Finite Group Databasebeta

← #22622133

Subgroups — #22622133

Order 9344.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989285C211yesmaximal, characteristic, complemented
2#17989225C211yesmaximal, characteristic, complemented
3#17988943C211yesmaximal, characteristic, complemented
4#17988926C211yesmaximal, characteristic, complemented
5#17988900C211yesmaximal, characteristic, complemented
6#17988889C211yesmaximal, characteristic, complemented
7#17988840C211yesmaximal, characteristic, complemented
8#17988836C211yesmaximal, characteristic, complemented
9#17988805C211yesmaximal, characteristic, complemented
10#17988732C211yesmaximal, characteristic, complemented
11#17988722C211yesmaximal, characteristic, complemented
12#17988667C211yesmaximal, characteristic, complemented
13#17988663C211yesmaximal, characteristic, complemented
14#17988590C211yesmaximal, characteristic, complemented
15#417×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73C2211yescharacteristic
17C2×#11924015C2211yescharacteristic, complemented
18C2×D584C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21#14556586—21no—
22#14556582C2211yescharacteristic, complemented
23#14556580C2211yescharacteristic
24#14556576—21no—
25#14556574—21no—
26#14556567C2211yescharacteristic
27#14556566C2211yescharacteristic
28#14556565—21no—
29#14556565C2211yescharacteristic
30#14556565C2211yescharacteristic, complemented
31#14556563—21no—
32#14556559—21no—
33D4×Dic73C2211yescharacteristic
34#14556553C2211yescharacteristic, complemented
35C4×C22⋊D73—21no—
36C4×C22⋊D73C2211yescharacteristic
37#14556549C2211yescharacteristic
38C2×#11924005—21no—
39#14556524C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556523C2211yescharacteristic, complemented
42#14556520C2211yescharacteristic, complemented
43#14556515C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic, complemented
46#14556512C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic, complemented
52C2×#41×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic, complemented
54C2×C4⋊C4×C73C2211yescharacteristic, complemented
55#103×C73C2211yescharacteristic, complemented
56#103×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C23×D73—21no—
60C2×D292—21no—
61C2×D292C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73D411yescharacteristic
67D4×D73—22no—
68D4×D73—41no—
69C22×Dic73—21no—
70C2×C4×D73—21no—
71C2×C4×D73C2311yescharacteristic
72#11924015—41no—
73D584—41no—
74#11924013—22no—
75#11924011—41no—
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84C22⋊Dic73—21no—
85C22⋊Dic73D411yescharacteristic
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97#41×C73—22no—
98#41×C73—41no—
99C2×Q8×C73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73C2311yescharacteristic
105M16×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—42no—
116C22×D73—42no—
117C22×D73—81no—
118C22×D73C2×D411yescharacteristic
119Q8×C73—21no—
120Q8×C73—21no—
121D4×C73—21no—
122D4×C73—42no—
123D4×C73#4112yes—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—42no—
130C2×C4×C73—81no—
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2411yescharacteristic
133C22⋊D73—41no—
134C22⋊D73—42no—
135C22⋊D73—42no—
136C22⋊D73—81no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—81no—
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143D292—21no—
144D292—21no—
145D292—21no—
146D292—21no—
147D292—81no—
148C4×D73—21no—
149C4×D73—21no—
150C4×D73—81no—
151C8×C73—21no—
152C8×C73—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—22no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73C22×D411yescharacteristic
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—21no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—84no—
172C4×C73—21no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73—41no—
176C4×C73C2×#4111yescharacteristic
177C4×C73H(5,𝔽2)11yescharacteristic
178Dic73—21no—
179Dic73—21no—
180Dic73—21no—
181Dic73—41no—
182Dic73—41no—
183C2×C73—42no—
184C2×C73—41no—
185C2×C73#54611yescharacteristic
186C2×C73#57511yescharacteristic
187C2×C73#57611yescharacteristic
188D73—41no—
189D73—81no—
190D73—81no—
191#3322—731nomaximal, Sylow
192C73#332211yescharacteristic, complemented, Sylow
193#553—731no—
194#546—731no—
195#488—731no—
