Finite Group Databasebeta

← #32976367

Subgroups — #32976367

Order 18688.

522 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618563C211yesmaximal, characteristic
2#22618561C211yesmaximal, characteristic
3#432×D73C211yesmaximal, characteristic
4#22607842C211yesmaximal, characteristic, complemented
5#22607841C211yesmaximal, characteristic, complemented
6#22607841C211yesmaximal, characteristic, complemented
7C73×#1307C211yesmaximal, characteristic, complemented
8C2×C42×D73C2211yescharacteristic
9#17988644C2211yescharacteristic
10#17988644C2211yescharacteristic
11#17988643—21no—
12#17988643—21no—
13#17988643—21no—
14#17988642—21no—
15#17988642—21no—
16#17988641C412yes—
17#17988639—21no—
18#17988639—21no—
19#17988639—21no—
20#17988637C412yes—
21#17988611C2211yescharacteristic
22#17988609—21no—
23C4⋊C8×D73—21no—
24#17988550C412yes—
25#17988549C412yes—
26C22⋊C8×D73C412yes—
27#17988539—21no—
28M16×Dic73C412yes—
29#97×D73—21no—
30#432×C73C2211yescharacteristic
31#432×C73C2211yescharacteristic
32#423×C73C2211yescharacteristic
33C22×C4×D73C2×C411yescharacteristic
34C22×C4×D73C2×C411yescharacteristic
35C22×C4×D73C2×C411yescharacteristic
36C2×#11924012C2×C412yes—
37C2×#11924011—22no—
38C2×C8×D73—22no—
39C2×C4×Dic73C2×C411yescharacteristic
40C2×C4×Dic73C2×C411yescharacteristic
41C2×C4×Dic73C2×C411yescharacteristic
42C42×D73D411yescharacteristic
43C42×D73D411yescharacteristic
44C42×D73D411yescharacteristic
45C42×D73D411yescharacteristic
46C42×D73D411yescharacteristic
47C42×D73D411yescharacteristic
48C42×D73Q811yescharacteristic
49C42×D73Q811yescharacteristic
50C4⋊#10596831—21no—
51C4⋊#10596831—21no—
52C4⋊#10596831—21no—
53C4⋊#10596831—21no—
54#14556520—22no—
55#14556520—22no—
56C22⋊#10596831C2×C412yes—
57C22⋊#10596831C2×C412yes—
58#14556503—22no—
59#14556503—22no—
60#14556503—22no—
61#14556503—22no—
62#14556502—21no—
63#14556502—21no—
64#14556501—22no—
65#14556501—22no—
66C8×Dic73—22no—
67C8×Dic73—22no—
68C2×M16×C73C2×C412yes—
69C2×C42×C73C2311yescharacteristic
70C4⋊C8×C73—21no—
71C4⋊C8×C73—21no—
72C4⋊C8×C73—21no—
73C4⋊C8×C73—21no—
74C22⋊C8×C73C2×C412yes—
75C22⋊C8×C73C2×C412yes—
76#97×C73—21no—
77#97×C73—21no—
78C23×D73C4211yescharacteristic
79C22×Dic73C4211yescharacteristic
80C22×Dic73C4211yescharacteristic
81C22×Dic73C4211yescharacteristic
82C2×C4×D73—42no—
83C2×C4×D73—41no—
84C2×C4×D73—41no—
85C2×C4×D73—42no—
86C2×C4×D73C22⋊C411yescharacteristic
87C2×C4×D73C22⋊C411yescharacteristic
88C2×C4×D73C22⋊C411yescharacteristic
89C2×C4×D73C22⋊C411yescharacteristic
90C2×C4×D73C22⋊C411yescharacteristic
91C2×C4×D73C22⋊C411yescharacteristic
92C2×C4×D73C4⋊C411yescharacteristic
93C2×C4×D73C4⋊C411yescharacteristic
94C2×C4×D73C4⋊C411yescharacteristic
95C2×C4×D73C4⋊C411yescharacteristic
96C2×C4×D73C4⋊C411yescharacteristic
97C2×C4×D73C4⋊C411yescharacteristic
98#11924012—42no—
99#11924011—44no—
100C2×#10596831—22no—
101C2×#10596831—22no—
102C2×#10596831—22no—
103C8×D73—44no—
104C4×Dic73C22⋊C411yescharacteristic
105C4×Dic73C22⋊C411yescharacteristic
106C4×Dic73C22⋊C411yescharacteristic
107C4×Dic73C22⋊C411yescharacteristic
