Finite Group Databasebeta

← #22616430

Subgroups — #22616430

Order 9344.

536 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556571C211yesmaximal, characteristic, complemented
2C2×#14556570C211yesmaximal, characteristic, complemented
3#17988522C211yesmaximal, characteristic, complemented
4#17988520C211yesmaximal, characteristic, complemented
5#17988510C211yesmaximal, characteristic, complemented
6#17988507C211yesmaximal, characteristic, complemented
7#17988500C211yesmaximal, characteristic, complemented
8#17988499C211yesmaximal, characteristic, complemented
9#17988491C211yesmaximal, characteristic, complemented
10#17988487C211yesmaximal, characteristic
11#17988472C211yesmaximal, characteristic, complemented
12#17988466C211yesmaximal, characteristic
13#17988463C211yesmaximal, characteristic
14#17988446C211yesmaximal, characteristic, complemented
15#385×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556571—24no—
21#14556570—24no—
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C23×D73C2311yescharacteristic
54C2×Dic146—22no—
55C2×Dic146—22no—
56C2×Dic146—22no—
57C2×Dic146—41no—
58C2×Dic146—41no—
59C2×Dic146—41no—
60C2×C22⋊D73—41no—
61C2×C22⋊D73—41no—
62C2×C22⋊D73Q814yescomplemented
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—22no—
74C4⋊Dic73D414yescomplemented
75#11924007—22no—
76#11924007—22no—
77#11924007—41no—
78#11924007—41no—
79#11924007—41no—
80C22⋊Dic73—22no—
81C22⋊Dic73—22no—
82C22⋊Dic73—41no—
83#11924005—22no—
84#11924005—22no—
85#11924005—41no—
86#11924005—41no—
87#11924005—41no—
88C4×Dic73—41no—
89C24×C73C2311yescharacteristic
90C22×C4×C73—22no—
91C22×C4×C73—41no—
92C22×C4×C73—41no—
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—41no—
101C22⋊C4×C73—22no—
102C22⋊C4×C73—41no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73C2×Q812yes—
110C23×C73C2411yescharacteristic
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73C2×Q812yes—
118C2×C4×C73—21no—
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×C73#4112yes—
137C22⋊D73—44no—
138C2×Dic73—21no—
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×Dic73C2×D412yes—
157C2×Dic73C2×D412yes—
158C2×Dic73C2×Q812yes—
159C4×D73—44no—
160Dic146—44no—
161Dic146—44no—
162C22×C73—22no—
163C22×C73—22no—
164C22×C73—22no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73C22×D411yescharacteristic
170C22×C73C22×Q811yescharacteristic
171C22×C73C2×#4111yescharacteristic
172C22×C73H(5,𝔽2)11yescharacteristic
173C22×C73H(5,𝔽2)11yescharacteristic
174C22×C73H(5,𝔽2)11yescharacteristic
175C22×C732−1+411yescharacteristic
176C2×D73—22no—
177C2×D73—22no—
178C2×D73—22no—
179C2×D73—41no—
180C2×D73—41no—
181C2×D73—41no—
182C2×D73—41no—
183C4×C73—22no—
184C4×C73—22no—
185C4×C73—41no—
186C4×C73—41no—
187C4×C73—41no—
188C4×C73—41no—
189Dic73—22no—
190Dic73—22no—
191Dic73—22no—
192Dic73—41no—
193Dic73—41no—
194Dic73—41no—
195Dic73—41no—
196C2×C73—42no—
197C2×C73#53511yescharacteristic
198C2×C73#54211yescharacteristic
199C2×C73#54311yescharacteristic
200C2×C73#54611yescharacteristic
201C2×C73D4×Q811yescharacteristic
202C2×C73#55411yescharacteristic
203C2×C73#56211yescharacteristic
204D73—42no—
205#2692—731nomaximal, Sylow
206C73#269211yescharacteristic, complemented, Sylow
207C2×C22⋊Q8—731no—
208C2×C22⋊Q8—731no—
209#399—731no—
210#398—731no—
211#396—731no—
212#395—731no—
