Finite Group Databasebeta

← #22621571

Subgroups — #22621571

Order 9344.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556620C211yesmaximal, characteristic, complemented
2Q8×C22⋊D73C211yesmaximal, characteristic, complemented
3#17989236C211yesmaximal, characteristic
4#17988965C211yesmaximal, characteristic, complemented
5#17988845C211yesmaximal, characteristic, complemented
6#17988842C211yesmaximal, characteristic, complemented
7#17988795C211yesmaximal, characteristic, complemented
8#17988790C211yesmaximal, characteristic, complemented
9#17988749C211yesmaximal, characteristic, complemented
10#17988746C211yesmaximal, characteristic, complemented
11#17988743C211yesmaximal, characteristic, complemented
12#17988741C211yesmaximal, characteristic, complemented
13SD16×Dic73C211yesmaximal, characteristic, complemented
14#17988663C211yesmaximal, characteristic, complemented
15C2×#137×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18#14556620—24no—
19C2×Dic292C2211yescharacteristic
20C2×#11924018C2211yescharacteristic
21C2×#11924018C2211yescharacteristic
22C2×#11924018C2211yescharacteristic
23C2×#11924016C2211yescharacteristic
24C2×#11924011C2211yescharacteristic
25#14556589—21no—
26#14556589C2211yescharacteristic
27#14556589C2211yescharacteristic
28#14556574—21no—
29#14556572—21no—
30#14556570—21no—
31#14556570C2211yescharacteristic
32#14556570C2211yescharacteristic
33#14556567—21no—
34#14556567C2211yescharacteristic
35#14556567C2211yescharacteristic
36#14556563—21no—
37Q8×Dic73C2211yescharacteristic
38D4×Dic73C2211yescharacteristic
39C4×C22⋊D73—21no—
40C4×C22⋊D73C2211yescharacteristic
41C2×#11924007—21no—
42#14556523C2211yescharacteristic
43#14556520C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556516C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556515C2211yescharacteristic
48#14556515C2211yescharacteristic
49#14556512C2211yescharacteristic
50C22⋊#10596831C2211yescharacteristic
51#14556503C2211yescharacteristic
52C8×Dic73C2211yescharacteristic
53C2×#41×C73C2211yescharacteristic
54C22×Q8×C73C2211yescharacteristic
55#137×C73—24no—
56C2×Q16×C73C2211yescharacteristic
57C2×Q16×C73C2211yescharacteristic
58C2×SD16×C73C2211yescharacteristic
59C2×SD16×C73C2211yescharacteristic
60C2×M16×C73C2211yescharacteristic
61#11924027—22no—
62#11924027—41no—
63C2×Dic146—21no—
64C2×Dic146C2311yescharacteristic
65C2×Dic146C2311yescharacteristic
66Q8×D73—22no—
67Q8×D73—41no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73D411yescharacteristic
70C22×Dic73—21no—
71C22×Dic73—21no—
72C2×C4×D73—21no—
73C2×C4×D73C2311yescharacteristic
74Dic292—22no—
75#11924018—22no—
76#11924018—41no—
77#11924018—41no—
78#11924016—22no—
79#11924011—22no—
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89#11924007—21no—
90#11924007—21no—
91#11924007—21no—
92#11924007—21no—
93#11924007D411yescharacteristic
94C22⋊Dic73—21no—
95C22⋊Dic73—21no—
96C22⋊Dic73—21no—
97C22⋊Dic73D411yescharacteristic
98#11924005—21no—
99#11924005—21no—
100#11924005D411yescharacteristic
101C4×Dic73—21no—
