Finite Group Databasebeta

← #22616211

Subgroups — #22616211

Order 9344.

562 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×#14556589C211yesmaximal, characteristic, complemented
2C2×#14556577C211yesmaximal, characteristic
3C2×#14556573C211yesmaximal, characteristic
4C2×#14556567C211yesmaximal, characteristic, complemented
5#17988523C211yesmaximal, characteristic, complemented
6#17988516C211yesmaximal, characteristic, complemented
7#17988510C211yesmaximal, characteristic, complemented
8#17988508C211yesmaximal, characteristic, complemented
9#17988502C211yesmaximal, characteristic
10#17988484C211yesmaximal, characteristic, complemented
11#17988481C211yesmaximal, characteristic, complemented
12#17988476C211yesmaximal, characteristic, complemented
13#17988474C211yesmaximal, characteristic, complemented
14#17988461C211yesmaximal, characteristic, complemented
15#393×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19#14556589—24no—
20#14556577—24no—
21#14556573—24no—
22#14556567—24no—
23C2×C4⋊Dic73C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×#11924007C2211yescharacteristic
32C2×#11924007C2211yescharacteristic
33C2×C22⋊Dic73C2211yescharacteristic
34C2×C22⋊Dic73C2211yescharacteristic
35C2×C22⋊Dic73C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×#11924005C2211yescharacteristic
38C2×#11924005C2211yescharacteristic
39C2×#11924005C2211yescharacteristic
40C2×#11924005C2211yescharacteristic
41C2×C4×Dic73C2211yescharacteristic
42C2×C4×Dic73C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46#14556498C2211yescharacteristic
47#14556498C2211yescharacteristic
48C22×Q8×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53#95×C73C2211yescharacteristic
54#95×C73C2211yescharacteristic
55C23×D73C2311yescharacteristic
56C2×Dic146—22no—
57C2×Dic146—22no—
58C2×Dic146—41no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C2×C22⋊D73—41no—
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C2×C4×D73—22no—
70C2×C4×D73—22no—
71C2×C4×D73—41no—
72C4⋊Dic73—22no—
73C4⋊Dic73—22no—
74C4⋊Dic73—41no—
75#11924007—22no—
76#11924007—22no—
77#11924007—22no—
78#11924007—22no—
79#11924007—22no—
80#11924007—22no—
81#11924007D414yes—
82C22⋊Dic73—22no—
83C22⋊Dic73—22no—
84C22⋊Dic73—22no—
85#11924005—22no—
86#11924005—22no—
87#11924005—22no—
88#11924005—22no—
89#11924005D414yes—
90C4×Dic73—22no—
91C4×Dic73—22no—
92C24×C73C2311yescharacteristic
93C2×Q8×C73—22no—
94C2×Q8×C73—22no—
95C2×Q8×C73—41no—
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
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—21no—
112C23×C73C2411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—21no—
119C22×D73C2×D412yes—
120Q8×C73—44no—
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—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73C2×D412yes—
138C2×C4×C73C2×D412yes—
139C22⋊D73—44no—
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×Dic73C2×D412yes—
158C2×Dic73C2×D412yes—
159C2×Dic73C2×D412yes—
160C2×Dic73#4112yes—
161C4×D73—44no—
162Dic146—44no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73C22×D411yescharacteristic
171C22×C73C22×D411yescharacteristic
172C22×C73C2×#4111yescharacteristic
173C22×C73H(5,𝔽2)11yescharacteristic
174C22×C732−1+411yescharacteristic
175C22×C732−1+411yescharacteristic
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—41no—
187C4×C73—41no—
188C4×C73—41no—
189C4×C73—41no—
190Dic73—22no—
191Dic73—22no—
192Dic73—22no—
193Dic73—22no—
194Dic73—41no—
195Dic73—41no—
196Dic73—41no—
197C2×C73—81no—
198C2×C73#53611yescharacteristic
199C2×C73#53611yescharacteristic
200C2×C73#54211yescharacteristic
201C2×C73D4211yescharacteristic
202C2×C73#54711yescharacteristic
