Finite Group Databasebeta

← #22613751

Subgroups — #22613751

Order 9344.

584 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556551C211yesmaximal, characteristic
2#17988525C211yesmaximal, characteristic, complemented
3#17988520C211yesmaximal, characteristic, complemented
4#17988509C211yesmaximal, characteristic, complemented
5#17988498C211yesmaximal, characteristic, complemented
6#17988494C211yesmaximal, characteristic, complemented
7#17988468C211yesmaximal, characteristic, complemented
8#17988466C211yesmaximal, characteristic
9#17988464C211yesmaximal, characteristic
10#17988462C211yesmaximal, characteristic, complemented
11#17988459C211yesmaximal, characteristic, complemented
12#17988458C211yesmaximal, characteristic, complemented
13#17988444C211yesmaximal, characteristic, complemented
14C2×#14556498C211yesmaximal, characteristic, complemented
15C2×C22⋊Q8×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C23×Dic73C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556551—24no—
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×C22⋊Dic73C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×C4×Dic73C2211yescharacteristic
33#14556498C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45C22×Q8×C73C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47C22⋊Q8×C73—24no—
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C4⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×C22⋊D73—22no—
55C2×C22⋊D73—22no—
56C2×C22⋊D73Q814yescomplemented
57C22×Dic73—22no—
58C22×Dic73—22no—
59C22×Dic73—22no—
60C22×Dic73—41no—
61C22×Dic73—41no—
62C22×Dic73—41no—
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C2×C4×D73—22no—
71C2×C4×D73—22no—
72C2×C4×D73—41no—
73C4⋊Dic73—41no—
74C4⋊Dic73—41no—
75#11924007—22no—
76#11924007—22no—
77#11924007—41no—
78C22⋊Dic73—22no—
79#11924005—22no—
80#11924005—22no—
81#11924005—41no—
82#11924005—41no—
83#11924005—41no—
84C4×Dic73—22no—
85C24×C73C2311yescharacteristic
86C2×Q8×C73—22no—
87C2×Q8×C73—22no—
88C2×Q8×C73—41no—
89C22×C4×C73—22no—
90C22×C4×C73—22no—
91C22×C4×C73—41no—
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C4⋊C4×C73—22no—
99C4⋊C4×C73—22no—
100C4⋊C4×C73—22no—
101C22⋊C4×C73—22no—
102C22⋊C4×C73D414yes—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73C2×D412yes—
108C23×C73C2×Q812yes—
109C23×C73#4112yes—
110C23×C73C2411yescharacteristic
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73C2×Q812yes—
118Q8×C73—44no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
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—44no—
135C2×C4×C73C2×D412yes—
136C2×C4×C73C2×D412yes—
137C2×C4×C73#4112yes—
138C22⋊D73—28no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
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—44no—
159C2×Dic73—44no—
160C2×Dic73C2×Q812yes—
161C2×Dic73#4112yes—
162C4×D73—44no—
163C22×C73—22no—
164C22×C73—22no—
165C22×C73—22no—
166C22×C73—22no—
167C22×C73—22no—
168C22×C73—22no—
169C22×C73C22⋊Q814yes—
170C22×C73C22×D411yescharacteristic
171C22×C73C22×Q811yescharacteristic
172C22×C73C2×#4111yescharacteristic
173C22×C73C2×#4111yescharacteristic
174C22×C73C2×#4111yescharacteristic
175C22×C73H(5,𝔽2)11yescharacteristic
176C22×C73H(5,𝔽2)11yescharacteristic
177C2×D73—22no—
178C2×D73—22no—
179C2×D73—22no—
180C2×D73—41no—
181C2×D73—41no—
182C2×D73—41no—
183C2×D73—41no—
184C4×C73—22no—
185C4×C73—22no—
186C4×C73—22no—
187C4×C73—41no—
188C4×C73—41no—
189C4×C73—41no—
190Dic73—22no—
191Dic73—22no—
192Dic73—41no—
193Dic73—41no—
194Dic73—41no—
195Dic73—41no—
196Dic73—41no—
197C2×C73—24no—
198C2×C73C2×C22⋊Q811yescharacteristic
199C2×C73#52911yescharacteristic
200C2×C73#53811yescharacteristic
201C2×C73#54611yescharacteristic
202C2×C73#54611yescharacteristic
203C2×C73#55411yescharacteristic
204C2×C73#55411yescharacteristic
205D73—42no—
206#2450—731nomaximal, Sylow
207C73#245011yescharacteristic, complemented, Sylow
