Finite Group Databasebeta

← #32975906

Subgroups — #32975906

Order 18688.

608 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#22618561C211yesmaximal, characteristic
2#432×D73C211yesmaximal, characteristic
3C4×M16×D73C211yesmaximal, characteristic
4#22607804C211yesmaximal, characteristic, complemented
5#22607803C211yesmaximal, characteristic, complemented
6#22607802C211yesmaximal, characteristic, complemented
7C73×#1291C211yesmaximal, characteristic, complemented
8C2×M16×D73—21no—
9C2×C42×D73C2211yescharacteristic
10#17988644C2211yescharacteristic
11#17988644C2211yescharacteristic
12#17988643—21no—
13#17988642—21no—
14#17988642—21no—
15#17988641C412yes—
16#17988639C412yes—
17#17988637—21no—
18#17988609C412yes—
19C4⋊C8×D73—21no—
20#17988549—21no—
21C22⋊C8×D73C412yes—
22C4×#11924012C2211yescharacteristic
23#17988539—21no—
24#17988539—21no—
25M16×Dic73—21no—
26C4×#11924011C412yes—
27#97×D73—21no—
28#97×D73—21no—
29C4×C8×D73C412yes—
30#432×C73C2211yescharacteristic
31#432×C73C2211yescharacteristic
32C4×M16×C73C2211yescharacteristic
33C22×C4×D73C2×C411yescharacteristic
34C22×C4×D73D411yescharacteristic
35C22×C4×D73Q811yescharacteristic
36C2×#11924012—21no—
37C2×#11924011—22no—
38C2×#11924011—22no—
39M16×D73—28no—
40C2×C8×D73—22no—
41C2×C8×D73—22no—
42C2×C4×Dic73C2×C411yescharacteristic
43C2×C4×Dic73D411yescharacteristic
44C2×C4×Dic73Q811yescharacteristic
45C42×D73C2×C411yescharacteristic
46C42×D73C2×C411yescharacteristic
47C42×D73C2×C411yescharacteristic
48C42×D73C2×C411yescharacteristic
49C42×D73D411yescharacteristic
50C42×D73D411yescharacteristic
51C42×D73D411yescharacteristic
52C42×D73D411yescharacteristic
53C4⋊#10596831—21no—
54C4⋊#10596831C2×C412yes—
55#14556520—22no—
56#14556520—22no—
57C22⋊#10596831—21no—
58C22⋊#10596831C2×C412yes—
59#14556503—22no—
60#14556503—22no—
61#14556502—21no—
62#14556502—21no—
63#14556502—21no—
64#14556501—22no—
65#14556501—22no—
66C4×#10596831C2×C412yes—
67C8×Dic73—22no—
68C8×Dic73—22no—
69C2×M16×C73—21no—
70C2×C42×C73C2311yescharacteristic
71C4⋊C8×C73—21no—
72C4⋊C8×C73C2×C412yes—
73C22⋊C8×C73—21no—
74C22⋊C8×C73C2×C412yes—
75#97×C73—21no—
76#97×C73—21no—
77#97×C73—21no—
78C4×C8×C73C2×C412yes—
79C23×D73C4⋊C411yescharacteristic
80C22×Dic73C4⋊C411yescharacteristic
81C22×Dic73C4⋊C411yescharacteristic
82C22×Dic73C4⋊C411yescharacteristic
83C2×C4×D73—24no—
84C2×C4×D73—42no—
85C2×C4×D73—42no—
86C2×C4×D73C4211yescharacteristic
87C2×C4×D73C4211yescharacteristic
88C2×C4×D73C22⋊C411yescharacteristic
89C2×C4×D73C22⋊C411yescharacteristic
90C2×C4×D73C22⋊C411yescharacteristic
91C2×C4×D73C22⋊C411yescharacteristic
92C2×C4×D73C22⋊C411yescharacteristic
93C2×C4×D73C22⋊C411yescharacteristic
94C2×C4×D73C4⋊C411yescharacteristic
95C2×C4×D73C4⋊C411yescharacteristic
96C2×C4×D73C4⋊C411yescharacteristic
97C2×C4×D73C4⋊C411yescharacteristic
98#11924012—24no—
99#11924011—28no—
100#11924011—44no—
101C2×#10596831—22no—
102C2×#10596831—22no—
103C2×#10596831—22no—
104C8×D73—28no—
105C8×D73—44no—
106C4×Dic73C4211yescharacteristic
107C4×Dic73C4211yescharacteristic
108C4×Dic73C22⋊C411yescharacteristic
109C4×Dic73C22⋊C411yescharacteristic
110C4×Dic73C22⋊C411yescharacteristic
111C4×Dic73C22⋊C411yescharacteristic
112C4×Dic73C22⋊C411yescharacteristic