213#393—731no—
214#393—731no—
215#391—731no—
216#390—731no—
217#387—731no—
218#386—731no—
219#386—731no—
220#385D7311yescharacteristic, complemented
221#380—731no—
222C22×Q8—731no—
223C22×Q8—731no—
224C22×D4—731no—
225C23×C4—731no—
226C23×C4C2×D7311yescharacteristic
227C22⋊Q8—1464no—
228C22⋊Q8—1464no—
229C2×C4⋊C4—731no—
230C2×C4⋊C4—731no—
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⋊C4—731no—
245C2×C22⋊C4—731no—
246C2×C22⋊C4C2×D7311yescharacteristic
247C2×C22⋊C4C2×D7311yescharacteristic
248C2×C42—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#95C2×D7311yescharacteristic
258#95C2×D7311yescharacteristic
259C24—731no—
260C24C22×D7311yescharacteristic
261C2×Q8—2921no—
262C2×Q8—2921no—
263C2×Q8—2921no—
264C2×Q8—1462no—
265C2×Q8—1462no—
266C2×Q8—1462no—
267C2×D4—2921no—
268C2×D4—2921no—
269C2×D4—734no—
270C22×C4—22no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—2921no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—1462no—
282C22×C4—1462no—
283C22×C4C22×D7311yescharacteristic
284C22×C4C22×D7311yescharacteristic
285C22×C4C22×D7311yescharacteristic
286C22×C4C22×D7311yescharacteristic
287C22×C4C22×D7311yescharacteristic
288C22×C4C22×D7311yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—2921no—
292C4⋊C4—2921no—
293C4⋊C4—2921no—
294C4⋊C4—734no—
295C4⋊C4—1462no—
296C4⋊C4—1462no—
297C4⋊C4—1462no—
298C22⋊C4—22no—
299C22⋊C4—41no—
300C22⋊C4—2921no—
301C22⋊C4—2921no—
302C22⋊C4—2921no—
303C22⋊C4—2921no—
304C22⋊C4—1462no—
305C22⋊C4—1462no—
306C22⋊C4—1462no—
307C22⋊C4—1462no—
308C42—2921no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—732no—
316C23—1461no—
317C23—1461no—
318C23—1461no—
319C23—1461no—
320C23—1461no—
321C23—1461no—
322C23Q8×D7312yes—
323C23C23×D7311yescharacteristic
324Q8—2924no—
325Q8—2924no—
326D4—2924no—
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—21no—
343C2×C4—44no—
344C2×C4—2924no—
345C2×C4—732no—
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×C4D4×D7312yes—
367C2×C4#1192402812yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—2921no—
376C22—2921no—
377C22—2921no—
378C22—2921no—
379C22—1462no—
380C22—1462no—
381C22—1462no—
382C22C2×D4×D7311yescharacteristic
383C22C2×Q8×D7311yescharacteristic
384C22C2×#1192402811yescharacteristic
385C22#1455663611yescharacteristic
386C22#1455663611yescharacteristic
387C22#1455663711yescharacteristic
388C22#1455663811yescharacteristic
389C4—22no—
390C4—22no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—2921no—
396C4—2921no—
397C4—2921no—
398C4—2921no—
399C4—1462no—
400C4—1462no—
401C4—1462no—
402C2—42no—
403C2—2922no—
404C2#1798915211yescharacteristic
405C2#1798920211yescharacteristic
406C2#1798921211yescharacteristic
407C2#1798923311yescharacteristic
408C2#1798925011yescharacteristic
409C2#1798929211yescharacteristic
410C2#1798933411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2692
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14556571C2semidirect
2. C2×#14556570C2semidirect
3. #17988522C2semidirect
4. #17988520C2semidirect
5. #17988510C2semidirect
6. #17988507C2semidirect
7. #17988500C2semidirect
8. #17988499C2semidirect
9. #17988491C2semidirect
11. #17988472C2semidirect
14. #17988446C2semidirect
15. #385×C73C2semidirect
62. C2×C22⋊D73Q8semidirect
74. C4⋊Dic73D4semidirect
206. C73#2692semidirect
220. #385D73semidirect