102C4×Dic73C2311yescharacteristic
103#41×C73—22no—
104#41×C73—41no—
105C2×Q8×C73—21no—
106C2×Q8×C73—22no—
107C2×Q8×C73—41no—
108C2×Q8×C73C2311yescharacteristic
109C2×Q8×C73C2311yescharacteristic
110C2×Q8×C73C2311yescharacteristic
111C2×D4×C73—21no—
112C2×D4×C73C2311yescharacteristic
113C22×C4×C73—21no—
114C22×C4×C73—21no—
115C22×C4×C73C2311yescharacteristic
116Q16×C73—22no—
117Q16×C73—22no—
118SD16×C73—22no—
119SD16×C73D414yescomplemented
120M16×C73—22no—
121C2×C8×C73C2311yescharacteristic
122C2×C8×C73C2311yescharacteristic
123C23×C73—21no—
124C23×C73C2×D411yescharacteristic
125C22×D73C2×D411yescharacteristic
126Q8×C73—21no—
127Q8×C73—21no—
128Q8×C73—21no—
129Q8×C73—21no—
130Q8×C73—21no—
131Q8×C73—42no—
132Q8×C73C2×D412yes—
133D4×C73—21no—
134D4×C73—42no—
135D4×C73C2×D412yes—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—42no—
142C2×C4×C73—42no—
143C2×C4×C73C2×D411yescharacteristic
144C2×C4×C73C2411yescharacteristic
145C22⋊D73—22no—
146C22⋊D73—42no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—21no—
151C2×Dic73—42no—
152C2×Dic73—42no—
153C2×Dic73C2×D411yescharacteristic
154C2×Dic73C2×D411yescharacteristic
155C2×Dic73C2×D411yescharacteristic
156C4×D73—21no—
157C4×D73—21no—
158C4×D73—42no—
159Dic146—21no—
160Dic146—21no—
161Dic146—21no—
162Dic146—21no—
163Dic146—42no—
164C8×C73—21no—
165C8×C73C2×D412yes—
166#10596831—21no—
167#10596831—21no—
168C22×C73—22no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73C22×D411yescharacteristic
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—21no—
178C4×C73—22no—
179C4×C73—21no—
180C4×C73—41no—
181C4×C73—41no—
182C4×C73C22×D411yescharacteristic
183C4×C73H(5,𝔽2)11yescharacteristic
184Dic73—21no—
185Dic73—21no—
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189Dic73—41no—
190Dic73#13712yescomplemented
191C2×C73—41no—
192C2×C73—42no—
193C2×C73D4211yescharacteristic
194C2×C73C2×#13711yescharacteristic
195C2×C73#57811yescharacteristic
196D73—41no—
197#3276—731nomaximal, Sylow
198C73#327611yescharacteristic, complemented, Sylow
199C2×#137—731no—
200C2×#137D7311yescharacteristic, complemented
201D4×Q8—731no—
202#547—731no—
203#494—731no—
204#470—731no—
205#470—731no—
206#462—731no—
207#461—731no—
208#452—731no—
209#452—731no—
210#451—731no—
211#451—731no—
212C4×SD16—731no—
213#436—731no—
214C2×#41—731no—
215C2×#41C2×D7311yescharacteristic
216C22×Q8—731no—
217C22×Q8C2×D7311yescharacteristic
218#137—24no—
219#137—1464no—
220C2×Q16—731no—
221C2×Q16—731no—
222C2×Q16—731no—
223C2×Q16—731no—
224C2×Q16C2×D7311yescharacteristic
225C2×Q16C2×D7311yescharacteristic
226C2×SD16—731no—
227C2×SD16C2×D7311yescharacteristic
228C2×SD16C2×D7311yescharacteristic
229C2×M16—731no—
230C2×M16C2×D7311yescharacteristic
231C4⋊Q8—731no—
232C4⋊Q8—731no—
233C4⋊Q8—1461no—
234#123—1461no—
235#123—1461no—
236C22⋊Q8—731no—
237C22⋊Q8—731no—
238C22⋊Q8—731no—
239C22⋊Q8—731no—
240C22⋊Q8—1461no—
241C22⋊Q8—1461no—
242#121—1461no—
243C4×Q8—731no—
244C4×D4—731no—
245C4×D4—731no—
246C4×D4—1461no—
247C2×C4⋊C4—1461no—
248#106—731no—
249C4⋊C8—731no—