196#485—731no—
197#480—731no—
198#478—731no—
199#469—731no—
200#468—731no—
201#463—731no—
202#449—731no—
203#447—731no—
204C4×D8—731no—
205#436—731no—
206#418—731no—
207#417D7311yescharacteristic, complemented
208C2×#41C2×D7311yescharacteristic
209C22×D4—731no—
210C2×SD16—731no—
211C2×D8—731no—
212C2×D8—731no—
213C2×M16—731no—
214C2×M16C2×D7311yescharacteristic, complemented
215#126—1461no—
216#125—731no—
217#124—731no—
218#123—1461no—
219#123—1461no—
220C22⋊Q8—731no—
221#121—731no—
222#121—731no—
223#121—731no—
224#121—1461no—
225#121—1461no—
226#120—1461no—
227C4×D4—731no—
228C4×D4—731no—
229C4×D4—731no—
230C4×D4—1461no—
231#117—731no—
232C2×C4⋊C4C2×D7311yescharacteristic, complemented
233C2×C22⋊C4—1461no—
234#107—731no—
235#107—731no—
236#106—731no—
237C4⋊C8—731no—
238#103—731no—
239#103C2×D7311yescharacteristic, complemented
240#103C2×D7311yescharacteristic, complemented
241#102—731no—
242#102—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102C2×D7311yescharacteristic
247#102C2×D7311yescharacteristic
248C22⋊C8—731no—
249C22⋊C8—731no—
250C4×C8—731no—
251C24—1461no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D7311yescharacteristic
255C2×D4—21no—
256C2×D4—2921no—
257C2×D4—731no—
258C2×D4—731no—
259C2×D4—731no—
260C2×D4—1461no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1462no—
264C2×D4—1461no—
265C2×D4C22×D7311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—731no—
269C22×C4—1461no—
270C22×C4—1461no—
271C22×C4C22×D7311yescharacteristic
272SD16—2921no—
273D8—2921no—
274D8—1462no—
275M16—41no—
276M16—2921no—
277C2×C8—731no—
278C2×C8—731no—
279C2×C8C22×D7311yescharacteristic
280C2×C8C22×D7311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—731no—
283C4⋊C4—731no—
284C4⋊C4—731no—
285C4⋊C4—1461no—
286C4⋊C4—1461no—
287C4⋊C4—1461no—
288C4⋊C4C22×D7311yescharacteristic
289C4⋊C4C22×D7311yescharacteristic
290C22⋊C4—731no—
291C22⋊C4—731no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C42—731no—
302C42—1461no—
303C23—21no—
304C23—2922no—
305C23—2922no—
306C23—5841no—
307C23—731no—
308C23—1461no—
309C23—1461no—
310C23D4×D7311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—42no—
315D4—2922no—
316D4—2922no—
317D4—2921no—
318D4—5841no—
319D4—5841no—
320D4—1461no—
321D4—1461no—
322D4—1461no—
323D4—1461no—
324D4#1192402812yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—5841no—
333C2×C4—5841no—
334C2×C4—731no—
335C2×C4—731no—
336C2×C4—731no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4D4×D7311yescharacteristic
342C2×C4C23×D7311yescharacteristic
343C8—21no—
344C8—21no—
345C8—1461no—
346C8—1461no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—2921no—
354C22—2921no—
355C22—2921no—
356C22—2921no—
357C22—2921no—
358C22—2921no—
359C22—5844no—
360C22—1461no—
361C22—1461no—
362C22—1461no—
363C22C2×D4×D7311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—2921no—
369C4—2921no—
370C4—1461no—
371C4—1461no—
372C4—1461no—
373C4C2×#1192402811yescharacteristic
374C4#1455663611yescharacteristic
375C2—41no—
376C2—42no—
377C2—2921no—
378C2—5841no—
379C2—5841no—
380C2#1798922711yescharacteristic
381C2#1798938611yescharacteristic
382C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3322
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #17989285C2semidirect
2. #17989225C2semidirect
3. #17988943C2semidirect
4. #17988926C2semidirect
5. #17988900C2semidirect
6. #17988889C2semidirect
7. #17988840C2semidirect
8. #17988836C2semidirect
9. #17988805C2semidirect
10. #17988732C2semidirect
11. #17988722C2semidirect
12. #17988667C2semidirect
13. #17988663C2semidirect
14. #17988590C2semidirect
15. #417×C73C2semidirect
17. C2×#11924015C22semidirect
22. #14556582C22semidirect
30. #14556565C22semidirect
34. #14556553C22semidirect
39. #14556524C22semidirect
40. #14556524C22semidirect
41. #14556523C22semidirect
42. #14556520C22semidirect
43. #14556515C22semidirect
45. #14556513C22semidirect
49. C22⋊#10596831C22semidirect
51. C8×Dic73C22semidirect
53. C2×M16×C73C22semidirect
54. C2×C4⋊C4×C73C22semidirect
55. #103×C73C22semidirect
56. #103×C73C22semidirect
192. C73#3322semidirect
207. #417D73semidirect
214. C2×M16C2×D73semidirect
232. C2×C4⋊C4C2×D73semidirect
239. #103C2×D73semidirect
240. #103C2×D73semidirect