Finite Group Databasebeta

← #33055248

Subgroups — #33055248

Order 18688.

588 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618597C212yesmaximal
2#22608720C212yesmaximal, complemented
3#22608716C212yesmaximal, complemented
4#22608711C212yesmaximal, complemented
5#22608698C212yesmaximal, complemented
6#22608694C211yesmaximal, characteristic, complemented
7#22608683C212yesmaximal, complemented
8#22608679C211yesmaximal, characteristic, complemented
9C73×#2965C211yesmaximal, characteristic
10#17988648—22no—
11#17988648—22no—
12#17988644C2212yes—
13#17988644C2212yes—
14#17988640C2212yes—
15#17988640C2212yes—
16#17988611C2212yes—
17C2×C4⋊#10596831C2212yes—
18#17988554—22no—
19#17988543—22no—
20#17988340C2212yes—
21#17988340C2212yes—
22#17988340C2212yes—
23#17988340C2212yes—
24#17988338C2211yescharacteristic
25#17988338C2211yescharacteristic
26#17988338C2212yes—
27#17988338C2211yescharacteristic
28#17988338C2211yescharacteristic
29#17988338C2212yes—
30C4×#41×C73C2211yescharacteristic
31#446×C73C411yescharacteristic
32#446×C73C411yescharacteristic
33#436×C73C411yescharacteristic
34#436×C73C411yescharacteristic
35#435×C73C412yes—
36#435×C73C412yes—
37#431×C73C2211yescharacteristic
38#431×C73C2212yes—
39C4×M16×C73C2212yes—
40C2×C4×C8×C73C2211yescharacteristic
41C2×#11924012—22no—
42C22×#10596831—22no—
43C4⋊#10596831—22no—
44C4⋊#10596831—22no—
45C4⋊#10596831C2312yes—
46C4⋊#10596831C2312yes—
47C4⋊#10596831C2312yes—
48C4⋊#10596831C2312yes—
49C22⋊#10596831—22no—
50C22⋊#10596831—22no—
51C22⋊#10596831—22no—
52C22⋊#10596831—22no—
53#14556502—22no—
54#14556502—22no—
55C4×#10596831—22no—
56C4×#10596831—22no—
57C2×#41×C73D411yescharacteristic
58C2×M16×C73C2×C412yes—
59C2×M16×C73C2×C412yes—
60C22×C8×C73C2×C411yescharacteristic
61C22×C8×C73C2×C411yescharacteristic
62C4×Q8×C73C2×C411yescharacteristic
63C4×Q8×C73Q811yescharacteristic
64C4×D4×C73C2×C412yes—
65C4×D4×C73C2×C411yescharacteristic
66C4×D4×C73Q812yes—
67C4×D4×C73Q811yescharacteristic
68#117×C73D411yescharacteristic
69#117×C73D412yes—
70C2×C42×C73C2312yes—
71C2×C42×C73C2311yescharacteristic
72C4⋊C8×C73C2×C412yes—
73C4⋊C8×C73C2×C412yes—
74C4⋊C8×C73C2×C411yescharacteristic
75C4⋊C8×C73C2×C411yescharacteristic
76C22⋊C8×C73C2×C412yes—
77C22⋊C8×C73C2×C412yes—
78C22⋊C8×C73C2×C412yes—
79#97×C73C2×C412yes—
80#97×C73C2×C412yes—
81C4×C8×C73C2×C411yescharacteristic
82C4×C8×C73C2×C411yescharacteristic
83C4×C8×C73C2311yescharacteristic
84C4×C8×C73C2311yescharacteristic
85C4×C8×C73C2312yes—
86#11924012—44no—
87C2×#10596831—22no—
88C2×#10596831—22no—
89C2×#10596831—22no—
90C2×#10596831—22no—
91C2×#10596831—44no—
92#41×C73—42no—
93C2×Q8×C73C4⋊C411yescharacteristic
94C2×D4×C73C4⋊C412yes—
95C2×D4×C73C4⋊C411yescharacteristic
96C22×C4×C73C22×C411yescharacteristic
97C22×C4×C73C22×C412yes—
98C22×C4×C73C2×D411yescharacteristic
99C22×C4×C73C2×D412yes—
100C22×C4×C73C2×Q812yes—
101C22×C4×C73C2×Q811yescharacteristic
102M16×C73—24no—
103M16×C73—42no—
104C2×C8×C73—22no—
105C2×C8×C73—41no—
106C2×C8×C73C22×C411yescharacteristic
107C2×C8×C73C22×C411yescharacteristic
108C2×C8×C73C22×C411yescharacteristic
109C2×C8×C73C22×C412yes—
110C2×C8×C73C22×C412yes—