250#103—731no—
251#103—731no—
252#103—731no—
253#103—731no—
254#103—731no—
255#102—731no—
256C22⋊C8—731no—
257C22⋊C8—731no—
258C4×C8—731no—
259#41—22no—
260#41—41no—
261#41—2921no—
262#41—1462no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—2921no—
267C2×Q8—731no—
268C2×Q8—731no—
269C2×Q8—1461no—
270C2×Q8—1462no—
271C2×Q8C22×D7311yescharacteristic
272C2×Q8C22×D7311yescharacteristic
273C2×Q8C22×D7311yescharacteristic
274C2×D4—21no—
275C2×D4—731no—
276C2×D4—1461no—
277C2×D4C22×D7311yescharacteristic
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—731no—
281C22×C4—1461no—
282C22×C4—1461no—
283C22×C4—1461no—
284C22×C4C22×D7311yescharacteristic
285Q16—22no—
286Q16—22no—
287Q16—2921no—
288Q16—2921no—
289Q16—1462no—
290Q16—1462no—
291SD16—22no—
292SD16—1462no—
293SD16C22⋊D7314yescomplemented
294M16—22no—
295M16—1462no—
296C2×C8—731no—
297C2×C8—731no—
298C2×C8C22×D7311yescharacteristic
299C2×C8C22×D7311yescharacteristic
300C4⋊C4—731no—
301C4⋊C4—731no—
302C4⋊C4—731no—
303C4⋊C4—1461no—
304C4⋊C4—1461no—
305C4⋊C4—1461no—
306C4⋊C4—1461no—
307C4⋊C4—1461no—
308C4⋊C4—1461no—
309C4⋊C4—1461no—
310C4⋊C4—1461no—
311C4⋊C4—1461no—
312C22⋊C4—731no—
313C22⋊C4—731no—
314C22⋊C4—1461no—
315C22⋊C4—1461no—
316C22⋊C4—1461no—
317C22⋊C4—1461no—
318C22⋊C4—1461no—
319C42—731no—
320C42—1461no—
321C23—21no—
322C23—731no—
323C23D4×D7311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—2922no—
331Q8—1461no—
332Q8—1461no—
333Q8—1461no—
334Q8—1461no—
335Q8C2×C22⋊D7312yes—
336D4—21no—
337D4—42no—
338D4—2922no—
339D4—1462no—
340D4C2×C22⋊D7312yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—2922no—
349C2×C4—2922no—
350C2×C4—2922no—
351C2×C4—731no—
352C2×C4—731no—
353C2×C4—731no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4D4×D7311yescharacteristic
361C2×C4C23×D7311yescharacteristic
362C8—21no—
363C8—1461no—
364C8—1461no—
365C8C2×C22⋊D7312yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—41no—
371C22—41no—
372C22—1461no—
373C22—1461no—
374C22—1461no—
375C22C2×D4×D7311yescharacteristic
376C4—21no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—2921no—
381C4—2921no—
382C4—2921no—
383C4—2921no—
384C4—732no—
385C4—1461no—
386C4—1461no—
387C4C22×C22⋊D7311yescharacteristic
388C4#1455663611yescharacteristic
389C2—41no—
390C2—42no—
391C2—2921no—
392C2D4×C22⋊D7311yescharacteristic
393C2#137×D7311yescharacteristic
394C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#137×C73C2
socleC22×C73C22×D4
hypercenterC2×#137D73
hypocenterC73#3276
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#14556620C2semidirect
2. Q8×C22⋊D73C2semidirect
4. #17988965C2semidirect
5. #17988845C2semidirect
6. #17988842C2semidirect
7. #17988795C2semidirect
8. #17988790C2semidirect
9. #17988749C2semidirect
10. #17988746C2semidirect
11. #17988743C2semidirect
12. #17988741C2semidirect
13. SD16×Dic73C2semidirect
14. #17988663C2semidirect
15. C2×#137×C73C2semidirect
119. SD16×C73D4semidirect
190. Dic73#137semidirect
198. C73#3276semidirect
200. C2×#137D73semidirect
293. SD16C22⋊D73semidirect