Finite Group Databasebeta

← #22621464

Subgroups — #22621464

Order 9344.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556618C211yesmaximal, characteristic, complemented
2C2×#14556611C211yesmaximal, characteristic, complemented
3#17989256C211yesmaximal, characteristic, complemented
4#17989234C211yesmaximal, characteristic, complemented
5#17988975C211yesmaximal, characteristic, complemented
6#17988832C211yesmaximal, characteristic, complemented
7#17988821C211yesmaximal, characteristic, complemented
8#17988807C211yesmaximal, characteristic, complemented
9#17988781C211yesmaximal, characteristic, complemented
10#17988752C211yesmaximal, characteristic, complemented
11#17988734C211yesmaximal, characteristic, complemented
12#17988719C211yesmaximal, characteristic, complemented
13#17988690C211yesmaximal, characteristic, complemented
14#17988655C211yesmaximal, characteristic, complemented
15#449×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924028C2211yescharacteristic
18C2×D4×D73C2211yescharacteristic
19#14556618—24no—
20#14556611—24no—
21C2×#11924018C2211yescharacteristic, complemented
22C2×#11924017C2211yescharacteristic, complemented
23C2×#11924016C2211yescharacteristic, complemented
24C2×#11924015C2211yescharacteristic
25C2×D584C2211yescharacteristic
26C2×#11924013C2211yescharacteristic
27C2×#11924013C2211yescharacteristic
28C2×#11924011C2211yescharacteristic
29C22×#10596831C2211yescharacteristic, complemented
30#14556587—21no—
31#14556587C2211yescharacteristic, complemented
32#14556578C2211yescharacteristic
33#14556573—21no—
34#14556571C2211yescharacteristic
35#14556565—21no—
36#14556565C2211yescharacteristic, complemented
37#14556562—21no—
38#14556562—21no—
39#14556562C2211yescharacteristic
40#14556559—21no—
41Q8×Dic73C2211yescharacteristic, complemented
42#14556553C2211yescharacteristic
43C4×C22⋊D73—21no—
44C4×C22⋊D73C2211yescharacteristic
45C22⋊C4×D73—21no—
46#14556524C2211yescharacteristic, complemented
47#14556520C2211yescharacteristic, complemented
48#14556516C2211yescharacteristic, complemented
49#14556513C2211yescharacteristic
50#14556512C2211yescharacteristic
51#14556511C2211yescharacteristic, complemented
52#14556503C2211yescharacteristic
53#14556501C2211yescharacteristic, complemented
54C2×#41×C73C2211yescharacteristic, complemented
55C2×SD16×C73C2211yescharacteristic
56C2×D8×C73C2211yescharacteristic
57#121×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic, complemented
59#102×C73C2211yescharacteristic, complemented
60C22⋊C8×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62#11924029—22no—
63#11924029—41no—
64#11924028—22no—
65#11924028—41no—
66C2×Dic146C2311yescharacteristic
67C2×D292—21no—
68C2×D292C2311yescharacteristic
69C2×D292C2311yescharacteristic
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73—21no—
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75C2×C22⋊D73—21no—
76C2×C22⋊D73D411yescharacteristic
77D4×D73—22no—
78D4×D73—41no—
79C2×C4×D73—21no—
80C2×C4×D73—21no—
81C2×C4×D73—21no—
82C2×C4×D73C2311yescharacteristic
83#11924018—22no—
84#11924017—41no—
85#11924016—22no—
86#11924015D414yescomplemented
87D584—22no—
88#11924013—22no—
89#11924013—22no—
90#11924011—22no—
91C2×#10596831—22no—
92C2×#10596831C2311yescharacteristic
93C2×#10596831C2311yescharacteristic
94C4⋊Dic73—21no—
95C4⋊Dic73—21no—
96C4⋊Dic73C2311yescharacteristic
97#11924007D411yescharacteristic
98C22⋊Dic73—21no—
99C22⋊Dic73—21no—
100C22⋊Dic73—21no—
101C22⋊Dic73D411yescharacteristic
102#11924005—21no—
103#11924005—21no—
104#11924005—21no—
105#11924005D411yescharacteristic
