Finite Group Databasebeta

← #22622210

Subgroups — #22622210

Order 9344.

374 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989305C211yesmaximal, characteristic
2Q8×C22⋊D73C211yesmaximal, characteristic
3#17988936C211yesmaximal, characteristic, complemented
4#17988928C211yesmaximal, characteristic, complemented
5#17988926C211yesmaximal, characteristic, complemented
6#17988870C211yesmaximal, characteristic, complemented
7#17988845C211yesmaximal, characteristic, complemented
8#17988844C211yesmaximal, characteristic, complemented
9#17988796C211yesmaximal, characteristic, complemented
10#17988744C211yesmaximal, characteristic, complemented
11#17988743C211yesmaximal, characteristic, complemented
12#17988679C211yesmaximal, characteristic, complemented
13#17988663C211yesmaximal, characteristic
14#17988594C211yesmaximal, characteristic, complemented
15#419×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924018C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556589—21no—
23#14556589C2211yescharacteristic
24#14556585—21no—
25#14556584—21no—
26#14556577—21no—
27#14556571C2211yescharacteristic
28#14556570—21no—
29#14556570C2211yescharacteristic
30#14556570C2211yescharacteristic
31#14556567—21no—
32#14556567C2211yescharacteristic
33Q8×Dic73C2211yescharacteristic
34C4×Dic146—21no—
35#14556556C2211yescharacteristic
36C4×C22⋊D73—21no—
37C4×C22⋊D73C2211yescharacteristic
38#14556549C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556514C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C22×Q8×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54#117×C73C2211yescharacteristic
55#103×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146—21no—
61C2×Dic146C2311yescharacteristic
62C2×Dic146C2311yescharacteristic
63Q8×D73—22no—
64Q8×D73—41no—
65C2×C22⋊D73D411yescharacteristic
66C2×C4×D73—21no—
67C2×C4×D73C2311yescharacteristic
68Dic292—41no—
69#11924018—22no—
70#11924018—41no—
71#11924011—41no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007D411yescharacteristic
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73D411yescharacteristic
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005D411yescharacteristic
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73—21no—
98C2×Q8×C73—22no—
99C2×Q8×C73—41no—
100C2×Q8×C73C2311yescharacteristic
101C2×Q8×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73C2311yescharacteristic
104M16×C73—41no—
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C22⋊C4×C73—21no—
110C42×C73—21no—
111C23×C73C2×D411yescharacteristic
112C22×D73C2×D411yescharacteristic
113Q8×C73—21no—
114Q8×C73—21no—
115Q8×C73—21no—
116Q8×C73—42no—
117Q8×C73#4112yes—
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—42no—
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2411yescharacteristic
127C22⋊D73—22no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134C2×Dic73C2×D411yescharacteristic
135C4×D73—21no—
136C4×D73—21no—
137C4×D73—42no—
138Dic146—21no—
139Dic146—21no—
140Dic146—21no—
141Dic146—21no—
142Dic146—42no—
143Dic146—42no—
144C8×C73—21no—
145C8×C73—21no—
146#10596831—21no—
147#10596831—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73C22×D411yescharacteristic
152C2×D73—21no—
153C2×D73—21no—
154C2×D73—21no—
155C4×C73—22no—
156C4×C73—21no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73C2×#4111yescharacteristic
161C4×C73H(5,𝔽2)11yescharacteristic
162Dic73—21no—
163Dic73—21no—
164Dic73—41no—
165Dic73—41no—
166Dic73—41no—
167Dic73—41no—
168Dic73#13712yes—
169C2×C73—41no—