108C4×Dic73C22⋊C411yescharacteristic
109C4×Dic73C22⋊C411yescharacteristic
110C4×Dic73C4⋊C411yescharacteristic
111C4×Dic73C4⋊C411yescharacteristic
112C4×Dic73C4⋊C411yescharacteristic
113C4×Dic73C4⋊C411yescharacteristic
114C4×Dic73C4⋊C411yescharacteristic
115C4×Dic73C4⋊C411yescharacteristic
116C22×C4×C73C22×C411yescharacteristic
117C22×C4×C73C22×C411yescharacteristic
118C22×C4×C73C22×C411yescharacteristic
119M16×C73—42no—
120C2×C8×C73—22no—
121C2×C8×C73—22no—
122C2×C8×C73—22no—
123C42×C73C2×D411yescharacteristic
124C42×C73C2×D411yescharacteristic
125C42×C73C2×D411yescharacteristic
126C42×C73C2×Q811yescharacteristic
127C23×C73C2×C4211yescharacteristic
128C22×D73—22no—
129C22×D73—41no—
130C22×D73—41no—
131C22×D73#9511yescharacteristic
132C22×D73#9511yescharacteristic
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73C2×C22⋊C411yescharacteristic
138C2×C4×C73C2×C22⋊C411yescharacteristic
139C2×C4×C73C2×C22⋊C411yescharacteristic
140C2×C4×C73C2×C4⋊C411yescharacteristic
141C2×C4×C73C2×C4⋊C411yescharacteristic
142C2×C4×C73C2×C4⋊C411yescharacteristic
143C2×Dic73—22no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146C2×Dic73#9511yescharacteristic
147C2×Dic73#9511yescharacteristic
148C2×Dic73#9511yescharacteristic
149C2×Dic73#9511yescharacteristic
150C2×Dic73#9511yescharacteristic
151C2×Dic73#9511yescharacteristic
152C4×D73—22no—
153C4×D73—22no—
154C4×D73—21no—
155C4×D73—21no—
156C4×D73—21no—
157C4×D73—21no—
158C4×D73—22no—
159C4×D73—22no—
160C4×D73—41no—
161C4×D73—41no—
162C4×D73—41no—
163C4×D73—41no—
164C4×D73—41no—
165C4×D73—41no—
166C8×C73—42no—
167C8×C73—42no—
168C8×C73—42no—
169#10596831—42no—
170#10596831—42no—
171#10596831—42no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—21no—
175C22×C73C2×#9511yescharacteristic
176C2×D73—21no—
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—21no—
181C2×D73—44no—
182C2×D73#34412yes—
183C4×C73—21no—
184C4×C73—21no—
185C4×C73—21no—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73#41311yescharacteristic
189C4×C73#41311yescharacteristic
190Dic73—21no—
191Dic73—21no—
192Dic73—21no—
193Dic73—21no—
194Dic73—21no—
195Dic73#34412yes—
196#8118—731nomaximal, Sylow
197C2×C73—41no—
198C2×C73#174211yescharacteristic
199C2×C73C2×#34411yescharacteristic
200C2×C73C2×#34411yescharacteristic
201D73—22no—
202D73—41no—
203#2920—731no—
204#2920—731no—
205C2×#432—731no—
206#1307—731no—
207#1307—731no—
208#1307—731no—
209#1307D7311yescharacteristic, complemented
210C73#811811yescharacteristic, complemented, Sylow
211C22×C42—731no—
212#432—731no—
213#432—731no—
214#432—732no—
215#432—1461no—
216#432—1461no—
217#432—1461no—
218#432—1461no—
219#432—1461no—
220#432C2×D7311yescharacteristic
221#432C2×D7311yescharacteristic
222#431—732no—
223#431—1461no—
224#431—1461no—
225#431—1461no—
226#423—731no—
227#423—1461no—
228#423C2×D7311yescharacteristic
229C2×C4⋊C8—1461no—
230#407—732no—
231#407—732no—
232C2×C22⋊C8—732no—
233C4×M16—732no—
234C4×M16—1461no—
235C2×#97—1461no—
236C23×C4—731no—
237C23×C4—731no—
238C23×C4—731no—
239C2×M16—732no—
240C2×M16—1462no—