208C2×C22⋊Q8D7311yescharacteristic, complemented
209C2×C4×D4—731no—
210#400—731no—
211#398—731no—
212#396—731no—
213#393—731no—
214#391—731no—
215#387—731no—
216#386—731no—
217#386—731no—
218#385—731no—
219#385—731no—
220#385—731no—
221#380—731no—
222C2×#95—731no—
223C22×Q8C2×D7311yescharacteristic
224C22×D4—731no—
225C23×C4—731no—
226C23×C4—731no—
227C23×C4—731no—
228C23×C4C2×D7311yescharacteristic
229C22⋊Q8—24no—
230C4×D4—1464no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C4⋊C4C2×D7311yescharacteristic
237C2×C4⋊C4C2×D7311yescharacteristic
238C2×C4⋊C4C2×D7311yescharacteristic
239C2×C22⋊C4—731no—
240C2×C22⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C22⋊C4—731no—
243C2×C22⋊C4—731no—
244C2×C22⋊C4—731no—
245C2×C22⋊C4C2×D7311yescharacteristic
246C2×C22⋊C4C2×D7311yescharacteristic
247C2×C42—731no—
248#95—731no—
249#95—731no—
250#95—731no—
251#95—731no—
252#95—731no—
253#95—731no—
254#95—731no—
255#95—731no—
256#95—731no—
257#95—731no—
258#95—731no—
259#95—731no—
260C24—731no—
261C24C22×D7311yescharacteristic
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×D4—734no—
266C2×D4—1462no—
267C2×D4—1462no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—2921no—
272C22×C4—2921no—
273C22×C4—2921no—
274C22×C4—2921no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—731no—
282C22×C4—1462no—
283C22×C4—1462no—
284C22×C4—1462no—
285C22×C4—1462no—
286C22×C4—1462no—
287C22×C4C22×D7311yescharacteristic
288C22×C4C22×D7311yescharacteristic
289C22×C4C22×D7311yescharacteristic
290C22×C4C22×D7311yescharacteristic
291C22×C4C22×D7311yescharacteristic
292C22×C4C22×D7311yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—2921no—
297C4⋊C4—2921no—
298C4⋊C4—2921no—
299C4⋊C4—1462no—
300C4⋊C4—1462no—
301C22⋊C4—22no—
302C22⋊C4—2921no—
303C22⋊C4—2921no—
304C22⋊C4—2921no—
305C22⋊C4—1462no—
306C22⋊C4—1462no—
307C22⋊C4—1462no—
308C22⋊C4C22⋊D7314yes—
309C42—1462no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—732no—
315C23—1461no—
316C23—1461no—
317C23—1461no—
318C23—1461no—
319C23—1461no—
320C23—1461no—
321C23C2×C22⋊D7312yes—
322C23Q8×D7312yes—
323C23#1192402912yes—
324C23C23×D7311yescharacteristic
325Q8—44no—
326D4—1468no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—2924no—
344C2×C4—2924no—
345C2×C4—2924no—
346C2×C4—732no—
347C2×C4—732no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4—1461no—
363C2×C4—1461no—
364C2×C4—1461no—
365C2×C4—1461no—
366C2×C4—1461no—
367C2×C4C2×C22⋊D7312yes—
368C2×C4C2×C22⋊D7312yes—
369C2×C4#1192402712yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—2921no—
377C22—2921no—
378C22—2921no—
379C22—2921no—
380C22—1462no—
381C22—1462no—
382C22—1462no—
383C22#1455656714yes—
384C22C22×C22⋊D7311yescharacteristic
385C22C2×Q8×D7311yescharacteristic
386C22#41×D7311yescharacteristic
387C22C2×#1192402711yescharacteristic
388C22C2×#1192402911yescharacteristic
389C22#1455663611yescharacteristic
390C22#1455663711yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—2921no—
398C4—2921no—
399C4—2921no—
400C4—2921no—
401C4—2921no—
402C4—1462no—
403C4—1462no—
404C2—24no—
405C2—2922no—
406C2C2×#1455656711yescharacteristic
407C2#1798912311yescharacteristic
408C2#1798917711yescharacteristic
409C2#1798922511yescharacteristic
410C2#1798923111yescharacteristic
411C2#1798929111yescharacteristic
412C2#1798929511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×C22⋊Q8×C73C2
hypercenterC2×C22⋊Q8D73
hypocenterC73#2450
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #17988525C2semidirect
3. #17988520C2semidirect
4. #17988509C2semidirect
5. #17988498C2semidirect
6. #17988494C2semidirect
7. #17988468C2semidirect
10. #17988462C2semidirect
11. #17988459C2semidirect
12. #17988458C2semidirect
13. #17988444C2semidirect
14. C2×#14556498C2semidirect
15. C2×C22⋊Q8×C73C2semidirect
56. C2×C22⋊D73Q8semidirect
207. C73#2450semidirect
208. C2×C22⋊Q8D73semidirect