Finite Group Databasebeta

← #22613839

Subgroups — #22613839

Order 9344.

596 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556575C211yesmaximal, characteristic, complemented
2C2×#14556553C211yesmaximal, characteristic, complemented
3#17988526C211yesmaximal, characteristic, complemented
4#17988504C211yesmaximal, characteristic, complemented
5#17988496C211yesmaximal, characteristic
6#17988479C211yesmaximal, characteristic, complemented
7#17988477C211yesmaximal, characteristic, complemented
8#17988473C211yesmaximal, characteristic, complemented
9#17988464C211yesmaximal, characteristic, complemented
10#17988463C211yesmaximal, characteristic, complemented
11#17988463C211yesmaximal, characteristic, complemented
12#17988449C211yesmaximal, characteristic, complemented
13#17988444C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
15#396×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C23×Dic73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21C22×C4×D73C2211yescharacteristic
22#14556575—24no—
23#14556553—24no—
24C2×C4⋊Dic73C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26C2×C22⋊Dic73C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C23×D73C2311yescharacteristic
55C2×D292—22no—
56C2×D292—22no—
57C2×D292—22no—
58C2×C22⋊D73—22no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C2×C22⋊D73—22no—
62C2×C22⋊D73—41no—
63C2×C22⋊D73—41no—
64C22×Dic73—22no—
65C22×Dic73—22no—
66C22×Dic73—41no—
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C22×Dic73C2311yescharacteristic
72C22×Dic73C2311yescharacteristic
73C2×C4×D73—22no—
74C2×C4×D73—22no—
75C2×C4×D73—22no—
76C2×C4×D73—22no—
77C2×C4×D73—41no—
78C2×C4×D73—41no—
79C4⋊Dic73—22no—
80C4⋊Dic73—22no—
81C22⋊Dic73—22no—
82#11924005—22no—
83#11924005—22no—
84#11924005—22no—
85#11924005—41no—
86#11924005—41no—
87#11924005—41no—
88#11924005—41no—
89#11924005D414yescomplemented
90C4×Dic73—22no—
91C4×Dic73—41no—
92C24×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C4⋊C4×C73—22no—
100C4⋊C4×C73—22no—
101C4⋊C4×C73—41no—
102C22⋊C4×C73—22no—
103C22⋊C4×C73—22no—
104C22⋊C4×C73—41no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73#4112yes—
112C23×C73C2411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
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×D73C2×D412yes—
126C22×D73#4112yes—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73C2×D412yes—
144C2×C4×C73#4112yes—
145C22⋊D73—44no—
146C22⋊D73—44no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—21no—
151C2×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159C2×Dic73—21no—
160C2×Dic73—21no—
161C2×Dic73—21no—
162C2×Dic73—21no—
163C2×Dic73—44no—
164C2×Dic73C2×D412yes—
165C2×Dic73#4112yes—
166D292—28no—
167C4×D73—44no—
168C4×D73—44no—
169C22×C73—22no—
170C22×C73—22no—
171C22×C73—22no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73C22×D411yescharacteristic
177C22×C73C2×#4111yescharacteristic
178C22×C73C2×#4111yescharacteristic
179C22×C73C2×#4111yescharacteristic
180C22×C73C2×#4111yescharacteristic
181C22×C73H(5,𝔽2)11yescharacteristic
182C22×C73H(5,𝔽2)11yescharacteristic
183C2×D73—22no—
184C2×D73—22no—
185C2×D73—22no—
186C2×D73—22no—
187C2×D73—22no—
188C2×D73—22no—
189C2×D73—41no—
190C2×D73—41no—
191C2×D73—41no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—41no—
195C2×D73—41no—
196C2×D73—41no—
197C4×C73—22no—
198C4×C73—22no—
199C4×C73—41no—
200C4×C73—41no—
201C4×C73—41no—
202C4×C73—41no—
203Dic73—22no—
204Dic73—22no—
205Dic73—41no—
206Dic73—41no—
207Dic73—41no—
208Dic73—41no—
209C2×C73—42no—
210C2×C73#52511yescharacteristic
211C2×C73#52911yescharacteristic
212C2×C73#54011yescharacteristic
213C2×C73#54611yescharacteristic
214C2×C73#54611yescharacteristic
215C2×C73#55111yescharacteristic
216C2×C73#55311yescharacteristic
217D73—42no—
218D73—42no—
219#2457—731nomaximal, Sylow
220C73#245711yescharacteristic, complemented, Sylow
221C2×#123—731no—
222C2×C4×D4—731no—
223#400—731no—
224#396D7311yescharacteristic, complemented
225#394—731no—
226#392—731no—
227#388—731no—
228#388—731no—
229#387—731no—
230#386—731no—
231#386—731no—
232#386—731no—
233#381—731no—
234#380—731no—