113C4×Dic73C22⋊C411yescharacteristic
114C4×Dic73C4⋊C411yescharacteristic
115C4×Dic73C4⋊C411yescharacteristic
116C4×Dic73C4⋊C411yescharacteristic
117C4×Dic73C4⋊C411yescharacteristic
118C22×C4×C73C22×C411yescharacteristic
119C22×C4×C73C2×D411yescharacteristic
120C22×C4×C73C2×Q811yescharacteristic
121M16×C73—24no—
122C2×C8×C73—22no—
123C2×C8×C73—22no—
124C2×C8×C73—22no—
125C42×C73C22×C411yescharacteristic
126C42×C73C22×C411yescharacteristic
127C42×C73C2×D411yescharacteristic
128C42×C73C2×D411yescharacteristic
129C23×C73C2×C4⋊C411yescharacteristic
130C22×D73—22no—
131C22×D73—22no—
132C22×D73—41no—
133C22×D73#9511yescharacteristic
134C22×D73#9511yescharacteristic
135C2×C4×C73—22no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73C2×C4211yescharacteristic
139C2×C4×C73C2×C22⋊C411yescharacteristic
140C2×C4×C73C2×C22⋊C411yescharacteristic
141C2×C4×C73C2×C22⋊C411yescharacteristic
142C2×C4×C73C2×C4⋊C411yescharacteristic
143C2×C4×C73C2×C4⋊C411yescharacteristic
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—41no—
147C2×Dic73#9511yescharacteristic
148C2×Dic73#9511yescharacteristic
149C2×Dic73#9511yescharacteristic
150C2×Dic73#9511yescharacteristic
151C2×Dic73#9511yescharacteristic
152C2×Dic73#9511yescharacteristic
153C4×D73—22no—
154C4×D73—22no—
155C4×D73—22no—
156C4×D73—22no—
157C4×D73—22no—
158C4×D73—22no—
159C4×D73—22no—
160C4×D73—41no—
161C4×D73—41no—
162C4×D73—41no—
163C4×D73—41no—
164C4×D73#10414yes—
165C8×C73—24no—
166C8×C73—42no—
167C8×C73—42no—
168#10596831—24no—
169#10596831—42no—
170#10596831—42no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73C2×#9511yescharacteristic
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—44no—
180C2×D73#33812yes—
181C2×D73#33912yes—
182C4×C73—21no—
183C4×C73—21no—
184C4×C73—21no—
185C4×C73—21no—
186C4×C73—21no—
187C4×C73C2×#10412yes—
188Dic73—21no—
189Dic73—21no—
190Dic73—21no—
191Dic73—21no—
192Dic73#33912yes—
193Dic73#34412yes—
194#7994—731nomaximal, Sylow
195C2×C73—41no—
196C2×C73C2×#33811yescharacteristic
197C2×C73C2×#33911yescharacteristic
198C2×C73C2×#34411yescharacteristic
199D73—22no—
200D73—22no—
201#2920—731no—
202C2×#432—731no—
203C2×C4×M16—731no—
204#1291—731no—
205#1291—731no—
206#1291—731no—
207#1291D7311yescharacteristic, complemented
208C73#799411yescharacteristic, complemented, Sylow
209C22×M16—1461no—
210C22×C42—731no—
211#432—731no—
212#432—732no—
213#432—731no—
214#432—1461no—
215#432—1461no—
216#432—1461no—
217#432C2×D7311yescharacteristic
218#432C2×D7311yescharacteristic
219#431—732no—
220#431—1461no—
221#423—732no—
222C2×C4⋊C8—1461no—
223#407—1461no—
224C2×C22⋊C8—732no—
225C4×M16—731no—
226C4×M16—732no—
227C4×M16—1461no—
228C4×M16—1461no—
229C4×M16—1461no—
230C4×M16C2×D7311yescharacteristic
231C2×#97—1461no—
232C2×#97—1461no—
233C2×C4×C8—732no—
234C23×C4—731no—
235C23×C4—731no—
236C23×C4—731no—
237C2×M16—21no—
238C2×M16—1462no—
239C2×M16—1462no—
240C2×M16—1468no—
241C2×M16—1461no—
242C22×C8—1462no—
243C22×C8—1462no—
244C2×C42—731no—
245C2×C42—731no—
246C2×C42—731no—
247C2×C42—731no—
248C2×C42—731no—
249C2×C42—731no—
250C2×C42—731no—
251C2×C42—731no—
252C2×C42—731no—
253C2×C42—731no—
254C2×C42—731no—
255C2×C42C22×D7311yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—732no—
258C4⋊C8—1462no—
