Finite Group Databasebeta

← #22612923

Subgroups — #22612923

Order 9344.

652 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×#14556574C211yesmaximal, characteristic
2C2×#14556551C211yesmaximal, characteristic
3#17988482C211yesmaximal, characteristic, complemented
4#17988478C211yesmaximal, characteristic, complemented
5#17988477C211yesmaximal, characteristic, complemented
6#17988471C211yesmaximal, characteristic, complemented
7#17988468C211yesmaximal, characteristic, complemented
8#17988464C211yesmaximal, characteristic
9#17988459C211yesmaximal, characteristic, complemented
10#17988458C211yesmaximal, characteristic, complemented
11C4×#11924007C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
13C4×#11924005C211yesmaximal, characteristic, complemented
14C2×#14556498C211yesmaximal, characteristic, complemented
15C2×#117×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C23×Dic73C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556574C418yescomplemented
21#14556551—24no—
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×C4×Dic73C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47#117×C73—24no—
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C42×C73C2211yescharacteristic
53C2×C42×C73C2211yescharacteristic
54C23×D73C2311yescharacteristic
55C2×C22⋊D73—22no—
56C2×C22⋊D73—22no—
57C2×C22⋊D73C2×C414yes—
58C22×Dic73—22no—
59C22×Dic73—22no—
60C22×Dic73—22no—
61C22×Dic73—22no—
62C22×Dic73—41no—
63C22×Dic73—41no—
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C22×Dic73C2311yescharacteristic
71C2×C4×D73—22no—
72C2×C4×D73—22no—
73C2×C4×D73—41no—
74#11924007—22no—
75#11924007—22no—
76#11924007—41no—
77#11924007C2×C414yescomplemented
78#11924007C2×C414yescomplemented
79C22⋊Dic73C2×C414yescomplemented
80#11924005—22no—
81#11924005—22no—
82#11924005—41no—
83#11924005C2×C414yescomplemented
84#11924005C2×C414yescomplemented
85C4×Dic73—22no—
86C4×Dic73—22no—
87C4×Dic73—41no—
88C24×C73C2311yescharacteristic
89C22×C4×C73—22no—
90C22×C4×C73—22no—
91C22×C4×C73C2×C414yescomplemented
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—
100C22⋊C4×C73—22no—
101C22⋊C4×C73D414yes—
102C42×C73—22no—
103C42×C73—22no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73C22×C412yes—
109C23×C73C2×D412yes—
110C23×C73#4112yes—
111C23×C73C2411yescharacteristic
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73C22×C412yes—
119C2×C4×C73—28no—
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×C73C22×C412yes—
135C2×C4×C73C22×C412yes—
136C2×C4×C73C2×D412yes—
137C2×C4×C73C2×D412yes—
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—44no—
156C2×Dic73—44no—
157C2×Dic73C22×C412yes—
158C2×Dic73C22×C412yes—
159C2×Dic73C22×C412yes—
160C2×Dic73#4112yes—
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×C73C4×D414yes—
170C22×C73C23×C411yescharacteristic
171C22×C73C22×D411yescharacteristic
172C22×C73C2×#4111yescharacteristic
173C22×C73C2×#4111yescharacteristic
174C22×C73C2×#4111yescharacteristic
175C22×C73H(5,𝔽2)11yescharacteristic
176C22×C732−1+411yescharacteristic
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—22no—
188C4×C73—41no—
189C4×C73—41no—
190Dic73—22no—
191Dic73—22no—
192Dic73—22no—
193Dic73—22no—
194Dic73—22no—
195Dic73—41no—
196Dic73—41no—
197C2×C73—24no—
198C2×C73C2×C4×D411yescharacteristic
199C2×C73C4×#4111yescharacteristic
200C2×C73#52011yescharacteristic
201C2×C73#54611yescharacteristic
202C2×C73#54711yescharacteristic
203C2×C73#55111yescharacteristic
204C2×C73#55211yescharacteristic
205D73—42no—
206#2359—731nomaximal, Sylow
207C73#235911yescharacteristic, complemented, Sylow
208C2×#123—731no—
209C2×C4×D4—731no—
210C2×#117D7311yescharacteristic, complemented
211#389—731no—
212#388—731no—
213#388—731no—
214#387—731no—
