Finite Group Databasebeta

← #22622243

Subgroups — #22622243

Order 9344.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989292C211yesmaximal, characteristic, complemented
2#17989236C211yesmaximal, characteristic
3#17988936C211yesmaximal, characteristic, complemented
4#17988917C211yesmaximal, characteristic, complemented
5#17988916C211yesmaximal, characteristic, complemented
6#17988875C211yesmaximal, characteristic, complemented
7#17988845C211yesmaximal, characteristic, complemented
8#17988844C211yesmaximal, characteristic, complemented
9#17988796C211yesmaximal, characteristic, complemented
10#17988750C211yesmaximal, characteristic, complemented
11#17988749C211yesmaximal, characteristic, complemented
12#17988678C211yesmaximal, characteristic, complemented
13#17988663C211yesmaximal, characteristic, complemented
14#17988585C211yesmaximal, characteristic, complemented
15#417×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556589C2211yescharacteristic
23#14556581—21no—
24#14556574—21no—
25#14556572—21no—
26#14556571C2211yescharacteristic
27#14556570—21no—
28#14556570C2211yescharacteristic
29#14556570C2211yescharacteristic
30#14556569—21no—
31#14556567C2211yescharacteristic
32#14556563—21no—
33#14556556C2211yescharacteristic
34D4×Dic73C2211yescharacteristic
35C4×C22⋊D73—21no—
36C4×C22⋊D73C2211yescharacteristic
37C2×#11924007—21no—
38C4⋊C4×D73C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C2×C4⋊C4×C73C2211yescharacteristic
55#103×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924027—22no—
60#11924027—41no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C22⋊D73D411yescharacteristic
66C22×Dic73—21no—
67C22×Dic73—21no—
68C2×C4×D73—21no—
69C2×C4×D73C2311yescharacteristic
70Dic292—41no—
71#11924018—41no—
72#11924016—22no—
73#11924011—41no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007D411yescharacteristic
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73D411yescharacteristic
92#11924005—21no—
93#11924005—21no—
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97#41×C73—22no—
98#41×C73—41no—
99C2×Q8×C73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73C2311yescharacteristic
105M16×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73C2×D411yescharacteristic
114Q8×C73—21no—
115Q8×C73—21no—
116D4×C73—21no—
117D4×C73—42no—
118D4×C73#4112yes—
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×C73—81no—
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2411yescharacteristic
128C22⋊D73—22no—
129C22⋊D73—42no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—42no—
135C2×Dic73—42no—
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139C4×D73—21no—
140C4×D73—21no—
141C4×D73—81no—
142Dic146—21no—
143Dic146—21no—
144Dic146—21no—
145Dic146—21no—
146Dic146—81no—
147C8×C73—21no—
148C8×C73—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—22no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73C22×D411yescharacteristic
158C2×D73—21no—
159C2×D73—21no—
160C2×D73—21no—
161C4×C73—21no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73—41no—
165C4×C73C2×#4111yescharacteristic
166C4×C73H(5,𝔽2)11yescharacteristic
167Dic73—21no—
168Dic73—21no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172Dic73—41no—
173Dic73#13712yes—
174C2×C73—41no—
175C2×C73—42no—
176C2×C73#54611yescharacteristic
177C2×C73C2×#13711yescharacteristic
178C2×C73#57711yescharacteristic
179D73—41no—
180#3331—731nomaximal, Sylow
181C73#333111yescharacteristic, complemented, Sylow
182#554—731no—
183#547—731no—
184#487—731no—
185#483—731no—
186#483—731no—
187#476—731no—
188#470—731no—
189#470—731no—
190#462—731no—
191#452—731no—
192#452—731no—
193C4×SD16—731no—
194#436—731no—
195#417—731no—
196#417D7311yescharacteristic, complemented
197C2×#41—731no—
198C2×#41C2×D7311yescharacteristic
199C2×Q16—731no—
200C2×Q16—731no—
201C2×SD16—731no—
202C2×M16—731no—
203C2×M16C2×D7311yescharacteristic
204C4⋊Q8—731no—
205C4⋊Q8—731no—
206#125—1461no—
207#123—1461no—
208#123—1461no—
209C22⋊Q8—731no—
210C22⋊Q8—731no—
211C22⋊Q8—731no—
212C22⋊Q8—731no—
213C22⋊Q8—1461no—
214C22⋊Q8—1461no—
215#121—1461no—
216C4×Q8—731no—
217C4×D4—731no—
218C4×D4—731no—
219C4×D4—1461no—
220C2×C4⋊C4—731no—
221C2×C4⋊C4—1461no—
222C2×C4⋊C4C2×D7311yescharacteristic
223#106—731no—
224#106—731no—
225#106—731no—
226C4⋊C8—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#103C2×D7311yescharacteristic
233#103C2×D7311yescharacteristic
234#102—731no—
235#102C2×D7311yescharacteristic
236#102C2×D7311yescharacteristic
237C22⋊C8—731no—
238C22⋊C8—731no—
239C4×C8—731no—
240#41—22no—
241#41—41no—
242#41—2921no—
243#41—1462no—
244C2×Q8—731no—
245C2×Q8—731no—
246C2×Q8—1461no—
247C2×Q8C22×D7311yescharacteristic
248C2×D4—21no—
249C2×D4—731no—
250C2×D4—1461no—
251C2×D4C22×D7311yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—731no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4C22×D7311yescharacteristic
259Q16—2921no—
260Q16—2921no—
261SD16—1462no—
262M16—41no—
263M16—2921no—
264C2×C8—731no—
265C2×C8—731no—
266C2×C8C22×D7311yescharacteristic
267C2×C8C22×D7311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—731no—
270C4⋊C4—731no—
271C4⋊C4—731no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4C22×D7311yescharacteristic
282C4⋊C4C22×D7311yescharacteristic
283C22⋊C4—731no—
284C22⋊C4—731no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C42—731no—
291C42—1461no—
292C23—21no—
293C23—731no—
294C23D4×D7311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—5841no—
298Q8—1461no—
299Q8—1461no—
300Q8—1461no—
301Q8—1461no—
302D4—21no—
303D4—42no—
304D4—2922no—
305D4—1462no—
306D4#1192402812yes—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—2922no—
315C2×C4—2922no—
316C2×C4—5841no—
317C2×C4—731no—
318C2×C4—731no—
319C2×C4—731no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4D4×D7311yescharacteristic
327C2×C4C23×D7311yescharacteristic
328C8—21no—
329C8—21no—
330C8—1461no—
331C8—1461no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—1461no—
339C22—1461no—
340C22—1461no—
341C22C2×D4×D7311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—2921no—
347C4—2921no—
348C4—2921no—
349C4—2921no—
350C4—732no—
351C4—1461no—
352C4—1461no—
353C4C2×#1192402811yescharacteristic
354C4#1455663611yescharacteristic
355C2—41no—
356C2—42no—
357C2—2921no—
358C2#1798922711yescharacteristic
359C2#137×D7311yescharacteristic
360C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3331
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #17989292C2semidirect
3. #17988936C2semidirect
4. #17988917C2semidirect
5. #17988916C2semidirect
6. #17988875C2semidirect
7. #17988845C2semidirect
8. #17988844C2semidirect
9. #17988796C2semidirect
10. #17988750C2semidirect
11. #17988749C2semidirect
12. #17988678C2semidirect
13. #17988663C2semidirect
14. #17988585C2semidirect
15. #417×C73C2semidirect
181. C73#3331semidirect
196. #417D73semidirect