Finite Group Databasebeta

← #22615741

Subgroups — #22615741

Order 9344.

668 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556569C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D73C211yesmaximal, characteristic
3#17988523C211yesmaximal, characteristic, complemented
4#17988522C211yesmaximal, characteristic, complemented
5#17988510C211yesmaximal, characteristic, complemented
6#17988509C211yesmaximal, characteristic, complemented
7#17988509C211yesmaximal, characteristic, complemented
8#17988500C211yesmaximal, characteristic, complemented
9#17988499C211yesmaximal, characteristic, complemented
10#17988461C211yesmaximal, characteristic, complemented
11#17988458C211yesmaximal, characteristic, complemented
12#17988444C211yesmaximal, characteristic, complemented
13#17988442C211yesmaximal, characteristic
14#17988442C211yesmaximal, characteristic
15#396×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C22×Dic146C2211yescharacteristic, complemented
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556569—24no—
21C2×C4⋊Dic73C2211yescharacteristic, complemented
22C2×C4⋊Dic73C2211yescharacteristic, complemented
23C2×#11924007C2211yescharacteristic, complemented
24C2×#11924007C2211yescharacteristic, complemented
25C2×#11924007C2211yescharacteristic, complemented
26C2×#11924007C2211yescharacteristic, complemented
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C22⋊C4×D73—24no—
41#14556498C2211yescharacteristic, complemented
42#14556498C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44#14556498C2211yescharacteristic, complemented
45#14556498C2211yescharacteristic, complemented
46C2×C4⋊C4×C73C2211yescharacteristic, complemented
47C2×C4⋊C4×C73C2211yescharacteristic, complemented
48C2×C4⋊C4×C73C2211yescharacteristic, complemented
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic, complemented
53C23×D73—22no—
54C23×D73—22no—
55C23×D73—41no—
56C23×D73—41no—
57C23×D73—41no—
58C23×D73—41no—
59C23×D73Q814yescomplemented
60C23×D73C2311yescharacteristic
61C23×D73C2311yescharacteristic
62C2×Dic146—22no—
63C2×Dic146—41no—
64C2×Dic146—41no—
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C2×C4×D73—22no—
72C2×C4×D73—41no—
73C2×C4×D73—41no—
74C2×C4×D73—41no—
75C2×C4×D73—41no—
76C2×C4×D73D414yes—
77C4⋊Dic73—41no—
78C4⋊Dic73—41no—
79#11924007—22no—
80#11924007—22no—
81#11924007—41no—
82#11924007—41no—
83C22⋊Dic73—22no—
84C22⋊Dic73—41no—
85C22⋊Dic73—41no—
86#11924005—22no—
87#11924005—22no—
88#11924005—22no—
89#11924005—22no—
90#11924005—22no—
91#11924005—22no—
92#11924005—41no—
93#11924005—41no—
94#11924005—41no—
95#11924005—41no—
96C24×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C4⋊C4×C73—22no—
104C4⋊C4×C73—41no—
105C4⋊C4×C73—41no—
106C22⋊C4×C73—22no—
107C22⋊C4×C73—41no—
108C22⋊C4×C73—41no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73C2×Q812yes—
116C23×C73C2411yescharacteristic
117C22×D73—21no—
118C22×D73—21no—
119C22×D73—21no—
120C22×D73—21no—
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—21no—
125C22×D73—21no—
126C22×D73—21no—
127C22×D73—28no—
128C22×D73—44no—
129C22×D73—44no—
130C22×D73—44no—
131C22×D73—44no—
132C22×D73—44no—
133C22×D73—44no—
134C22×D73C2×D412yes—
135C22×D73C2×Q812yes—
136C22×D73C2×Q812yes—
137C22×D73#4112yes—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—21no—
155C2×C4×C73C2×D412yes—