215#387—731no—
216#386—731no—
217#385—731no—
218#385—731no—
219C4×C4⋊C4—731no—
220C4×C22⋊C4—731no—
221C4×C22⋊C4—731no—
222C2×#95—731no—
223C22×D4—731no—
224C23×C4—731no—
225C23×C4—731no—
226C23×C4—731no—
227C23×C4C2×D7311yescharacteristic
228#123—738no—
229C4×D4—1464no—
230#117—24no—
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×C22⋊C4—731no—
239C2×C22⋊C4—731no—
240C2×C22⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C22⋊C4—731no—
243C2×C22⋊C4—731no—
244C2×C22⋊C4C2×D7311yescharacteristic
245C2×C22⋊C4C2×D7311yescharacteristic
246C2×C42—731no—
247C2×C42—731no—
248C2×C42—731no—
249C2×C42C2×D7311yescharacteristic
250C2×C42C2×D7311yescharacteristic
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—
260#95—731no—
261C24—731no—
262C24C22×D7311yescharacteristic
263C2×D4—734no—
264C2×D4—1462no—
265C2×D4—1462no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—2921no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—1462no—
279C22×C4—1462no—
280C22×C4—1462no—
281C22×C4—1462no—
282C22×C4—1462no—
283C22×C4—1462no—
284C22×C4C4×D7314yescomplemented
285C22×C4C22×D7311yescharacteristic
286C22×C4C22×D7311yescharacteristic
287C22×C4C22×D7311yescharacteristic
288C22×C4C22×D7311yescharacteristic
289C22×C4C22×D7311yescharacteristic
290C22×C4C22×D7311yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—2921no—
294C4⋊C4—734no—
295C4⋊C4—734no—
296C4⋊C4—1462no—
297C4⋊C4—1462no—
298C22⋊C4—22no—
299C22⋊C4—2921no—
300C22⋊C4—734no—
301C22⋊C4—734no—
302C22⋊C4—734no—
303C22⋊C4—1462no—
304C22⋊C4—1462no—
305C22⋊C4C22⋊D7314yes—
306C42—22no—
307C42—22no—
308C42—2921no—
309C42—1462no—
310C42—1462no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—732no—
316C23—1461no—
317C23—1461no—
318C23—1461no—
319C23—1461no—
320C23—1461no—
321C23—1461no—
322C23C2×C4×D7312yes—
323C23C2×C22⋊D7312yes—
324C23#1192402812yes—
325C23C23×D7311yescharacteristic
326D4—1468no—
327C2×C4—28no—
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—2924no—
343C2×C4—2924no—
344C2×C4—2924no—
345C2×C4—732no—
346C2×C4—732no—
347C2×C4—732no—
348C2×C4—732no—
349C2×C4—732no—
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×C4C2×C4×D7312yes—
367C2×C4C2×C4×D7312yes—
368C2×C4C2×C22⋊D7312yes—
369C2×C4C2×C22⋊D7312yes—
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—
383C22C4×C22⋊D7314yes—
384C22C22×C4×D7311yescharacteristic
385C22C22×C22⋊D7311yescharacteristic
386C22#41×D7311yescharacteristic
387C22#41×D7311yescharacteristic
388C22C2×#1192402811yescharacteristic
389C22#1455663711yescharacteristic
390C22#1455663811yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—2921no—
398C4—2921no—
399C4—1462no—
400C4—1462no—
401C4—1462no—
402C4—1462no—
403C4—1462no—
404C2—24no—
405C2—2922no—
406C2C2×C4×C22⋊D7311yescharacteristic
407C2#1798905511yescharacteristic
408C2#1798906711yescharacteristic
409C2#1798922511yescharacteristic
410C2#1798923611yescharacteristic
411C2#1798926111yescharacteristic
412C2#1798927011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutatorC22×C73C23×C4
FittingC2×#117×C73C2
socleC23×C73C24
hypercenterC2×#117D73
hypocenterC73#2359
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #17988482C2semidirect
4. #17988478C2semidirect
5. #17988477C2semidirect
6. #17988471C2semidirect
7. #17988468C2semidirect
9. #17988459C2semidirect
10. #17988458C2semidirect
11. C4×#11924007C2semidirect
12. C22⋊C4×Dic73C2semidirect
13. C4×#11924005C2semidirect
14. C2×#14556498C2semidirect
15. C2×#117×C73C2semidirect
20. #14556574C4semidirect
77. #11924007C2×C4semidirect
78. #11924007C2×C4semidirect
79. C22⋊Dic73C2×C4semidirect
83. #11924005C2×C4semidirect
84. #11924005C2×C4semidirect
91. C22×C4×C73C2×C4semidirect
207. C73#2359semidirect
210. C2×#117D73semidirect
284. C22×C4C4×D73semidirect