235C4×C22⋊C4—731no—
236C22×D4—731no—
237C22×D4—731no—
238C22×D4—731no—
239C23×C4—731no—
240C23×C4—731no—
241C23×C4—731no—
242#123—1464no—
243C4×D4—1464no—
244C2×C4⋊C4—731no—
245C2×C4⋊C4—731no—
246C2×C4⋊C4C2×D7311yescharacteristic
247C2×C4⋊C4C2×D7311yescharacteristic
248C2×C4⋊C4C2×D7311yescharacteristic
249C2×C22⋊C4—731no—
250C2×C22⋊C4—731no—
251C2×C22⋊C4—731no—
252C2×C22⋊C4—731no—
253C2×C22⋊C4—731no—
254C2×C22⋊C4—731no—
255C2×C22⋊C4—731no—
256C2×C22⋊C4—731no—
257C2×C22⋊C4—731no—
258C2×C22⋊C4C2×D7311yescharacteristic
259C2×C22⋊C4C2×D7311yescharacteristic
260C2×C22⋊C4C2×D7311yescharacteristic
261C2×C42—731no—
262C2×C42—731no—
263#95—731no—
264#95—731no—
265#95—731no—
266#95—731no—
267#95—731no—
268#95—731no—
269#95—731no—
270#95—731no—
271#95—731no—
272#95C2×D7311yescharacteristic
273C24—731no—
274C24—731no—
275C24C22×D7311yescharacteristic
276C2×D4—2921no—
277C2×D4—2921no—
278C2×D4—1462no—
279C2×D4—1462no—
280C2×D4—1462no—
281C2×D4—1462no—
282C2×D4—1462no—
283C2×D4—1462no—
284C2×D4—1462no—
285C22×C4—2921no—
286C22×C4—2921no—
287C22×C4—2921no—
288C22×C4—731no—
289C22×C4—731no—
290C22×C4—731no—
291C22×C4—731no—
292C22×C4—731no—
293C22×C4—731no—
294C22×C4—1462no—
295C22×C4—1462no—
296C22×C4—1462no—
297C22×C4—1462no—
298C22×C4—1462no—
299C22×C4—1462no—
300C22×C4C22×D7311yescharacteristic
301C22×C4C22×D7311yescharacteristic
302C22×C4C22×D7311yescharacteristic
303C22×C4C22×D7311yescharacteristic
304C22×C4C22×D7311yescharacteristic
305C22×C4C22×D7311yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—1462no—
310C4⋊C4—1462no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—41no—
314C22⋊C4—2921no—
315C22⋊C4—2921no—
316C22⋊C4—2921no—
317C22⋊C4—2921no—
318C22⋊C4—734no—
319C22⋊C4—1462no—
320C22⋊C4—1462no—
321C22⋊C4—1462no—
322C22⋊C4—1462no—
323C42—2921no—
324C42—1462no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—732no—
332C23—732no—
333C23—1461no—
334C23—1461no—
335C23—1461no—
336C23—1461no—
337C23—1461no—
338C23—1461no—
339C23—1461no—
340C23—1461no—
341C23—1461no—
342C23—1461no—
343C23—1461no—
344C23—1461no—
345C23#1192402912yes—
346C23C23×D7311yescharacteristic
347D4—2924no—
348D4—2924no—
349D4—1468no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—2924no—
367C2×C4—2924no—
368C2×C4—2924no—
369C2×C4—732no—
370C2×C4—732no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4—1461no—
374C2×C4—1461no—
375C2×C4—1461no—
376C2×C4—1461no—
377C2×C4—1461no—
378C2×C4—1461no—
379C2×C4—1461no—
380C2×C4—1461no—
381C2×C4—1461no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4—1461no—
385C2×C4—1461no—
386C2×C4—1461no—
387C2×C4D4×D7312yes—
388C2×C4#1192402712yes—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—2921no—
397C22—2921no—
398C22—2921no—
399C22—2921no—
400C22—2921no—
401C22—2921no—
402C22—2921no—
403C22—2921no—
404C22—1462no—
405C22—1462no—
406C22—1462no—
407C22—1462no—
408C22—1462no—
409C22—1462no—
410C22C2×D4×D7311yescharacteristic
411C22#41×D7311yescharacteristic
412C22#41×D7311yescharacteristic
413C22C2×#1192402711yescharacteristic
414C22C2×#1192402911yescharacteristic
415C22#1455663611yescharacteristic
416C22#1455663711yescharacteristic
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—2921no—
424C4—2921no—
425C4—2921no—
426C4—2921no—
427C4—1462no—
428C4—1462no—
429C2—42no—
430C2—2922no—
431C2—2922no—
432C2#1798909711yescharacteristic
433C2#1798912311yescharacteristic
434C2#1798919011yescharacteristic
435C2#1798922611yescharacteristic
436C2#1798922811yescharacteristic
437C2#1798926411yescharacteristic
438C2#1798928811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#396×C73C2
hypercenter#396D73
hypocenterC73#2457
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14556575C2semidirect
2. C2×#14556553C2semidirect
3. #17988526C2semidirect
4. #17988504C2semidirect
6. #17988479C2semidirect
7. #17988477C2semidirect
8. #17988473C2semidirect
9. #17988464C2semidirect
10. #17988463C2semidirect
11. #17988463C2semidirect
12. #17988449C2semidirect
13. #17988444C2semidirect
14. C22⋊C4×Dic73C2semidirect
15. #396×C73C2semidirect
89. #11924005D4semidirect
220. C73#2457semidirect
224. #396D73semidirect