106C4×Dic73—21no—
107C4×Dic73C2311yescharacteristic
108#41×C73—22no—
109#41×C73—41no—
110C2×Q8×C73C2311yescharacteristic
111C2×D4×C73—21no—
112C2×D4×C73—21no—
113C2×D4×C73C2311yescharacteristic
114C2×D4×C73C2311yescharacteristic
115C22×C4×C73—21no—
116C22×C4×C73C2311yescharacteristic
117SD16×C73—22no—
118D8×C73—41no—
119C2×C8×C73C2311yescharacteristic
120C2×C8×C73C2311yescharacteristic
121C4⋊C4×C73C2311yescharacteristic
122C22⋊C4×C73—21no—
123C23×C73—21no—
124C23×C73—21no—
125C23×C73C2×D411yescharacteristic
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—42no—
129C22×D73—42no—
130C22×D73—81no—
131C22×D73C2×D411yescharacteristic
132Q8×C73—21no—
133Q8×C73C2×D412yes—
134D4×C73—21no—
135D4×C73—21no—
136D4×C73—21no—
137D4×C73—21no—
138D4×C73—42no—
139D4×C73—81no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—42no—
145C2×C4×C73C2×D411yescharacteristic
146C2×C4×C73C2411yescharacteristic
147C22⋊D73—41no—
148C22⋊D73—42no—
149C22⋊D73—42no—
150C22⋊D73—42no—
151C22⋊D73—81no—
152C22⋊D73—81no—
153C22⋊D73—81no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73C2×D411yescharacteristic
157C2×Dic73C2×D411yescharacteristic
158C2×Dic73C2×D411yescharacteristic
159D292—21no—
160D292—21no—
161D292—21no—
162D292—42no—
163D292C2×D412yes—
164C4×D73—21no—
165C4×D73—21no—
166C4×D73—42no—
167C4×D73—42no—
168C4×D73—81no—
169Dic146—21no—
170Dic146—21no—
171C8×C73—21no—
172C8×C73—21no—
173#10596831—21no—
174#10596831C2×D412yes—
175C22×C73—21no—
176C22×C73—21no—
177C22×C73—21no—
178C22×C73—41no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73—41no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73C22×D411yescharacteristic
185C2×D73—21no—
186C2×D73—22no—
187C2×D73—21no—
188C2×D73—21no—
189C2×D73—41no—
190C2×D73—41no—
191C2×D73—41no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—84no—
195C4×C73—21no—
196C4×C73—22no—
197C4×C73—41no—
198C4×C73C22×D411yescharacteristic
199C4×C73H(5,𝔽2)11yescharacteristic
200Dic73—21no—
201Dic73—21no—
202Dic73—21no—
203Dic73—41no—
204Dic73—41no—
205C2×C73—41no—
206C2×C73—81no—
207C2×C73—81no—
208C2×C73D4211yescharacteristic
209C2×C73#57511yescharacteristic
210C2×C73#57611yescharacteristic
211D73—41no—
212D73—42no—
213D73—81no—
214#3268—731nomaximal, Sylow
215C73#326811yescharacteristic, complemented, Sylow
216C2×AGL(1,ℤ/8)—731no—
217C2×#135—731no—
218#550—731no—
219#546—731no—
220#496—731no—
221#468—731no—
222#466—731no—
223#464—731no—
224#459—731no—
225#452—731no—
226#449—731no—
227#449D7311yescharacteristic, complemented
228#447—731no—
229#440—731no—
230#435—731no—
231C2×#41—731no—
232C2×#41—731no—
233C2×#41C2×D7311yescharacteristic, complemented
234C22×D4—731no—
235AGL(1,ℤ/8)—1464no—
236#135—1464no—
237C2×Q16—731no—
238C2×SD16—731no—
239C2×SD16—731no—
240C2×SD16—731no—
241C2×SD16C2×D7311yescharacteristic
242C2×D8—731no—
243C2×D8—731no—
244C2×D8—731no—
245C2×D8C2×D7311yescharacteristic
246C2×M16—731no—
247C22×C8—731no—
248#127—731no—
249#127—1461no—
250#124—731no—
251#123—1461no—
252C22⋊Q8—731no—
253#121—731no—
254#121—731no—
255#121—1461no—
256#121—1461no—
257#121—1461no—
258#121C2×D7311yescharacteristic
259#120—1461no—
260C4×Q8—731no—
261C4×D4—731no—
262C4×D4—731no—
263C4×D4—1461no—
264C2×C22⋊C4—1461no—
265#107—731no—
266C4⋊C8—731no—
267#103—731no—
268#103C2×D7311yescharacteristic, complemented
269#102—731no—
270#102—731no—
271#102—731no—
272#102C2×D7311yescharacteristic, complemented
273C22⋊C8—731no—
274C22⋊C8C2×D7311yescharacteristic, complemented
275#97—731no—
276C24—1461no—
277#41—22no—
278#41—41no—
279#41—2921no—
280#41—2921no—
281#41—1462no—