111C2×C8×C73C22×C411yescharacteristic
112C4⋊C4×C73C4⋊C411yescharacteristic
113C4⋊C4×C73C4⋊C412yes—
114C4⋊C4×C73C4⋊C411yescharacteristic
115C4⋊C4×C73C4⋊C412yes—
116C22⋊C4×C73C4⋊C412yes—
117C22⋊C4×C73C4⋊C412yes—
118C22⋊C4×C73C4⋊C412yes—
119C42×C73C22×C411yescharacteristic
120C42×C73C22×C412yes—
121C42×C73C2×D411yescharacteristic
122C42×C73C2×D412yes—
123C42×C73C2×Q812yes—
124C42×C73C2×Q811yescharacteristic
125C42×C73C2411yescharacteristic
126C23×C73C2×C4⋊C411yescharacteristic
127C23×C73C2×C4⋊C412yes—
128Q8×C73—41no—
129D4×C73—41no—
130D4×C73—42no—
131C2×C4×C73—21no—
132C2×C4×C73—22no—
133C2×C4×C73—21no—
134C2×C4×C73—22no—
135C2×C4×C73—22no—
136C2×C4×C73—22no—
137C2×C4×C73—22no—
138C2×C4×C73—42no—
139C2×C4×C73—41no—
140C2×C4×C73C2×C4⋊C411yescharacteristic
141C2×C4×C73C2×C4⋊C412yes—
142C2×C4×C73C2×C4⋊C411yescharacteristic
143C2×C4×C73C2×C4⋊C412yes—
144C2×C4×C73C2×C4⋊C411yescharacteristic
145C2×C4×C73C2×C4⋊C412yes—
146C2×C4×C73C23×C411yescharacteristic
147C2×C4×C73C22×D411yescharacteristic
148C2×C4×C73C22×Q811yescharacteristic
149C8×C73—21no—
150C8×C73—22no—
151C8×C73—21no—
152C8×C73—21no—
153C8×C73—22no—
154C8×C73#13112yes—
155#10596831—42no—
156#10596831—42no—
157#10596831—42no—
158#10596831—42no—
159C22×C73—21no—
160C22×C73—22no—
161C22×C73—21no—
162C22×C73—22no—
163C22×C73—21no—
164C22×C73—22no—
165C22×C73C22×C4⋊C411yescharacteristic
166C4×C73—21no—
167C4×C73—22no—
168C4×C73—21no—
169C4×C73—22no—
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—22no—
173C4×C73C2×#13111yescharacteristic
174C4×C73#56811yescharacteristic
175C4×C73#57512yes—
176#17831—731nomaximal, Sylow
177C2×C73—41no—
178C2×C73—42no—
179C2×C73#290611yescharacteristic
180C2×C73#291111yescharacteristic
181C2×C73#291611yescharacteristic
182#2965D7311yescharacteristic
183#2925—732no—
184#1574—732no—
185#1573—732no—
186#1572—732no—
187#1569—732no—
188#1568—731no—
189#1565—732no—
190#1564—731no—
191C73#1783111yescharacteristic, complemented, Sylow
192C4×#41C2×D7311yescharacteristic
193#446Dic7311yescharacteristic
194#446Dic7311yescharacteristic
195#436Dic7311yescharacteristic
196#436Dic7311yescharacteristic
197#435Dic7312yes—
198#435Dic7312yes—
199#433—1462no—
200#433—1462no—
201#432—732no—
202#432—732no—
203#431—732no—
204#431—732no—
205#431C2×D7311yescharacteristic
206#431C2×D7312yes—
207#423—732no—
208C2×C4⋊C8—732no—
209#408—1462no—
210#405—1462no—
211C4×M16C2×D7312yes—
212C2×C4×C8C2×D7311yescharacteristic
213#335—732no—
214#335—732no—
215#335—732no—
216#335—732no—
217#334—731no—
218#334—731no—
219#334—732no—
220#334—731no—
221#334—731no—
222#334—732no—
223C2×#41D29211yescharacteristic
224C2×M16—1462no—
225C2×M16C2×Dic7312yes—
226C2×M16C2×Dic7312yes—
227C22×C8—1462no—
228C22×C8C2×Dic7311yescharacteristic
229C22×C8C2×Dic7311yescharacteristic
230C4×Q8Dic14611yescharacteristic
231C4×Q8C2×Dic7311yescharacteristic
232C4×D4Dic14611yescharacteristic
233C4×D4Dic14612yes—
234C4×D4C2×Dic7312yes—
235C4×D4C2×Dic7311yescharacteristic
236#117D29212yes—
237#117D29211yescharacteristic
238C2×C42C22×D7311yescharacteristic
239C2×C42C22×D7312yes—
240C4⋊C8—732no—
241C4⋊C8—732no—
242C4⋊C8—732no—
243C4⋊C8—732no—
244C4⋊C8—1462no—
245C4⋊C8—1462no—
