Finite Group Databasebeta

← #22619604

Subgroups — #22619604

Order 9344.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556618C211yesmaximal, characteristic, complemented
2C2×#14556597C211yesmaximal, characteristic, complemented
3#17989167C211yesmaximal, characteristic, complemented
4#17989153C211yesmaximal, characteristic, complemented
5#17988841C211yesmaximal, characteristic, complemented
6#17988838C211yesmaximal, characteristic, complemented
7#17988835C211yesmaximal, characteristic, complemented
8#17988830C211yesmaximal, characteristic, complemented
9#17988823C211yesmaximal, characteristic, complemented
10#17988822C211yesmaximal, characteristic, complemented
11#17988819C211yesmaximal, characteristic, complemented
12#17988626C211yesmaximal, characteristic, complemented
13#17988582C211yesmaximal, characteristic, complemented
14#102×D73C211yesmaximal, characteristic, complemented
15#465×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924028C2211yescharacteristic
18C2×D4×D73C2211yescharacteristic
19#14556618—24no—
20C2×#11924015C2211yescharacteristic
21C2×D584C2211yescharacteristic
22C2×#11924013C2211yescharacteristic
23#14556597—24no—
24C2×#11924012C2211yescharacteristic, complemented
25C2×#11924011C2211yescharacteristic
26C2×#11924011C2211yescharacteristic, complemented
27C2×C8×D73C2211yescharacteristic
28C2×C8×D73C2211yescharacteristic, complemented
29#14556587—21no—
30#14556577—21no—
31#14556569—21no—
32#14556567C2211yescharacteristic, complemented
33#14556566—21no—
34#14556566C2211yescharacteristic
35#14556566C2211yescharacteristic, complemented
36#14556565C2211yescharacteristic
37#14556565C2211yescharacteristic, complemented
38#14556564—21no—
39#14556564—21no—
40#14556562C2211yescharacteristic
41#14556561—21no—
42#14556559—21no—
43#14556549C2211yescharacteristic
44C4⋊C4×D73C2211yescharacteristic
45#14556525C2211yescharacteristic, complemented
46#14556524C2211yescharacteristic, complemented
47#14556522C2211yescharacteristic, complemented
48#14556515C2211yescharacteristic, complemented
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic, complemented
51#14556512C2211yescharacteristic
52#14556511C2211yescharacteristic
53#14556511C2211yescharacteristic, complemented
54C2×SD16×C73C2211yescharacteristic
55C22×C8×C73C2211yescharacteristic, complemented
56C22⋊Q8×C73C2211yescharacteristic, complemented
57#121×C73C2211yescharacteristic
58#106×C73C2211yescharacteristic, complemented
59#103×C73C2211yescharacteristic, complemented
60#102×C73C2211yescharacteristic
61C23×D73—21no—
62#11924029—22no—
63#11924029—22no—
64#11924028—22no—
65#11924028—22no—
66C2×Dic146D411yescharacteristic
67C2×D292—21no—
68C2×D292—21no—
69C2×D292—21no—
70C2×D292D411yescharacteristic
71C2×D292C2311yescharacteristic
72C2×D292C2311yescharacteristic
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75C2×C22⋊D73—21no—
76C2×C22⋊D73—21no—
77C2×C22⋊D73D411yescharacteristic
78C2×C22⋊D73D411yescharacteristic
79D4×D73—22no—
80D4×D73—22no—
81C2×C4×D73—21no—
82C2×C4×D73—21no—
83C2×C4×D73C2311yescharacteristic
84C2×C4×D73C2311yescharacteristic
85#11924015—22no—
86D584—22no—
87#11924013—22no—
88#11924012—22no—
89#11924011—22no—
90#11924011D414yescomplemented
91C2×#10596831C2311yescharacteristic
92C2×#10596831C2311yescharacteristic
93C8×D73—22no—
94C8×D73—22no—
95C4⋊Dic73C2311yescharacteristic
96C4⋊Dic73C2311yescharacteristic
97#11924007—21no—
98#11924007—21no—
99C22⋊Dic73—21no—
100#11924005—21no—
101#11924005—21no—
