Finite Group Databasebeta

← #22620837

Subgroups — #22620837

Order 9344.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989165C211yesmaximal, characteristic, complemented
2#17988917C211yesmaximal, characteristic, complemented
3#17988915C211yesmaximal, characteristic, complemented
4#17988905C211yesmaximal, characteristic, complemented
5#17988903C211yesmaximal, characteristic, complemented
6#17988843C211yesmaximal, characteristic, complemented
7#17988838C211yesmaximal, characteristic, complemented
8#17988818C211yesmaximal, characteristic, complemented
9#17988814C211yesmaximal, characteristic, complemented
10#17988749C211yesmaximal, characteristic, complemented
11#17988747C211yesmaximal, characteristic, complemented
12#17988732C211yesmaximal, characteristic, complemented
13#17988730C211yesmaximal, characteristic, complemented
14#17988554C211yesmaximal, characteristic, complemented
15#537×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21C2×#11924012C2211yescharacteristic
22C22×#10596831C2211yescharacteristic
23#14556570C2211yescharacteristic
24#14556570C2211yescharacteristic
25#14556567—21no—
26#14556565C2211yescharacteristic
27#14556565C2211yescharacteristic
28#14556563—21no—
29#14556563—21no—
30#14556562—21no—
31C2×C4⋊Dic73C2211yescharacteristic
32#14556522C2211yescharacteristic
33#14556522C2211yescharacteristic
34#14556522C2211yescharacteristic
35#14556522C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556514C2211yescharacteristic
39#14556514C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44C22⋊#10596831C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47C22⋊#10596831C2211yescharacteristic
48C2×#41×C73C2211yescharacteristic
49C2×#41×C73C2211yescharacteristic
50C22⋊Q8×C73—21no—
51C22⋊Q8×C73C2211yescharacteristic
52C22⋊Q8×C73C2211yescharacteristic
53#121×C73—21no—
54#121×C73—21no—
55#121×C73—21no—
56#121×C73C2211yescharacteristic
57#121×C73C2211yescharacteristic
58C2×C4⋊C4×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61C2×Dic146C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C22×Dic73—21no—
67C2×C4×D73—21no—
68#11924018—41no—
69#11924016—41no—
70#11924015—41no—
71#11924013—41no—
72#11924012—41no—
73C2×#10596831—41no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85#11924005—21no—
86#11924005—21no—
87#41×C73—41no—
88#41×C73—41no—
89#41×C73—41no—
90#41×C73—41no—
91C2×Q8×C73D411yescharacteristic
92C2×Q8×C73C2311yescharacteristic
93C2×D4×C73—21no—
94C2×D4×C73—21no—
95C2×D4×C73—21no—
96C2×D4×C73D411yescharacteristic
97C2×D4×C73D411yescharacteristic
98C2×D4×C73D411yescharacteristic
99C2×D4×C73C2311yescharacteristic
100C22×C4×C73—21no—
101C22×C4×C73—21no—
102C22×C4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105C4⋊C4×C73—21no—
106C4⋊C4×C73—21no—
107C4⋊C4×C73—21no—
108C4⋊C4×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C22⋊C4×C73—21no—
112C22⋊C4×C73—21no—
113C22⋊C4×C73—21no—
114C23×C73—21no—
115C23×C73C2×D411yescharacteristic
116C23×C73C2×D411yescharacteristic
117C23×C73C2×D411yescharacteristic
118C22×D73—21no—
119Q8×C73—21no—
120Q8×C73—21no—
121Q8×C73—41no—
122D4×C73—21no—
123D4×C73—21no—
124D4×C73—41no—
125D4×C73—41no—
126D4×C73—41no—
127D4×C73—42no—
128D4×C73—81no—
129D4×C73—81no—
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×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—42no—
140C2×C4×C73—81no—
141C2×C4×C73C2×D411yescharacteristic
142C2×C4×C73C2×D411yescharacteristic
143C2×C4×C73C2×D411yescharacteristic
144C2×C4×C73C2411yescharacteristic
145C22⋊D73—42no—
146C22⋊D73—81no—
147C22⋊D73—81no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—21no—
151C2×Dic73—81no—
152D292—21no—
153D292—21no—
154C4×D73—42no—
155Dic146—21no—
156Dic146—21no—
157#10596831—21no—
158#10596831—21no—
159#10596831—21no—
160#10596831—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—41no—
171C22×C73—41no—
172C22×C73—41no—
173C22×C73C22×D411yescharacteristic
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—41no—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—21no—
180C4×C73—41no—
181C4×C73—41no—
182C4×C73—41no—
183C4×C73H(5,𝔽2)11yescharacteristic