170C2×C73#54611yescharacteristic
171C2×C73C2×#13711yescharacteristic
172C2×C73#57811yescharacteristic
173D73—41no—
174#3328—731nomaximal, Sylow
175C73#332811yescharacteristic, complemented, Sylow
176#556—731no—
177D4×Q8—731no—
178#487—731no—
179#485—731no—
180#485—731no—
181#475—731no—
182#470—731no—
183#470—731no—
184#462—731no—
185#451—731no—
186#451—731no—
187C4×Q16—731no—
188#436—731no—
189#419—731no—
190#419D7311yescharacteristic, complemented
191C22×Q8—731no—
192C22×Q8C2×D7311yescharacteristic
193C2×Q16—731no—
194C2×Q16—731no—
195C2×Q16—731no—
196C2×M16—731no—
197C2×M16C2×D7311yescharacteristic
198C4⋊Q8—731no—
199C4⋊Q8—731no—
200C4⋊Q8—1461no—
201#126—1461no—
202#126—1461no—
203#124—1461no—
204C22⋊Q8—731no—
205C22⋊Q8—731no—
206C22⋊Q8—731no—
207C22⋊Q8—731no—
208C22⋊Q8—1461no—
209C22⋊Q8—1461no—
210C4×Q8—731no—
211C4×Q8—731no—
212C4×Q8—1461no—
213C4×D4—731no—
214C4×D4—1461no—
215#117—731no—
216#117C2×D7311yescharacteristic
217#107—731no—
218#106—731no—
219#106—731no—
220C4⋊C8—731no—
221#103—731no—
222#103—731no—
223#103—731no—
224#103—731no—
225#103—731no—
226#103—731no—
227#103C2×D7311yescharacteristic
228#103C2×D7311yescharacteristic
229#103C2×D7311yescharacteristic
230#103C2×D7311yescharacteristic
231C22⋊C8—731no—
232C22⋊C8—731no—
233C4×C8—731no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—2921no—
238C2×Q8—731no—
239C2×Q8—731no—
240C2×Q8—1461no—
241C2×Q8—1461no—
242C2×Q8—1462no—
243C2×Q8C22×D7311yescharacteristic
244C2×Q8C22×D7311yescharacteristic
245C2×D4—731no—
246C22×C4—21no—
247C22×C4—731no—
248C22×C4—1461no—
249C22×C4C22×D7311yescharacteristic
250Q16—2921no—
251Q16—2921no—
252Q16—1462no—
253M16—41no—
254M16—2921no—
255C2×C8—731no—
256C2×C8—731no—
257C2×C8C22×D7311yescharacteristic
258C2×C8C22×D7311yescharacteristic
259C4⋊C4—731no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4C22×D7311yescharacteristic
272C4⋊C4C22×D7311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—731no—
275C22⋊C4—731no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C42—21no—
282C42—731no—
283C42—1461no—
284C42—1461no—
285C42—1461no—
286C23—731no—
287C23D4×D7311yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—42no—
292Q8—2922no—
293Q8—2922no—
294Q8—1461no—
295Q8—1461no—
296Q8—1461no—
297Q8—1461no—
298Q8#1192402812yes—
299D4—1462no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—2922no—
308C2×C4—731no—
309C2×C4—731no—
310C2×C4—731no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4D4×D7311yescharacteristic
318C2×C4C23×D7311yescharacteristic
319C8—21no—
320C8—21no—
321C8—1461no—
322C8—1461no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—1461no—
327C22—1461no—
328C22—1461no—
329C22C2×D4×D7311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—2921no—
336C4—2921no—
337C4—2921no—
338C4—2921no—
339C4—732no—
340C4—1461no—
341C4—1461no—
342C4C2×#1192402811yescharacteristic
343C4#1455663611yescharacteristic
344C2—41no—
345C2—2921no—
346C2#1798922711yescharacteristic
347C2#137×D7311yescharacteristic
348C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#419×C73C2
socleC22×C73C22×D4
hypercenter#419D73
hypocenterC73#3328
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #17988936C2semidirect
4. #17988928C2semidirect
5. #17988926C2semidirect
6. #17988870C2semidirect
7. #17988845C2semidirect
8. #17988844C2semidirect
9. #17988796C2semidirect
10. #17988744C2semidirect
11. #17988743C2semidirect
12. #17988679C2semidirect
14. #17988594C2semidirect
15. #419×C73C2semidirect
175. C73#3328semidirect
190. #419D73semidirect