Finite Group Databasebeta

← #22619960

Subgroups — #22619960

Order 9344.

428 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989134C211yesmaximal, characteristic
2C4×Q8×D73C211yesmaximal, characteristic, complemented
3#17988907C211yesmaximal, characteristic, complemented
4#17988904C211yesmaximal, characteristic, complemented
5#17988871C211yesmaximal, characteristic, complemented
6#17988870C211yesmaximal, characteristic, complemented
7#17988786C211yesmaximal, characteristic, complemented
8#17988785C211yesmaximal, characteristic, complemented
9#17988727C211yesmaximal, characteristic, complemented
10#17988724C211yesmaximal, characteristic, complemented
11C4×#11924017C211yesmaximal, characteristic, complemented
12C4×#11924015C211yesmaximal, characteristic, complemented
13C4×#11924016C211yesmaximal, characteristic, complemented
14#17988638C211yesmaximal, characteristic, complemented
15C4×SD16×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17C2×Q8×D73C2211yescharacteristic
18C2×#11924017C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×#11924015C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556587C2211yescharacteristic
23#14556577—21no—
24#14556566C2211yescharacteristic
25#14556564—21no—
26#14556562C2211yescharacteristic
27Q8×Dic73C2211yescharacteristic
28C4×Dic146—21no—
29C4×Dic146C2211yescharacteristic
30#14556556—21no—
31#14556556C2211yescharacteristic
32C4×D292C2211yescharacteristic
33C4×C22⋊D73—21no—
34C4⋊C4×D73—21no—
35C4⋊C4×D73C2211yescharacteristic
36C42×D73—21no—
37C42×D73C2211yescharacteristic
38#14556523C2211yescharacteristic
39#14556522C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic
51C4×#10596831C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59#11924028—44no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63Q8×D73—22no—
64Q8×D73—22no—
65C2×D292—21no—
66C2×D292C2311yescharacteristic
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73D411yescharacteristic
74C2×C4×D73D411yescharacteristic
75C2×C4×D73C2311yescharacteristic
76#11924017—22no—
77#11924016—22no—
78#11924015—22no—
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C4⋊Dic73—21no—
82C4⋊Dic73C2311yescharacteristic
83C4⋊Dic73C2311yescharacteristic
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89#11924005—21no—
90#11924005—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73D411yescharacteristic
95C4×Dic73D411yescharacteristic
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73—21no—
100SD16×C73—22no—
101C2×C8×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C4⋊C4×C73—21no—
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C42×C73—21no—
108C42×C73C2311yescharacteristic
109C23×C73—21no—
110C22×D73—21no—
111C22×D73C2×D411yescharacteristic
112Q8×C73—21no—
113Q8×C73#4112yescomplemented
114D4×C73—21no—
115D4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—42no—
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2411yescharacteristic
123C22⋊D73—42no—
124C22⋊D73—42no—
125C22⋊D73—42no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132D292—21no—
133D292—21no—
134D292—42no—
135C4×D73—24no—
136C4×D73—21no—
137C4×D73—21no—
138C4×D73—41no—
139C4×D73—42no—
140C4×D73—42no—
141C4×D73SD1614yescomplemented
142Dic146—24no—
143Dic146—21no—
144Dic146—42no—
145Dic146#4112yescomplemented
146C8×C73—21no—
147C8×C73—21no—
148#10596831—21no—
149#10596831—21no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73C22×D411yescharacteristic
154C2×D73—21no—
155C2×D73—21no—
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C2×D73C2×SD1612yes—
160C4×C73—22no—
161C4×C73—21no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73C2×SD1612yes—
165C4×C73C2×#4111yescharacteristic
166C4×C73C2×#4111yescharacteristic
167Dic73—21no—
168Dic73—22no—
169Dic73—21no—
170Dic73—41no—
171Dic73—41no—
172Dic73C2×SD1612yes—
173C2×C73—81no—
174C2×C73#52511yescharacteristic
175C2×C73C22×SD1611yescharacteristic
176C2×C73#57511yescharacteristic