184C4×C73H(5,𝔽2)11yescharacteristic
185Dic73—41no—
186Dic73—41no—
187Dic73—41no—
188C2×C73—41no—
189C2×C73—41no—
190C2×C73—41no—
191C2×C73—81no—
192C2×C73#53411yescharacteristic
193C2×C73#57711yescharacteristic
194C2×C73#57711yescharacteristic
195D73—81no—
196#3204—731nomaximal, Sylow
197C73#320411yescharacteristic, complemented, Sylow
198#537—731no—
199#537D7311yescharacteristic, complemented
200#483—731no—
201#483—731no—
202#481—731no—
203#481—731no—
204#470—731no—
205#469—731no—
206#465—731no—
207#465—731no—
208#452—731no—
209#452—731no—
210#449—731no—
211#449—731no—
212#408—731no—
213C2×#41—731no—
214C2×#41C2×D7311yescharacteristic
215C2×#41C2×D7311yescharacteristic
216C2×Q16—731no—
217C2×SD16—731no—
218C2×SD16—731no—
219C2×D8—731no—
220C2×M16—731no—
221C22×C8—731no—
222C22⋊Q8—21no—
223C22⋊Q8—731no—
224C22⋊Q8—731no—
225C22⋊Q8—1461no—
226C22⋊Q8C2×D7311yescharacteristic
227C22⋊Q8C2×D7311yescharacteristic
228#121—21no—
229#121—21no—
230#121—21no—
231#121—731no—
232#121—731no—
233#121—1461no—
234#121—1461no—
235#121—1461no—
236#121C2×D7311yescharacteristic
237#121C2×D7311yescharacteristic
238C2×C4⋊C4—731no—
239C2×C4⋊C4C2×D7311yescharacteristic
240#106—731no—
241#106—731no—
242#106—731no—
243#106—731no—
244#103—731no—
245#103—731no—
246#103—731no—
247#103—731no—
248#102—731no—
249#102—731no—
250#102—731no—
251#102—731no—
252C22⋊C8—731no—
253C22⋊C8—731no—
254C22⋊C8—731no—
255C22⋊C8—731no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—2921no—
261#41—2921no—
262C2×Q8—731no—
263C2×Q8C22⋊D7311yescharacteristic
264C2×Q8C22×D7311yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—731no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4—1461no—
272C2×D4C22⋊D7311yescharacteristic
273C2×D4C22⋊D7311yescharacteristic
274C2×D4C22⋊D7311yescharacteristic
275C2×D4C22×D7311yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—1461no—
279C22×C4—1461no—
280C22×C4C22×D7311yescharacteristic
281C22×C4C22×D7311yescharacteristic
282C22×C4C22×D7311yescharacteristic
283Q16—2921no—
284SD16—2921no—
285SD16—2921no—
286D8—2921no—
287M16—2921no—
288C2×C8—2921no—
289C2×C8—731no—
290C2×C8—731no—
291C2×C8—731no—
292C2×C8—731no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—731no—
297C4⋊C4—731no—
298C4⋊C4—1461no—
299C4⋊C4—1461no—
300C4⋊C4—1461no—
301C4⋊C4C22×D7311yescharacteristic
302C4⋊C4C22×D7311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—1461no—
308C22⋊C4—1461no—
309C22⋊C4—1461no—
310C22⋊C4—1461no—
311C23—21no—
312C23—1461no—
313C23C2×C22⋊D7311yescharacteristic
314C23C2×C22⋊D7311yescharacteristic
315C23C2×C22⋊D7311yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—1461no—
320Q8—1461no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—2922no—
330D4—5841no—
331D4—5841no—
332D4—1461no—
333D4—1461no—
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—42no—
344C2×C4—81no—
345C2×C4—2922no—
346C2×C4—5841no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4C2×C22⋊D7311yescharacteristic
351C2×C4C2×C22⋊D7311yescharacteristic
352C2×C4C2×C22⋊D7311yescharacteristic
353C2×C4C23×D7311yescharacteristic
354C8—1461no—
355C8—1461no—
356C8—1461no—
357C8—1461no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—2921no—
371C22—2921no—
372C22—2921no—
373C22C22×C22⋊D7311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2921no—
381C4—2921no—
382C4—2921no—
383C4#1455663611yescharacteristic
384C4#1455663611yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—5841no—
390C2#1798914611yescharacteristic
391C2#1798939511yescharacteristic
392C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#537×C73C2
socleC22×C73C22×D4
hypercenter#537D73
hypocenterC73#3204
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #17989165C2semidirect
2. #17988917C2semidirect
3. #17988915C2semidirect
4. #17988905C2semidirect
5. #17988903C2semidirect
6. #17988843C2semidirect
7. #17988838C2semidirect
8. #17988818C2semidirect
9. #17988814C2semidirect
10. #17988749C2semidirect
11. #17988747C2semidirect
12. #17988732C2semidirect
13. #17988730C2semidirect
14. #17988554C2semidirect
15. #537×C73C2semidirect
197. C73#3204semidirect
199. #537D73semidirect