156C2×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159C2×Dic73—21no—
160C2×Dic73—21no—
161C2×Dic73—21no—
162C2×Dic73—21no—
163C2×Dic73—21no—
164C2×Dic73—21no—
165C2×Dic73—21no—
166C2×Dic73—21no—
167C2×Dic73—21no—
168C2×Dic73—21no—
169C2×Dic73—21no—
170C2×Dic73—21no—
171C2×Dic73—21no—
172C2×Dic73—21no—
173C2×Dic73C2×D412yes—
174C4×D73—44no—
175C4×D73—44no—
176Dic146—44no—
177C22×C73—22no—
178C22×C73—22no—
179C22×C73—22no—
180C22×C73—41no—
181C22×C73—41no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73C22×D411yescharacteristic
185C22×C73C22×Q811yescharacteristic
186C22×C73C2×#4111yescharacteristic
187C22×C73H(5,𝔽2)11yescharacteristic
188C22×C73H(5,𝔽2)11yescharacteristic
189C22×C73H(5,𝔽2)11yescharacteristic
190C22×C73H(5,𝔽2)11yescharacteristic
191C2×D73—22no—
192C2×D73—22no—
193C2×D73—22no—
194C2×D73—22no—
195C2×D73—22no—
196C2×D73—22no—
197C2×D73—22no—
198C2×D73—22no—
199C2×D73—22no—
200C2×D73—416no—
201C2×D73—41no—
202C2×D73—41no—
203C2×D73—41no—
204C2×D73—41no—
205C2×D73C22⋊Q814yes—
206C4×C73—22no—
207C4×C73—41no—
208C4×C73—41no—
209C4×C73—41no—
210C4×C73—41no—
211C4×C73—41no—
212Dic73—22no—
213Dic73—41no—
214Dic73—41no—
215Dic73—41no—
216Dic73—41no—
217Dic73—41no—
218C2×C73—42no—
219C2×C73C2×C22⋊Q811yescharacteristic
220C2×C73#53411yescharacteristic
221C2×C73#53511yescharacteristic
222C2×C73#53811yescharacteristic
223C2×C73#53811yescharacteristic
224C2×C73#54311yescharacteristic
225C2×C73#54311yescharacteristic
226D73—24no—
227D73—42no—
228#2626—731nomaximal, Sylow
229C73#262611yescharacteristic, complemented, Sylow
230C2×C22⋊Q8—731no—
231C22×C22⋊C4—731no—
232#399—731no—
233#399—731no—
234#396—731no—
235#396—731no—
236#396—731no—
237#396D7311yescharacteristic, complemented
238#393—731no—
239#393—731no—
240#385—731no—
241#385—731no—
242#380—731no—
243#379—731no—
244#379—731no—
245C25—731no—
246C22×Q8—731no—
247C23×C4—731no—
248C23×C4—731no—
249C22⋊Q8—1464no—
250C2×C4⋊C4—731no—
251C2×C4⋊C4—731no—
252C2×C4⋊C4—731no—
253C2×C4⋊C4—731no—
254C2×C4⋊C4—731no—
255C2×C4⋊C4—731no—
256C2×C4⋊C4C2×D7311yescharacteristic, complemented
257C2×C4⋊C4C2×D7311yescharacteristic, complemented
258C2×C4⋊C4C2×D7311yescharacteristic, complemented
259C2×C22⋊C4—731no—
260C2×C22⋊C4—731no—
261C2×C22⋊C4—731no—
262C2×C22⋊C4—731no—
263C2×C22⋊C4—731no—
264C2×C22⋊C4—731no—
265C2×C22⋊C4—731no—
266C2×C22⋊C4—731no—
267C2×C22⋊C4—731no—
268C2×C22⋊C4—731no—
269C2×C22⋊C4—731no—
270C2×C22⋊C4—731no—
271C2×C22⋊C4—731no—
272C2×C22⋊C4—1464no—
273C2×C22⋊C4C2×D7311yescharacteristic
274C2×C22⋊C4C2×D7311yescharacteristic
275C2×C22⋊C4C2×D7311yescharacteristic
276#95—731no—
277#95—731no—
278#95—731no—
279#95—731no—
280#95—731no—
281#95C2×D7311yescharacteristic, complemented
282C24—2921no—
283C24—2921no—
284C24—2921no—
285C24—2921no—
286C24—734no—
287C24—731no—
288C24—731no—
289C24—1462no—
290C24—1462no—
291C24C22×D7311yescharacteristic
292C2×Q8—2921no—
293C2×Q8—2921no—
294C2×Q8—1462no—
295C22×C4—2921no—
296C22×C4—2921no—
297C22×C4—2921no—
298C22×C4—2921no—
299C22×C4—734no—
300C22×C4—731no—
301C22×C4—731no—
302C22×C4—731no—
303C22×C4—731no—
304C22×C4—731no—
305C22×C4—731no—
306C22×C4—1462no—
307C22×C4C22×D7311yescharacteristic
308C22×C4C22×D7311yescharacteristic
309C22×C4C22×D7311yescharacteristic
310C22×C4C22×D7311yescharacteristic
311C22×C4C22×D7311yescharacteristic