102#11924005—21no—
103#11924005—21no—
104#11924005—21no—
105#11924005—21no—
106C4×Dic73—21no—
107C2×Q8×C73C2311yescharacteristic
108C2×D4×C73—21no—
109C2×D4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111SD16×C73—22no—
112C2×C8×C73—22no—
113C2×C8×C73C2311yescharacteristic
114C2×C8×C73C2311yescharacteristic
115C4⋊C4×C73—21no—
116C4⋊C4×C73C2311yescharacteristic
117C4⋊C4×C73C2311yescharacteristic
118C22⋊C4×C73—21no—
119C22⋊C4×C73—21no—
120C23×C73—21no—
121C23×C73C2×D411yescharacteristic
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—42no—
125C22×D73—81no—
126C22×D73—81no—
127C22×D73C2×D411yescharacteristic
128C22×D73C2×D411yescharacteristic
129Q8×C73—21no—
130Q8×C73—21no—
131D4×C73—21no—
132D4×C73—21no—
133D4×C73—81no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73C2×D411yescharacteristic
140C2×C4×C73C2411yescharacteristic
141C22⋊D73—22no—
142C22⋊D73—22no—
143C22⋊D73—42no—
144C22⋊D73—81no—
145C22⋊D73—81no—
146C22⋊D73—81no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73C2×D411yescharacteristic
150C2×Dic73C2×D411yescharacteristic
151D292—22no—
152D292—21no—
153D292—21no—
154D292—21no—
155D292—21no—
156D292—42no—
157D292—81no—
158D292—81no—
159C4×D73—21no—
160C4×D73—21no—
161C4×D73—42no—
162C4×D73—81no—
163C4×D73C2×D412yes—
164C4×D73#4112yes—
165Dic146—22no—
166C8×C73—21no—
167C8×C73C2×D412yes—
168#10596831—21no—
169#10596831C2×D412yes—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73C22×D411yescharacteristic
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—21no—
181C2×D73—21no—
182C2×D73—41no—
183C2×D73—41no—
184C2×D73—41no—
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—84no—
189C2×D73#12112yes—
190C4×C73—21no—
191C4×C73—41no—
192C4×C73—41no—
193C4×C73—41no—
194C4×C73C22×D411yescharacteristic
195C4×C73C2×#4111yescharacteristic
196Dic73—21no—
197Dic73—41no—
198Dic73—41no—
199Dic73#12112yes—
200C2×C73—41no—
201C2×C73—81no—
202C2×C73C2×#12111yescharacteristic
203C2×C73#57611yescharacteristic
204C2×C73#57711yescharacteristic
205D73—22no—
206D73—41no—
207D73—81no—
208D73—81no—
209#3062—731nomaximal, Sylow
210C73#306211yescharacteristic, complemented, Sylow
211C2×AGL(1,ℤ/8)—731no—
212C2×#131—731no—
213#537—731no—
214#535—731no—
215#469—731no—
216#469—731no—
217#468—731no—
218#468—731no—
219#466—731no—
220#466—731no—
221#465—731no—
222#465D7311yescharacteristic, complemented
223#428—731no—
224#416—731no—
225C2×#102—731no—
226C2×#41—731no—
227C2×#41—731no—
228C22×D4—731no—
229AGL(1,ℤ/8)—1464no—
230C2×SD16—731no—
231C2×SD16C2×D7311yescharacteristic
232C2×D8—731no—
233C2×D8—731no—
234#131—1464no—
235C2×M16—731no—
236C2×M16—731no—
237C2×M16—731no—
238C22×C8—731no—
239C22×C8—731no—
240C22×C8C2×D7311yescharacteristic, complemented
241#127—1461no—
242#124—1461no—
243C22⋊Q8—731no—
244C22⋊Q8—1461no—
245C22⋊Q8C2×D7311yescharacteristic, complemented
246#121—731no—
247#121—731no—
248#121—731no—
249#121—731no—
250#121—731no—
251#121—1461no—
252#121—1461no—
253#121—1461no—
254#121C2×D7311yescharacteristic
255#120—1461no—
256#120—1461no—
257#117—731no—
258C2×C4⋊C4—731no—
259#107—731no—
260#107—731no—
261#106—731no—
262#106C2×D7311yescharacteristic, complemented
263#103—731no—
264#103C2×D7311yescharacteristic, complemented
265#102—731no—
266#102—731no—
267#102—731no—
268#102—731no—
269#102—731no—
270#102C2×D7311yescharacteristic
271C24—1461no—
272#41—1462no—
273#41—1462no—
274#41—1462no—
275#41—1462no—
276C2×Q8—731no—
277C2×Q8C22×D7311yescharacteristic
278C2×D4—21no—
279C2×D4—731no—
