Finite Group Databasebeta

← #22623814

Subgroups — #22623814

Order 9344.

992 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989315C211yesmaximal, characteristic, complemented
2#17989312C212yesmaximal, complemented
3#17989311C211yesmaximal, characteristic, complemented
4#17989310C211yesmaximal, characteristic, complemented
5#17989309C212yesmaximal, complemented
6#17989278C212yesmaximal, complemented
7#17989275C212yesmaximal, complemented
8#17989269C214yesmaximal, complemented
9#17989196C214yesmaximal, complemented
10#17989162C212yesmaximal
11#17989143C212yesmaximal, complemented
12#17989141C212yesmaximal, complemented
13#17989141C211yesmaximal, characteristic, complemented
14C4⋊Q8×D73C211yesmaximal, characteristic, complemented
15#17989063C212yesmaximal, complemented
16C4×#11924029C211yesmaximal, characteristic
17#557×C73C211yesmaximal, characteristic, complemented
18C2×#11924029C2211yescharacteristic
19C2×Q8×D73C2212yes—
20#14556591C2211yescharacteristic
21#14556590C2212yes—
22#14556590C2212yes—
23#14556590C2211yescharacteristic
24#14556589C2212yes—
25#14556589C2211yescharacteristic
26#14556589C2212yes—
27#14556586C2214yes—
28#14556586C2214yes—
29#14556586C2214yes—
30#14556585C2214yes—
31#14556583C2212yes—
32#14556582C2214yes—
33#14556581C2212yes—
34#14556581C2214yes—
35#14556581C2214yes—
36#14556581C2214yes—
37#14556580C2212yes—
38#14556579C2212yes—
39#14556576C2214yes—
40#14556576C2214yes—
41#14556571C2211yescharacteristic
42#14556571C2212yes—
43#14556569C2214yes—
44#14556569C2212yes—
45#14556569C2214yes—
46#14556569C2214yes—
47#14556567C2211yescharacteristic
48#14556567C2212yes—
49Q8×Dic73C2212yes—
50Q8×Dic73C2211yescharacteristic
51C4×Dic146C2214yes—
52C4×Dic146C2212yes—
53C4×Dic146C2212yes—
54C4×Dic146C2211yescharacteristic
55C4×Dic146C2212yes—
56#14556556C2214yes—
57#14556556C2214yes—
58#14556556C2212yes—
59C4×D292C2212yes—
60C4×D292C2211yescharacteristic
61#14556553C2212yes—
62#14556553C2211yescharacteristic
63#14556549C2212yes—
64#14556549C2212yes—
65#14556549C2212yes—
66#14556549C2214yes—
67#14556549C2211yescharacteristic
68#14556548C2212yes—
69#14556548C2214yes—
70#14556548C2214yes—
71C4⋊C4×D73C2212yes—
72C4⋊C4×D73C2212yes—
73C42×D73C2211yescharacteristic
74C42×D73C2212yes—
75C4⋊Q8×C73C2211yescharacteristic
76C4⋊Q8×C73C2212yes—
77#125×C73C2212yes—
78#125×C73C2214yes—
79C4×Q8×C73C2212yes—
80C4×Q8×C73C2211yescharacteristic
81C4×Q8×C73C2212yes—
82C4×Q8×C73C2211yescharacteristic
83#11924029—24no—
84C2×Dic146C2312yes—
85C2×Dic146C2314yes—
86C2×Dic146C2312yes—
87C2×Dic146C2311yescharacteristic
88Q8×D73—28no—
89C2×D292C2312yes—
90C2×D292C2311yescharacteristic
91C2×C4×D73C2311yescharacteristic
92C2×C4×D73C2311yescharacteristic
93C2×C4×D73C2312yes—
94C2×C4×D73C2312yes—
95C2×C4×D73C2312yes—
96C2×C4×D73C2314yes—
97C2×C4×D73C2311yescharacteristic
98C4⋊Dic73C2312yes—
99C4⋊Dic73C2312yes—
100C4⋊Dic73C2311yescharacteristic
101C4⋊Dic73C2311yescharacteristic
102C4⋊Dic73C2312yes—
103C4⋊Dic73C2314yes—
104C4⋊Dic73C2312yes—
105#11924007C2314yes—
106#11924007C2314yes—
107#11924007C2312yes—
108#11924007C2312yes—
109#11924007C2314yes—
110#11924007C2314yes—
111#11924007C2312yes—
112#11924007C2314yes—
113#11924007C2312yes—
114#11924007C2314yes—
115#11924007C2312yes—