177D73—22no—
178D73—81no—
179#3103—731nomaximal, Sylow
180C73#310311yescharacteristic, complemented, Sylow
181#532—731no—
182C2×C4×Q8—731no—
183#481—731no—
184#481—731no—
185#475—731no—
186#475—731no—
187#460—731no—
188#460—731no—
189#448—731no—
190#448—731no—
191C4×SD16—731no—
192C4×SD16—731no—
193C4×SD16—731no—
194C4×SD16D7311yescharacteristic, complemented
195#431—731no—
196C2×#41—1461no—
197C22×Q8—731no—
198C2×SD16—731no—
199C2×SD16—731no—
200C2×SD16—731no—
201C2×SD16C2×D7311yescharacteristic
202C4⋊Q8—731no—
203#127—731no—
204#124—1461no—
205#121—731no—
206#121—731no—
207#121—1461no—
208C4×Q8—731no—
209C4×Q8—731no—
210C4×Q8—731no—
211C4×Q8—1461no—
212C4×Q8—1461no—
213C4×Q8C2×D7311yescharacteristic
214C4×D4—731no—
215C4×D4—1461no—
216C4×D4C2×D7311yescharacteristic
217C2×C4⋊C4—731no—
218C2×C4⋊C4—1461no—
219C2×C42—731no—
220C2×C42—1461no—
221#106—731no—
222#106—731no—
223#106—731no—
224#106C2×D7311yescharacteristic
225C4⋊C8—731no—
226C4⋊C8—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103C2×D7311yescharacteristic
231#102—731no—
232#102—731no—
233#102—731no—
234#102C2×D7311yescharacteristic
235C22⋊C8—731no—
236C22⋊C8—731no—
237C4×C8—731no—
238C4×C8C2×D7311yescharacteristic
239#41—2924no—
240C2×Q8—731no—
241C2×Q8—1461no—
242C2×Q8—1461no—
243C2×Q8—1462no—
244C2×Q8—1462no—
245C2×Q8C22×D7311yescharacteristic
246C2×D4—731no—
247C2×D4—1461no—
248C2×D4—1461no—
249C2×D4—1461no—
250C2×D4—1461no—
251C2×D4C22×D7311yescharacteristic
252C22×C4—21no—
253C22×C4—731no—
254C22×C4—731no—
255C22×C4—731no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4—1461no—
259SD16—22no—
260SD16—1462no—
261SD16—1462no—
262SD16—1462no—
263C2×C8—731no—
264C2×C8—731no—
265C2×C8C22×D7311yescharacteristic
266C2×C8C22×D7311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—731no—
269C4⋊C4—731no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4C22×D7311yescharacteristic
276C4⋊C4C22×D7311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C42—21no—
282C42—731no—
283C42—731no—
284C42—731no—
285C42—1461no—
286C42—1461no—
287C42—1461no—
288C42C22×D7311yescharacteristic
289C23—21no—
290C23—731no—
291C23—1461no—
292Q8—21no—
293Q8—2922no—
294Q8—732no—
295Q8—1464no—
296Q8—1461no—
297Q8#1192402812yescomplemented
298D4—21no—
299D4—21no—
300D4—2922no—
301D4—2922no—
302D4—2922no—
303D4—2922no—
304D4—1461no—
305D4—1461no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—2921no—
311C2×C4—2922no—
312C2×C4—2922no—
313C2×C4—731no—
314C2×C4—734no—
315C2×C4—731no—
316C2×C4—731no—
317C2×C4—1464no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4D4×D7311yescharacteristic
324C2×C4D4×D7311yescharacteristic
325C2×C4C23×D7311yescharacteristic
326C8—21no—
327C8—21no—
328C8—1461no—
329C8—1461no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—2921no—
334C22—2921no—
335C22—2921no—
336C22—732no—
337C22—1461no—
338C22—1461no—
339C22C2×D4×D7311yescharacteristic
340C4—21no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—2921no—
345C4—2921no—
346C4—732no—
347C4—1461no—
348C4—1461no—
349C4—1462no—
350C4SD16×D7312yes—
351C4#41×D7311yescharacteristic
352C4C2×#1192402811yescharacteristic
353C2—81no—
354C2—5841no—
355C2—1462no—
356C2#1798909611yescharacteristic
357C2C2×SD16×D7311yescharacteristic
358C2#1798938411yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×SD16×C73C2
socleC22×C73C22×D4
hypercenterC4×SD16D73
hypocenterC73#3103
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D73C2semidirect
3. #17988907C2semidirect
4. #17988904C2semidirect
5. #17988871C2semidirect
6. #17988870C2semidirect
7. #17988786C2semidirect
8. #17988785C2semidirect
9. #17988727C2semidirect
10. #17988724C2semidirect
11. C4×#11924017C2semidirect
12. C4×#11924015C2semidirect
13. C4×#11924016C2semidirect
14. #17988638C2semidirect
15. C4×SD16×C73C2semidirect
113. Q8×C73#41semidirect
141. C4×D73SD16semidirect
145. Dic146#41semidirect
180. C73#3103semidirect
194. C4×SD16D73semidirect
297. Q8#11924028semidirect