241C2×M16C4×D7312yes—
242C22×C8—1462no—
243C2×C42—731no—
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×C42C22×D7311yescharacteristic
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—1462no—
260C4⋊C8—1462no—
261C4⋊C8—1461no—
262C4⋊C8—1461no—
263C4⋊C8—1461no—
264C4⋊C8—1461no—
265C22⋊C8—732no—
266C22⋊C8—732no—
267C22⋊C8—1462no—
268C22⋊C8—1462no—
269C22⋊C8—1462no—
270C22⋊C8—1462no—
271C22⋊C8C4×D7312yes—
272C22⋊C8C4×D7312yes—
273#97—21no—
274#97—21no—
275#97—1462no—
276#97—1462no—
277#97—1461no—
278#97—1461no—
279C4×C8—1462no—
280C4×C8—1462no—
281C24—731no—
282C22×C4—2921no—
283C22×C4—2921no—
284C22×C4—2922no—
285C22×C4—2922no—
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—731no—
299C22×C4—731no—
300C22×C4—731no—
301C22×C4C2×C4×D7311yescharacteristic
302C22×C4C2×C4×D7311yescharacteristic
303C22×C4C2×C4×D7311yescharacteristic
304M16—42no—
305M16—2924no—
306M16—2922no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—2924no—
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—
326C42D4×D7311yescharacteristic
327C42D4×D7311yescharacteristic
328C42D4×D7311yescharacteristic
329C42Q8×D7311yescharacteristic
330C23—2921no—
331C23—2921no—
332C23—731no—
333C23—731no—
334C23—1462no—
335C23C42×D7311yescharacteristic
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—2921no—
341C2×C4—2921no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—2921no—
345C2×C4—2921no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—731no—
349C2×C4—731no—
350C2×C4—731no—
351C2×C4—731no—
352C2×C4—731no—
353C2×C4—731no—
354C2×C4—1462no—
355C2×C4—1462no—
356C2×C4—1462no—
357C2×C4—1462no—
358C2×C4—1462no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4—1461no—
363C2×C4C22⋊C4×D7311yescharacteristic
364C2×C4C22⋊C4×D7311yescharacteristic
365C2×C4C22⋊C4×D7311yescharacteristic
366C2×C4C4⋊C4×D7311yescharacteristic
367C2×C4C4⋊C4×D7311yescharacteristic
368C2×C4C4⋊C4×D7311yescharacteristic
369C8—42no—
370C8—42no—
371C8—42no—
372C8—2922no—
373C8—2922no—
374C8—2922no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—2924no—
379C22—732no—
380C22—1461no—
381C22—1461no—
382C22—1461no—
383C22—1461no—
384C22—1461no—
385C22#95×D7311yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—732no—
392C4—1461no—
393C4—1461no—
394C4—1461no—
395C4—1461no—
396C4—1461no—
397C4#1798856811yescharacteristic
398C4#1798857011yescharacteristic
399C2—41no—
400C2—2921no—
401C2—1462no—
402C2#2260966811yescharacteristic
403C2#344×D7311yescharacteristic
404C2#344×D7311yescharacteristic
subgroupG/H
centerC22#95×D73
commutatorC23×C73C2×C42
FrattiniC2×C42C22×D73
FittingC73×#1307C2
socleC22×C73C2×#95
prime radicalC23×D73C42
cosocleC2×C42×C73C23
hypercenter#1307D73
hypocenterC73#8118
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
4. #22607842C2semidirect
5. #22607841C2semidirect
6. #22607841C2semidirect
7. C73×#1307C2semidirect
209. #1307D73semidirect
210. C73#8118semidirect

Maximal subgroups

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

subgroupindex
#226185632
#226185612
#432×D732
#226078422
#226078412
C73×#13072
#811873