259C4⋊C8—1462no—
260C4⋊C8—1461no—
261C4⋊C8C4×D7312yes—
262C22⋊C8—21no—
263C22⋊C8—732no—
264C22⋊C8—1462no—
265C22⋊C8—1462no—
266C22⋊C8—1461no—
267C22⋊C8C4×D7312yes—
268#97—21no—
269#97—21no—
270#97—21no—
271#97—1462no—
272#97—1462no—
273#97—1461no—
274#97—1461no—
275#97—1461no—
276C4×C8—732no—
277C4×C8—1462no—
278C4×C8—1462no—
279C4×C8C4×D7312yes—
280C24—731no—
281C22×C4—2922no—
282C22×C4—2922no—
283C22×C4—731no—
284C22×C4—731no—
285C22×C4—731no—
286C22×C4—731no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—731no—
290C22×C4—731no—
291C22×C4—731no—
292C22×C4—731no—
293C22×C4—731no—
294C22×C4—731no—
295C22×C4—731no—
296C22×C4—731no—
297C22×C4—731no—
298C22×C4—1464no—
299C22×C4C2×C4×D7311yescharacteristic
300C22×C4D4×D7311yescharacteristic
301C22×C4Q8×D7311yescharacteristic
302M16—24no—
303M16—2924no—
304M16—1468no—
305M16—1464no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—2924no—
310C2×C8—1468no—
311C2×C8—1462no—
312C2×C8—1462no—
313C2×C8—1462no—
314C42—731no—
315C42—731no—
316C42—731no—
317C42—731no—
318C42—731no—
319C42—731no—
320C42—731no—
321C42—731no—
322C42—731no—
323C42—731no—
324C42—731no—
325C42—731no—
326C42C2×C4×D7311yescharacteristic
327C42C2×C4×D7311yescharacteristic
328C42D4×D7311yescharacteristic
329C42D4×D7311yescharacteristic
330C23—2921no—
331C23—731no—
332C23—731no—
333C23—1462no—
334C23—1462no—
335C23C4⋊C4×D7311yescharacteristic
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—2921no—
340C2×C4—2921no—
341C2×C4—2921no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—731no—
345C2×C4—731no—
346C2×C4—734no—
347C2×C4—731no—
348C2×C4—731no—
349C2×C4—731no—
350C2×C4—731no—
351C2×C4—1462no—
352C2×C4—1462no—
353C2×C4—1462no—
354C2×C4—1462no—
355C2×C4—1462no—
356C2×C4—1462no—
357C2×C4—1462no—
358C2×C4—1462no—
359C2×C4—1462no—
360C2×C4C42×D7311yescharacteristic
361C2×C4C22⋊C4×D7311yescharacteristic
362C2×C4C22⋊C4×D7311yescharacteristic
363C2×C4C22⋊C4×D7311yescharacteristic
364C2×C4C4⋊C4×D7311yescharacteristic
365C2×C4C4⋊C4×D7311yescharacteristic
366C8—24no—
367C8—42no—
368C8—42no—
369C8—2922no—
370C8—2922no—
371C8—1464no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—2924no—
376C22—732no—
377C22—732no—
378C22—1461no—
379C22—1461no—
380C22—1461no—
381C22—1461no—
382C22#95×D7311yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—732no—
389C4—732no—
390C4—1461no—
391C4—1461no—
392C4—1461no—
393C4—1461no—
394C4#104×D7312yes—
395C2—41no—
396C2—1462no—
397C2—1462no—
398C2#338×D7311yescharacteristic
399C2#339×D7311yescharacteristic
400C2#344×D7311yescharacteristic
subgroupG/H
centerC22#95×D73
commutatorC2×C4×C73C2×C42
FrattiniC2×C42C22×D73
FittingC73×#1291C2
socleC22×C73C2×#95
prime radicalC23×D73C4⋊C4
cosocleC2×C42×C73C23
hypercenter#1291D73
hypocenterC73#7994
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1291

Complements

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

NH ≅ G/Ntype
4. #22607804C2semidirect
5. #22607803C2semidirect
6. #22607802C2semidirect
7. C73×#1291C2semidirect
207. #1291D73semidirect
208. C73#7994semidirect

Maximal subgroups

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

subgroupindex
#226185612
#432×D732
C4×M16×D732
#226078042
#226078032
#226078022
C73×#12912
#799473