116#11924005C2312yes—
117#11924005C2312yes—
118#11924005C2312yes—
119#11924005C2314yes—
120#11924005C2314yes—
121#11924005C2312yes—
122#11924005C2312yes—
123#11924005C2314yes—
124#11924005C2314yes—
125C4×Dic73C2311yescharacteristic
126C4×Dic73C2312yes—
127C4×Dic73C2311yescharacteristic
128C4×Dic73C2312yes—
129C4×Dic73C2311yescharacteristic
130C4×Dic73C2314yes—
131C4×Dic73C2314yes—
132C4×Dic73C2312yes—
133C4×Dic73C2314yes—
134C2×Q8×C73C2311yescharacteristic
135C2×Q8×C73C2312yes—
136C2×Q8×C73C2311yescharacteristic
137C4⋊C4×C73C2311yescharacteristic
138C4⋊C4×C73C2311yescharacteristic
139C4⋊C4×C73C2312yes—
140C4⋊C4×C73C2314yes—
141C4⋊C4×C73C2312yes—
142C4⋊C4×C73C2312yes—
143C4⋊C4×C73C2314yes—
144C4⋊C4×C73C2312yes—
145C4⋊C4×C73C2314yes—
146C42×C73C2312yes—
147C42×C73C2314yes—
148C42×C73C2311yescharacteristic
149C42×C73C2312yes—
150C22×D73C2412yes—
151C22×D73C2411yescharacteristic
152Q8×C73—24no—
153Q8×C73—22no—
154Q8×C73—22no—
155C2×C4×C73C2412yes—
156C2×C4×C73C2412yes—
157C2×C4×C73C2412yes—
158C2×C4×C73C2411yescharacteristic
159C2×C4×C73C2414yes—
160C2×C4×C73C2412yes—
161C2×C4×C73C2411yescharacteristic
162C2×C4×C73C2411yescharacteristic
163C2×Dic73C2412yes—
164C2×Dic73C2412yes—
165C2×Dic73C2412yes—
166C2×Dic73C2411yescharacteristic
167C2×Dic73C2414yes—
168C2×Dic73C2411yescharacteristic
169C2×Dic73C2411yescharacteristic
170D292—24no—
171D292—22no—
172C4×D73—28no—
173C4×D73—22no—
174C4×D73—24no—
175C4×D73—24no—
176C4×D73—22no—
177C4×D73—24no—
178C4×D73#4114yes—
179Dic146—24no—
180Dic146—22no—
181Dic146—28no—
182Dic146—24no—
183C22×C73C2511yescharacteristic
184C2×D73—21no—
185C2×D73—21no—
186C2×D73—22no—
187C2×D73—22no—
188C2×D73—22no—
189C2×D73C2×#4112yes—
190C4×C73—24no—
191C4×C73—22no—
192C4×C73—22no—
193C4×C73—22no—
194C4×C73—21no—
195C4×C73—22no—
196C4×C73C2×#4112yes—
197C4×C732−1+412yes—
198Dic73—24no—
199Dic73—22no—
200Dic73—22no—
201Dic73—22no—
202Dic73—21no—
203Dic73C2×#4112yes—
204Dic732−1+412yes—
205C2×C73C22×#4111yescharacteristic
206C2×C73C2×2−1+411yescharacteristic
207C2×C73C2×2−1+411yescharacteristic
208D73—22no—
209D73—42no—
210#3509—731nomaximal, Sylow
211C73#350911yescharacteristic, complemented, Sylow
212#557—732no—
213#557—731no—
214#557D7311yescharacteristic, complemented
215#556—731no—
216#556—732no—
217#556—731no—
218#552—734no—
219#552—732no—
220#552—732no—
221#541—734no—
222#536—732no—
223#533—732no—
224#533—731no—
225#533—732no—
226C2×C4⋊Q8—731no—
227#519—732no—
228C4×#41—731no—
229C2×#41—731no—
230C22×Q8—732no—
231C4⋊Q8—732no—
232C4⋊Q8—731no—
233C4⋊Q8—732no—
234C4⋊Q8—732no—
235C4⋊Q8—732no—
236C4⋊Q8—731no—
237C4⋊Q8—731no—
238C4⋊Q8C2×D7311yescharacteristic
239C4⋊Q8C2×D7312yes—
240#126—734no—
241#126—734no—
242#126—734no—
243#126—734no—
244#125—732no—
245#125—734no—
246#125—734no—
247#125—734no—
248#125—734no—
249#125—732no—
250#125C2×D7312yes—
251#125C2×D7314yes—
252#124—732no—
253#124—732no—
254#123—734no—
255#123—734no—
256C22⋊Q8—731no—
257C22⋊Q8—732no—
258C22⋊Q8—734no—
259C22⋊Q8—734no—
260C22⋊Q8—732no—
261C22⋊Q8—731no—
262C22⋊Q8—734no—
263C22⋊Q8—732no—
264C4×Q8—731no—
265C4×Q8—732no—
266C4×Q8—734no—
267C4×Q8—732no—
268C4×Q8—734no—
269C4×Q8—734no—
270C4×Q8—732no—
271C4×Q8—732no—
272C4×Q8—732no—
273C4×Q8—731no—
274C4×Q8C2×D7311yescharacteristic