312C22×C4C22×D7311yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—2921no—
317C4⋊C4—2921no—
318C4⋊C4—2921no—
319C4⋊C4—2921no—
320C4⋊C4—1462no—
321C4⋊C4—1462no—
322C22⋊C4—22no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—2921no—
326C22⋊C4—2921no—
327C22⋊C4—2921no—
328C22⋊C4—2921no—
329C22⋊C4—2921no—
330C22⋊C4—2921no—
331C22⋊C4—1462no—
332C22⋊C4—1462no—
333C22⋊C4—1462no—
334C22⋊C4—1462no—
335C22⋊C4—1462no—
336C22⋊C4—1462no—
337C22⋊C4—1462no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—2924no—
345C23—2924no—
346C23—2924no—
347C23—2924no—
348C23—2924no—
349C23—2924no—
350C23—732no—
351C23—732no—
352C23—732no—
353C23—732no—
354C23—1468no—
355C23—1461no—
356C23—1461no—
357C23—1461no—
358C23—1461no—
359C23—1461no—
360C23—1461no—
361C23—1461no—
362C23—1461no—
363C23—1461no—
364C23—1461no—
365C23Q8×D7312yes—
366C23C23×D7311yescharacteristic
367Q8—2924no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—2924no—
386C2×C4—2924no—
387C2×C4—732no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4—1461no—
391C2×C4—1461no—
392C2×C4—1461no—
393C2×C4—1461no—
394C2×C4—1461no—
395C2×C4—1461no—
396C2×C4—1461no—
397C2×C4—1461no—
398C2×C4—1461no—
399C2×C4—1461no—
400C2×C4—1461no—
401C2×C4—1461no—
402C2×C4—1461no—
403C2×C4—1461no—
404C2×C4—1461no—
405C2×C4D4×D7312yes—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—29216no—
414C22—2921no—
415C22—2921no—
416C22—2921no—
417C22—2921no—
418C22—734no—
419C22—1462no—
420C22—1462no—
421C22—1462no—
422C22—1462no—
423C22—1462no—
424C22—1462no—
425C22—1462no—
426C22—1462no—
427C22—1462no—
428C22C2×D4×D7311yescharacteristic
429C22C2×Q8×D7311yescharacteristic
430C22#41×D7311yescharacteristic
431C22#1455663611yescharacteristic
432C22#1455663611yescharacteristic
433C22#1455663711yescharacteristic
434C22#1455663711yescharacteristic
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—2921no—
442C4—2921no—
443C4—2921no—
444C4—2921no—
445C4—2921no—
446C4—1462no—
447C2—42no—
448C2—2922no—
449C2—1464no—
450C2C22⋊Q8×D7311yescharacteristic
451C2#1798914511yescharacteristic
452C2#1798915311yescharacteristic
453C2#1798916911yescharacteristic
454C2#1798917611yescharacteristic
455C2#1798921211yescharacteristic
456C2#1798921211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#396×C73C2
hypercenter#396D73
hypocenterC73#2626
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14556569C2semidirect
3. #17988523C2semidirect
4. #17988522C2semidirect
5. #17988510C2semidirect
6. #17988509C2semidirect
7. #17988509C2semidirect
8. #17988500C2semidirect
9. #17988499C2semidirect
10. #17988461C2semidirect
11. #17988458C2semidirect
12. #17988444C2semidirect
15. #396×C73C2semidirect
17. C22×Dic146C22semidirect
21. C2×C4⋊Dic73C22semidirect
22. C2×C4⋊Dic73C22semidirect
23. C2×#11924007C22semidirect
24. C2×#11924007C22semidirect
25. C2×#11924007C22semidirect
26. C2×#11924007C22semidirect
41. #14556498C22semidirect
42. #14556498C22semidirect
43. #14556498C22semidirect
44. #14556498C22semidirect
45. #14556498C22semidirect
46. C2×C4⋊C4×C73C22semidirect
47. C2×C4⋊C4×C73C22semidirect
48. C2×C4⋊C4×C73C22semidirect
52. #95×C73C22semidirect
59. C23×D73Q8semidirect
229. C73#2626semidirect
237. #396D73semidirect
256. C2×C4⋊C4C2×D73semidirect
257. C2×C4⋊C4C2×D73semidirect
258. C2×C4⋊C4C2×D73semidirect
281. #95C2×D73semidirect