristic
109#11924003—21no—
110#11924003C22⋊C412yescomplemented
111C22×C4×C73C4211yescharacteristic
112C2×C8×C73—21no—
113C2×C8×C73—21no—
114C2×C8×C73C4211yescharacteristic
115C2×C8×C73C22×C411yescharacteristic
116C16×C73—21no—
117C16×C73C22⋊C412yescomplemented
118C23×C73#9711yescharacteristic
119C22×D73—22no—
120C22×D73—21no—
121C22×D73—21no—
122C22×D73—41no—
123C22×D73#9711yescharacteristic
124C22×D73C2×M1611yescharacteristic
125C2×#64408—41no—
126C2×#64408—41no—
127C2×#64408—41no—
128C2×#64408—41no—
129C2×#64408—41no—
130C2×#64408—41no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73#9711yescharacteristic
134C2×C4×C73C2×C4211yescharacteristic
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73#9711yescharacteristic
138C2×Dic73C2×M1611yescharacteristic
139C4×D73—21no—
140C4×D73—21no—
141C4×D73—21no—
142C4×D73—21no—
143C4×D73—21no—
144C4×D73—21no—
145C4×D73C4×D411yescharacteristic
146C4×D73C4×D411yescharacteristic
147C4×D73#13111yescharacteristic
148C4×D73#13111yescharacteristic
149#10596833—41no—
150#10596833—41no—
151C8×C73—21no—
152C8×C73C2×C22⋊C411yescharacteristic
153C8×C73#11711yescharacteristic
154#10596831—21no—
155#10596831C4×D411yescharacteristic
156#10596831C4×D411yescharacteristic
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73C2×#9711yescharacteristic
161C2×D73—21no—
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—21no—
165C2×D73—42no—
166C2×D73—42no—
167C2×D73#34712yescomplemented
168C2×D73#43511yescharacteristic
169C2×D73#43511yescharacteristic
170#64408—81no—
171#64408—81no—
172C4×C73—21no—
173C4×C73C4×C22⋊C411yescharacteristic
174C4×C73#40511yescharacteristic
175Dic73—21no—
176Dic73#43511yescharacteristic
177Dic73#43511yescharacteristic
178#12616—731nomaximal, Sylow
179C2×C73—41no—
180C2×C73#175211yescharacteristic
181C2×C73C2×#34711yescharacteristic
182C2×C73#211011yescharacteristic
183D73—21no—
184D73—21no—
185D73—22no—
186C22×M32—731no—
187#2112—731no—
188C2×#347—731no—
189C2×#347—731no—
190#1752—731no—
191#1375—731no—
192#1375—731no—
193C73#1261611yescharacteristic, complemented, Sylow
194C23×C8—731no—
195C2×M32—731no—
196C2×M32—731no—
197C2×M32—731no—
198C2×M32—731no—
199C2×M32—731no—
200C2×M32—1462no—
201C2×M32—1462no—
202C2×M32#6440811yescharacteristic, complemented
203C22×C16—731no—
204C22×C16—731no—
205C2×C22⋊C8—731no—
206C2×#97—731no—
207C2×#97—731no—
208C4×C22⋊C4—731no—
209C22⋊C16—732no—
210C22⋊C16—732no—
211#347—1462no—
212#347—1462no—
213#336—731no—
214#336—731no—
215C23×C4—731no—
216C22×C8—731no—
217C22×C8—731no—
218C22×C8—731no—
219C22×C8—731no—
220C22×C8—731no—
221C22×C8—731no—
222C22×C8—731no—
223C22×C8—1461no—
224C22×C8—1461no—
225C22×C8—1461no—
226C22×C8—1461no—
227C22×C8C2×#6440811yescharacteristic
228C2×C22⋊C4—1461no—
229C2×C42—731no—
230C2×C42—731no—
231M32—22no—
232M32—732no—
233M32—732no—
234M32—1461no—
235M32—1461no—
236M32—1462no—
237M32—1461no—
238M32—1461no—
239M32—1461no—
240M32—1461no—
241C2×C16—731no—
242C2×C16—732no—
243C2×C16—732no—
244C2×C16—731no—
245C2×C16—1462no—
246C2×C16—1462no—
247C2×C16C2×#6440811yescharacteristic