275C4×Q8C2×D7312yes—
276C4×Q8C2×D7312yes—
277C4×Q8C2×D7311yescharacteristic
278C4×D4—732no—
279C4×D4—731no—
280C4×D4—732no—
281C4×D4—731no—
282#117—731no—
283#117—732no—
284#117—734no—
285#117—732no—
286#117—732no—
287#117—732no—
288#117—734no—
289#117—734no—
290C2×C4⋊C4—732no—
291C2×C4⋊C4—732no—
292C2×C42—731no—
293C2×C42—732no—
294#41—1464no—
295C2×Q8—732no—
296C2×Q8—731no—
297C2×Q8—734no—
298C2×Q8—732no—
299C2×Q8—1468no—
300C2×Q8C22×D7312yes—
301C2×Q8C22×D7311yescharacteristic
302C2×Q8C22×D7311yescharacteristic
303C2×D4—732no—
304C2×D4—731no—
305C22×C4—731no—
306C22×C4—731no—
307C22×C4—731no—
308C22×C4—732no—
309C22×C4—732no—
310C22×C4—732no—
311C22×C4—734no—
312C4⋊C4—734no—
313C4⋊C4—734no—
314C4⋊C4—732no—
315C4⋊C4—732no—
316C4⋊C4—732no—
317C4⋊C4—734no—
318C4⋊C4—734no—
319C4⋊C4—734no—
320C4⋊C4—734no—
321C4⋊C4—732no—
322C4⋊C4—732no—
323C4⋊C4—732no—
324C4⋊C4—732no—
325C4⋊C4—731no—
326C4⋊C4—731no—
327C4⋊C4—732no—
328C4⋊C4—734no—
329C4⋊C4—732no—
330C4⋊C4C22×D7312yes—
331C4⋊C4C22×D7312yes—
332C4⋊C4C22×D7311yescharacteristic
333C4⋊C4C22×D7311yescharacteristic
334C4⋊C4C22×D7312yes—
335C4⋊C4C22×D7314yes—
336C4⋊C4C22×D7314yes—
337C4⋊C4C22×D7314yes—
338C4⋊C4C22×D7312yes—
339C22⋊C4—732no—
340C22⋊C4—732no—
341C22⋊C4—732no—
342C22⋊C4—732no—
343C22⋊C4—732no—
344C22⋊C4—734no—
345C22⋊C4—734no—
346C22⋊C4—734no—
347C22⋊C4—734no—
348C42—731no—
349C42—732no—
350C42—731no—
351C42—732no—
352C42—731no—
353C42—734no—
354C42—734no—
355C42—734no—
356C42—732no—
357C42C22×D7312yes—
358C42C22×D7311yescharacteristic
359C42C22×D7314yes—
360C42C22×D7312yes—
361C23—731no—
362C23—732no—
363Q8—24no—
364Q8—22no—
365Q8—22no—
366Q8—1468no—
367Q8—1464no—
368Q8—1464no—
369Q8—1462no—
370D4—1464no—
371D4—1462no—
372C2×C4—731no—
373C2×C4—731no—
374C2×C4—734no—
375C2×C4—732no—
376C2×C4—732no—
377C2×C4—732no—
378C2×C4—731no—
379C2×C4—734no—
380C2×C4—1464no—
381C2×C4—1464no—
382C2×C4—1462no—
383C2×C4—1468no—
384C2×C4—1464no—
385C2×C4—1462no—
386C2×C4C23×D7312yes—
387C2×C4C23×D7312yes—
388C2×C4C23×D7311yescharacteristic
389C2×C4C23×D7314yes—
390C2×C4C23×D7312yes—
391C2×C4C23×D7312yes—
392C2×C4C23×D7311yescharacteristic
393C2×C4C23×D7311yescharacteristic
394C22—732no—
395C22—1462no—
396C22—1462no—
397C22—1462no—
398C22—1461no—
399C22—1461no—
400C22C24×D7311yescharacteristic
401C4—22no—
402C4—24no—
403C4—22no—
404C4—21no—
405C4—22no—
406C4—22no—
407C4—732no—
408C4—732no—
409C4—1464no—
410C4—1462no—
411C4—1462no—
412C4—1461no—
413C4—1462no—
414C4#41×D7312yes—
415C4#1455663912yes—
416C2—2922no—
417C2—1462no—
418C2C2×#41×D7311yescharacteristic
419C22−1+4×D7311yescharacteristic
420C2C2×#1455663911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D73
commutator, socleC22×C73C25
Fitting#557×C73C2
hypercenter#557D73
hypocenterC73#3509
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #17989315C2semidirect
2. #17989312C2semidirect
3. #17989311C2semidirect
4. #17989310C2semidirect
5. #17989309C2semidirect
6. #17989278C2semidirect
7. #17989275C2semidirect
8. #17989269C2semidirect
9. #17989196C2semidirect
11. #17989143C2semidirect
12. #17989141C2semidirect
13. #17989141C2semidirect
14. C4⋊Q8×D73C2semidirect
15. #17989063C2semidirect
17. #557×C73C2semidirect
211. C73#3509semidirect
214. #557D73semidirect