203C2×C73#54811yescharacteristic
204C2×C73#56311yescharacteristic
205D73—42no—
206#2674—731nomaximal, Sylow
207C73#267411yescharacteristic, complemented, Sylow
208C2×C4⋊Q8—731no—
209C2×#124—731no—
210C2×#123—731no—
211C2×C22⋊Q8—731no—
212#399—731no—
213#397—731no—
214#396—731no—
215#395—731no—
216#394—731no—
217#393D7311yescharacteristic, complemented
218#389—731no—
219#388—731no—
220#388—731no—
221#387—731no—
222#385—731no—
223C22×Q8—731no—
224C22×Q8C2×D7311yescharacteristic
225C22×D4—731no—
226C23×C4—731no—
227C4⋊Q8—1464no—
228#124—1464no—
229#123—1464no—
230C22⋊Q8—1464no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C4⋊C4—731no—
237C2×C4⋊C4—731no—
238C2×C4⋊C4—731no—
239C2×C4⋊C4—731no—
240C2×C4⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C22⋊C4—731no—
243C2×C22⋊C4—731no—
244C2×C22⋊C4—731no—
245C2×C22⋊C4—731no—
246C2×C22⋊C4—731no—
247C2×C22⋊C4—731no—
248C2×C22⋊C4—731no—
249C2×C22⋊C4C2×D7311yescharacteristic
250C2×C22⋊C4C2×D7311yescharacteristic
251C2×C22⋊C4C2×D7311yescharacteristic
252C2×C42—731no—
253C2×C42—731no—
254#95—731no—
255#95—731no—
256#95—731no—
257#95—731no—
258#95—731no—
259#95C2×D7311yescharacteristic
260#95C2×D7311yescharacteristic
261#95C2×D7311yescharacteristic
262C24—731no—
263C24C22×D7311yescharacteristic
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—2921no—
268C2×Q8—1462no—
269C2×Q8—1462no—
270C2×D4—2921no—
271C2×D4—1462no—
272C2×D4—1462no—
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—2921no—
290C4⋊C4—734no—
291C4⋊C4—1462no—
292C4⋊C4—1462no—
293C4⋊C4—1462no—
294C4⋊C4—1462no—
295C4⋊C4—1462no—
296C4⋊C4—1462no—
297C4⋊C4—1462no—
298C4⋊C4—1462no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—41no—
302C22⋊C4—734no—
303C22⋊C4—1462no—
304C22⋊C4—1462no—
305C22⋊C4—1462no—
306C22⋊C4—1462no—
307C22⋊C4—1462no—
308C22⋊C4—1462no—
309C22⋊C4—1462no—
310C42—1462no—
311C42—1462no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—732no—
320C23—1461no—
321C23—1461no—
322C23—1461no—
323C23—1461no—
324C23—1461no—
325C23—1461no—
326C23C23×D7311yescharacteristic
327Q8—44no—
328Q8—2924no—
329D4—2924no—
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—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—2924no—
347C2×C4—732no—
348C2×C4—732no—
349C2×C4—732no—
350C2×C4—732no—
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×C4—1461no—
368C2×C4D4×D7312yes—
369C2×C4D4×D7312yes—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—2921no—
378C22—2921no—
379C22—2921no—
380C22—2921no—
381C22—1462no—
382C22—1462no—
383C22—1462no—
384C22C2×D4×D7311yescharacteristic
385C22C2×D4×D7311yescharacteristic
386C22#41×D7311yescharacteristic
387C22#1455663611yescharacteristic
388C22#1455663811yescharacteristic
389C22#1455663811yescharacteristic
390C22#1455663911yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—2921no—
398C4—2921no—
399C4—2921no—
400C4—1462no—
401C4—1462no—
402C4—1462no—
403C4—1462no—
404C2—81no—
405C2—2922no—
406C2#1798915711yescharacteristic
407C2#1798916011yescharacteristic
408C2#1798920111yescharacteristic
409C2#1798921911yescharacteristic
410C2#1798923911yescharacteristic
411C2#1798924511yescharacteristic
412C2#1798933811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#393×C73C2
hypercenter#393D73
hypocenterC73#2674
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#14556589C2semidirect
4. C2×#14556567C2semidirect
5. #17988523C2semidirect
6. #17988516C2semidirect
7. #17988510C2semidirect
8. #17988508C2semidirect
10. #17988484C2semidirect
11. #17988481C2semidirect
12. #17988476C2semidirect
13. #17988474C2semidirect
14. #17988461C2semidirect
15. #393×C73C2semidirect
207. C73#2674semidirect
217. #393D73semidirect