246C4⋊C8C2×Dic7312yes—
247C4⋊C8C2×Dic7312yes—
248C4⋊C8C2×Dic7311yescharacteristic
249C4⋊C8C2×Dic7311yescharacteristic
250C22⋊C8—1462no—
251C22⋊C8—1462no—
252C22⋊C8—1462no—
253C22⋊C8—1462no—
254C22⋊C8C2×Dic7312yes—
255C22⋊C8C2×Dic7312yes—
256C22⋊C8C2×Dic7312yes—
257#97—1462no—
258#97—1462no—
259#97C2×Dic7312yes—
260#97C2×Dic7312yes—
261C4×C8—1462no—
262C4×C8—1462no—
263C4×C8C2×Dic7311yescharacteristic
264C4×C8C2×Dic7311yescharacteristic
265C4×C8C22×D7311yescharacteristic
266C4×C8C22×D7311yescharacteristic
267C4×C8C22×D7312yes—
268#41—42no—
269C2×Q8C4⋊Dic7311yescharacteristic
270C2×D4C4⋊Dic7312yes—
271C2×D4C4⋊Dic7311yescharacteristic
272C22×C4C22×Dic7311yescharacteristic
273C22×C4C22×Dic7312yes—
274C22×C4C2×D29211yescharacteristic
275C22×C4C2×D29212yes—
276C22×C4C2×Dic14611yescharacteristic
277C22×C4C2×Dic14612yes—
278M16—24no—
279M16—42no—
280M16—2924no—
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—2924no—
284C2×C8—1462no—
285C2×C8—1462no—
286C2×C8—1462no—
287C2×C8—1462no—
288C2×C8C22×Dic7311yescharacteristic
289C2×C8C22×Dic7311yescharacteristic
290C2×C8C22×Dic7311yescharacteristic
291C2×C8C22×Dic7312yes—
292C2×C8C22×Dic7312yes—
293C2×C8C22×Dic7311yescharacteristic
294C4⋊C4C4⋊Dic7312yes—
295C4⋊C4C4⋊Dic7311yescharacteristic
296C4⋊C4C4⋊Dic7312yes—
297C4⋊C4C4⋊Dic7311yescharacteristic
298C22⋊C4C4⋊Dic7312yes—
299C22⋊C4C4⋊Dic7312yes—
300C22⋊C4C4⋊Dic7312yes—
301C42C22×Dic7311yescharacteristic
302C42C22×Dic7312yes—
303C42C2×D29211yescharacteristic
304C42C2×D29212yes—
305C42C2×Dic14611yescharacteristic
306C42C2×Dic14612yes—
307C42C23×D7311yescharacteristic
308C23C2×C4⋊Dic7311yescharacteristic
309C23C2×C4⋊Dic7312yes—
310Q8—41no—
311D4—42no—
312D4—41no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4C2×C4⋊Dic7311yescharacteristic
323C2×C4C2×C4⋊Dic7312yes—
324C2×C4C2×C4⋊Dic7311yescharacteristic
325C2×C4C2×C4⋊Dic7312yes—
326C2×C4C2×C4⋊Dic7311yescharacteristic
327C2×C4C2×C4⋊Dic7312yes—
328C2×C4C23×Dic7311yescharacteristic
329C2×C4C22×D29211yescharacteristic
330C2×C4C22×Dic14611yescharacteristic
331C8—21no—
332C8—22no—
333C8—21no—
334C8—21no—
335C8—22no—
336C8—2922no—
337C8—2922no—
338C8—2922no—
339C8—2922no—
340C8#1455659812yes—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22C22×C4⋊Dic7311yescharacteristic
348C4—21no—
349C4—22no—
350C4—22no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4C2×#1455659811yescharacteristic
356C4#1798935411yescharacteristic
357C4#1798938712yes—
358C2—41no—
359C2—42no—
360C2#2261849911yescharacteristic
361C2#2261852111yescharacteristic
362C2#2261854211yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2965C2
socleC22×C73C22×C4⋊C4
prime radicalC2×#41×C73D4
cosocleC42×C73C24
hypercenter#2965D73
hypocenterC73#17831
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #22608720C2semidirect
3. #22608716C2semidirect
4. #22608711C2semidirect
5. #22608698C2semidirect
6. #22608694C2semidirect
7. #22608683C2semidirect
8. #22608679C2semidirect
191. C73#17831semidirect

Maximal subgroups

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

subgroupindex
#226185972
#226087202
#226087162
#226087112
#226086982
#226086942
#226086832
#226086792
C73×#29652
#1783173