280C2×D4—731no—
281C2×D4—731no—
282C2×D4—731no—
283C2×D4—731no—
284C2×D4—1461no—
285C2×D4—1461no—
286C2×D4—1461no—
287C2×D4—1462no—
288C2×D4—1462no—
289C2×D4—1461no—
290C2×D4—1461no—
291C2×D4—1461no—
292C2×D4—1461no—
293C2×D4C22×D7311yescharacteristic
294C22×C4—731no—
295C22×C4—731no—
296C22×C4—1461no—
297C22×C4—1461no—
298C22×C4C22×D7311yescharacteristic
299SD16—22no—
300SD16—1462no—
301D8—1462no—
302D8—1462no—
303M16—734no—
304M16—1462no—
305M16—1462no—
306C2×C8—22no—
307C2×C8—731no—
308C2×C8—731no—
309C2×C8—1462no—
310C2×C8—1462no—
311C2×C8C22×D7311yescharacteristic
312C2×C8C22×D7311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—731no—
315C4⋊C4—731no—
316C4⋊C4—1461no—
317C4⋊C4—1461no—
318C4⋊C4C22×D7311yescharacteristic
319C4⋊C4C22×D7311yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—1461no—
323C22⋊C4—1461no—
324C22⋊C4—1461no—
325C22⋊C4—1461no—
326C22⋊C4—1461no—
327C22⋊C4—1461no—
328C22⋊C4—1461no—
329C42—1461no—
330C23—21no—
331C23—2922no—
332C23—5841no—
333C23—5841no—
334C23—731no—
335C23—731no—
336C23—1461no—
337C23—1461no—
338C23D4×D7311yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—1462no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—2922no—
346D4—2922no—
347D4—5841no—
348D4—5841no—
349D4—5841no—
350D4—5841no—
351D4—5841no—
352D4—1462no—
353D4—1462no—
354D4—1462no—
355D4—1461no—
356D4—1461no—
357D4—1461no—
358D4—1461no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—2922no—
365C2×C4—5841no—
366C2×C4—731no—
367C2×C4—732no—
368C2×C4—732no—
369C2×C4—731no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4—1461no—
374C2×C4D4×D7311yescharacteristic
375C2×C4C23×D7311yescharacteristic
376C8—21no—
377C8—732no—
378C8—1461no—
379C8D4×D7312yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—2921no—
387C22—2921no—
388C22—2921no—
389C22—2921no—
390C22—2921no—
391C22—2921no—
392C22—5844no—
393C22—732no—
394C22—1461no—
395C22—1461no—
396C22—1461no—
397C22—1461no—
398C22—1461no—
399C22C2×D4×D7311yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—2921no—
405C4—2921no—
406C4—732no—
407C4—1461no—
408C4C2×D4×D7311yescharacteristic
409C4#41×D7311yescharacteristic
410C2—41no—
411C2—81no—
412C2—2921no—
413C2—5841no—
414C2—5841no—
415C2—1462no—
416C2#121×D7311yescharacteristic
417C2#1798938911yescharacteristic
418C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#465×C73C2
socleC22×C73C22×D4
hypercenter#465D73
hypocenterC73#3062
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#14556618C2semidirect
2. C2×#14556597C2semidirect
3. #17989167C2semidirect
4. #17989153C2semidirect
5. #17988841C2semidirect
6. #17988838C2semidirect
7. #17988835C2semidirect
8. #17988830C2semidirect
9. #17988823C2semidirect
10. #17988822C2semidirect
11. #17988819C2semidirect
12. #17988626C2semidirect
13. #17988582C2semidirect
14. #102×D73C2semidirect
15. #465×C73C2semidirect
24. C2×#11924012C22semidirect
26. C2×#11924011C22semidirect
28. C2×C8×D73C22semidirect
32. #14556567C22semidirect
35. #14556566C22semidirect
37. #14556565C22semidirect
45. #14556525C22semidirect
46. #14556524C22semidirect
47. #14556522C22semidirect
48. #14556515C22semidirect
50. #14556513C22semidirect
53. #14556511C22semidirect
55. C22×C8×C73C22semidirect
56. C22⋊Q8×C73C22semidirect
58. #106×C73C22semidirect
59. #103×C73C22semidirect
90. #11924011D4semidirect
210. C73#3062semidirect
222. #465D73semidirect
240. C22×C8C2×D73semidirect
245. C22⋊Q8C2×D73semidirect
262. #106C2×D73semidirect
264. #103C2×D73semidirect