282#41—1462no—
283C2×Q8—731no—
284C2×Q8C22×D7311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—2921no—
288C2×D4—731no—
289C2×D4—731no—
290C2×D4—731no—
291C2×D4—1461no—
292C2×D4—1461no—
293C2×D4—1461no—
294C2×D4—1461no—
295C2×D4—1462no—
296C2×D4—1461no—
297C2×D4—1461no—
298C2×D4—1461no—
299C2×D4C22×D7311yescharacteristic
300C2×D4C22×D7311yescharacteristic
301C22×C4—21no—
302C22×C4—731no—
303C22×C4—1461no—
304C22×C4—1461no—
305C22×C4—1461no—
306C22×C4C22×D7311yescharacteristic
307Q16—1462no—
308SD16—22no—
309SD16—2921no—
310SD16—734no—
311SD16—1462no—
312D8—41no—
313D8—1462no—
314D8—1462no—
315D8—1462no—
316M16—1462no—
317C2×C8—731no—
318C2×C8—731no—
319C2×C8—1462no—
320C2×C8C22×D7311yescharacteristic
321C2×C8C22×D7311yescharacteristic
322C4⋊C4—731no—
323C4⋊C4—731no—
324C4⋊C4—1461no—
325C4⋊C4—1461no—
326C4⋊C4C22×D7311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—731no—
329C22⋊C4—731no—
330C22⋊C4—1461no—
331C22⋊C4—1461no—
332C22⋊C4—1461no—
333C22⋊C4—1461no—
334C22⋊C4—1461no—
335C22⋊C4—1461no—
336C42—731no—
337C42—1461no—
338C23—21no—
339C23—21no—
340C23—2922no—
341C23—2922no—
342C23—5841no—
343C23—731no—
344C23—1461no—
345C23—1461no—
346C23D4×D7311yescharacteristic
347Q8—21no—
348Q8—1461no—
349Q8—1461no—
350Q8D4×D7312yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—42no—
356D4—81no—
357D4—2922no—
358D4—2922no—
359D4—2921no—
360D4—2922no—
361D4—2922no—
362D4—5841no—
363D4—5841no—
364D4—5841no—
365D4—732no—
366D4—1461no—
367D4—1461no—
368D4—1461no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—2922no—
375C2×C4—2922no—
376C2×C4—5841no—
377C2×C4—731no—
378C2×C4—731no—
379C2×C4—731no—
380C2×C4—1461no—
381C2×C4—1461no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4D4×D7311yescharacteristic
385C2×C4C23×D7311yescharacteristic
386C8—21no—
387C8—21no—
388C8—732no—
389C8—1461no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—2921no—
400C22—2921no—
401C22—2921no—
402C22—2921no—
403C22—2921no—
404C22—5844no—
405C22—1461no—
406C22—1461no—
407C22—1462no—
408C22—1461no—
409C22C2×D4×D7311yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—2921no—
414C4—2921no—
415C4—1461no—
416C4—1461no—
417C4—1461no—
418C4C2×D4×D7311yescharacteristic
419C4#1455663611yescharacteristic
420C2—41no—
421C2—81no—
422C2—81no—
423C2—2922no—
424C2—2921no—
425C2—5841no—
426C2#1798921911yescharacteristic
427C2#1798938411yescharacteristic
428C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#449×C73C2
socleC22×C73C22×D4
hypercenter#449D73
hypocenterC73#3268
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#14556618C2semidirect
2. C2×#14556611C2semidirect
3. #17989256C2semidirect
4. #17989234C2semidirect
5. #17988975C2semidirect
6. #17988832C2semidirect
7. #17988821C2semidirect
8. #17988807C2semidirect
9. #17988781C2semidirect
10. #17988752C2semidirect
11. #17988734C2semidirect
12. #17988719C2semidirect
13. #17988690C2semidirect
14. #17988655C2semidirect
15. #449×C73C2semidirect
21. C2×#11924018C22semidirect
22. C2×#11924017C22semidirect
23. C2×#11924016C22semidirect
29. C22×#10596831C22semidirect
31. #14556587C22semidirect
36. #14556565C22semidirect
41. Q8×Dic73C22semidirect
46. #14556524C22semidirect
47. #14556520C22semidirect
48. #14556516C22semidirect
51. #14556511C22semidirect
53. #14556501C22semidirect
54. C2×#41×C73C22semidirect
58. #103×C73C22semidirect
59. #102×C73C22semidirect
60. C22⋊C8×C73C22semidirect
86. #11924015D4semidirect
215. C73#3268semidirect
227. #449D73semidirect
233. C2×#41C2×D73semidirect
268. #103C2×D73semidirect
272. #102C2×D73semidirect
274. C22⋊C8C2×D73semidirect