248C2×C16C2×#6440811yescharacteristic
249C22⋊C8—1461no—
250C22⋊C8—1461no—
251#97—1461no—
252#97—1461no—
253#97—1461no—
254#97—1461no—
255#95—1461no—
256C24—731no—
257C22×C4—731no—
258C22×C4—731no—
259C22×C4—731no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266C22×C4—1461no—
267C22×C4—1461no—
268C22×C4C4×#6440811yescharacteristic
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—731no—
272C2×C8—731no—
273C2×C8—731no—
274C2×C8—731no—
275C2×C8—731no—
276C2×C8—731no—
277C2×C8—1461no—
278C2×C8—1461no—
279C2×C8—1461no—
280C2×C8—1461no—
281C2×C8—1461no—
282C2×C8—1461no—
283C2×C8—1461no—
284C2×C8—1461no—
285C2×C8—1461no—
286C2×C8—1461no—
287C2×C8—1461no—
288C2×C8—1461no—
289C2×C8—1461no—
290C2×C8—1461no—
291C2×C8C4×#6440811yescharacteristic
292C2×C8C22×#6440811yescharacteristic
293C22⋊C4—2922no—
294C42—1461no—
295C42—1461no—
296C42—1461no—
297C42—1461no—
298C16—21no—
299C16—732no—
300C16—1462no—
301C16—1462no—
302C16—1461no—
303C16C22⋊#6440812yescomplemented
304C23—2921no—
305C23—731no—
306C23—731no—
307C23—1462no—
308C23—1461no—
309C23—1461no—
310C23#1455664511yescharacteristic
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—2921no—
314C2×C4—2921no—
315C2×C4—2921no—
316C2×C4—2921no—
317C2×C4—2921no—
318C2×C4—2921no—
319C2×C4—731no—
320C2×C4—731no—
321C2×C4—731no—
322C2×C4—731no—
323C2×C4—731no—
324C2×C4—731no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4#1455664511yescharacteristic
334C2×C4C2×C4×#6440811yescharacteristic
335C8—21no—
336C8—2921no—
337C8—2921no—
338C8—731no—
339C8—731no—
340C8—1461no—
341C8C2×C22⋊#6440811yescharacteristic
342C8#1455667011yescharacteristic
343C22—21no—
344C22—21no—
345C22—21no—
346C22—2922no—
347C22—2922no—
348C22—732no—
349C22—731no—
350C22—731no—
351C22—1461no—
352C22—1461no—
353C22—1461no—
354C22—1461no—
355C22C2×#1455664511yescharacteristic
356C4—21no—
357C4—5841no—
358C4—5841no—
359C4—731no—
360C4—731no—
361C4—1461no—
362C4C4×C22⋊#6440811yescharacteristic
363C4#1798955011yescharacteristic
364C2—41no—
365C2—1461no—
366C2—1461no—
367C2—1462no—
368C2#2262566711yescharacteristic
369C2#2262614611yescharacteristic
370C2#2262615111yescharacteristic
subgroupG/H
centerC2×C4C2×C4×#64408
commutatorC2×C4×C73C2×C42
FrattiniC2×C8C22×#64408
FittingC2×M32×C73C4
socleC22×C73C2×#97
prime radicalC23×D73M16
cosocleC2×C8×D73C23
hypercenterC2×M32#64408
hypocenterC73#12616
LCSG ▷ C2×C4×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
2. C2×#17989478C2semidirect
3. C2×#17989477C2semidirect
5. #22624971C2semidirect
6. #22624971C2semidirect
14. #17989482C4semidirect
15. C22⋊#11924031C4semidirect
21. C2×#14556531C4semidirect
26. C2×C16×D73C4semidirect
27. C2×C16×D73C4semidirect
28. C2×M32×C73C4semidirect
110. #11924003C22⋊C4semidirect
117. C16×C73C22⋊C4semidirect
167. C2×D73#347semidirect
193. C73#12616semidirect
202. C2×M32#64408semidirect
303. C16C22⋊#64408semidirect

Maximal subgroups

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

subgroupindex
#226261592
C2×#179894782
C2×#179894772
#226256672
#226249712
C2×M32×D732
#1261673