Finite Group Databasebeta

← #22618672

Subgroups — #22618672

Order 9344.

492 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556599C211yesmaximal, characteristic, complemented
2C2×#14556597C211yesmaximal, characteristic, complemented
3#17989134C211yesmaximal, characteristic
4#17988663C211yesmaximal, characteristic, complemented
5#17988662C211yesmaximal, characteristic, complemented
6#17988660C211yesmaximal, characteristic, complemented
7#17988659C211yesmaximal, characteristic, complemented
8#17988657C211yesmaximal, characteristic, complemented
9C8×C22⋊D73C211yesmaximal, characteristic, complemented
10#17988650C211yesmaximal, characteristic, complemented
11C4⋊C8×D73C211yesmaximal, characteristic, complemented
12#17988552C211yesmaximal, characteristic, complemented
13#17988552C211yesmaximal, characteristic, complemented
14#17988539C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924028C2211yescharacteristic
18#14556599—24no—
19#14556597—24no—
20C2×#11924012C2211yescharacteristic
21C2×#11924011C2211yescharacteristic
22C2×#11924011C2211yescharacteristic
23C2×#11924011C2211yescharacteristic
24C2×#11924011C2211yescharacteristic
25C22×#10596831C2211yescharacteristic
26C2×C8×D73C2211yescharacteristic
27C2×C8×D73C2211yescharacteristic
28C2×C8×D73C2211yescharacteristic
29C2×C8×D73C2211yescharacteristic
30#14556590C411yescharacteristic
31#14556587C411yescharacteristic
32#14556577C411yescharacteristic
33#14556577C411yescharacteristic
34#14556566C411yescharacteristic
35#14556564C411yescharacteristic
36#14556564C411yescharacteristic
37#14556562C411yescharacteristic
38C4×D292C2211yescharacteristic
39C4×C22⋊D73C2211yescharacteristic
40C4×C22⋊D73C2211yescharacteristic
41C42×D73C2211yescharacteristic
42C4⋊#10596831C2211yescharacteristic
43#14556520C2211yescharacteristic
44#14556520C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47#14556503C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556502C2211yescharacteristic
52C8×Dic73C2211yescharacteristic
53C8×Dic73C2211yescharacteristic
54C2×M16×C73C2211yescharacteristic
55C22×C8×C73C2211yescharacteristic
56C4×D4×C73C2211yescharacteristic
57C4⋊C8×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59C22⋊C8×C73C2211yescharacteristic
60#97×C73C2211yescharacteristic
61#11924028—22no—
62#11924028—22no—
63#11924028—22no—
64#11924028—22no—
65C2×Dic146C2×C411yescharacteristic
66C2×Dic146C2×C411yescharacteristic
67C2×D292C2×C411yescharacteristic
68C2×D292C2×C411yescharacteristic
69C2×D292C2×C411yescharacteristic
70C2×C22⋊D73C2×C411yescharacteristic
71C2×C22⋊D73C2×C411yescharacteristic
72C2×C22⋊D73C2×C411yescharacteristic
73C2×C22⋊D73C2×C411yescharacteristic
74C2×C22⋊D73C2×C411yescharacteristic
75C2×C22⋊D73C2×C411yescharacteristic
76C2×C4×D73C2×C411yescharacteristic
77C2×C4×D73C2×C411yescharacteristic
78C2×C4×D73C2311yescharacteristic
79C2×C4×D73C2311yescharacteristic
80C2×C4×D73C2311yescharacteristic
81#11924012—22no—
82#11924011—22no—
83#11924011—22no—
84#11924011—22no—
85#11924011D414yescomplemented
86C2×#10596831—22no—
87C2×#10596831C2311yescharacteristic
88C2×#10596831C2311yescharacteristic
89C2×#10596831C2311yescharacteristic
90C2×#10596831C2311yescharacteristic
91C8×D73—22no—
92C8×D73—22no—
93C8×D73—22no—
94C8×D73—22no—
95C4⋊Dic73C2×C411yescharacteristic
96#11924007C2×C411yescharacteristic
97#11924007C2×C411yescharacteristic
98C22⋊Dic73C2×C411yescharacteristic
99C22⋊Dic73C2×C411yescharacteristic
100#11924005C2×C411yescharacteristic
101#11924005C2×C411yescharacteristic
102#11924005C2×C411yescharacteristic
103#11924005C2×C411yescharacteristic
104C4×Dic73C2×C411yescharacteristic
105C4×Dic73C2×C411yescharacteristic
106C4×Dic73C2311yescharacteristic
107C2×D4×C73C2×C411yescharacteristic
108C22×C4×C73C2311yescharacteristic
109C22×C4×C73C2311yescharacteristic
110M16×C73—22no—
111C2×C8×C73—22no—
112C2×C8×C73C2311yescharacteristic
113C2×C8×C73C2311yescharacteristic
114C2×C8×C73C2311yescharacteristic
115C2×C8×C73C2311yescharacteristic
116C4⋊C4×C73C2×C411yescharacteristic
117C22⋊C4×C73C2×C411yescharacteristic
118C22⋊C4×C73C2×C411yescharacteristic
119C42×C73C2311yescharacteristic
120C23×C73C22×C411yescharacteristic
121C23×C73C22×C411yescharacteristic
122C22×D73C22×C411yescharacteristic
123C22×D73C22×C411yescharacteristic
124C22×D73C22×C411yescharacteristic
125D4×C73—41no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73C22×C411yescharacteristic
131C2×C4×C73C22×C411yescharacteristic
132C2×C4×C73C22×C411yescharacteristic
133C2×C4×C73C22×C411yescharacteristic
134C2×C4×C73C2411yescharacteristic
135C22⋊D73—22no—
136C22⋊D73—22no—
137C22⋊D73—22no—
138C22⋊D73—22no—
139C22⋊D73—22no—
140C22⋊D73—22no—
141C2×Dic73C22×C411yescharacteristic
142C2×Dic73C22×C411yescharacteristic
143C2×Dic73C22×C411yescharacteristic
144C2×Dic73C22×C411yescharacteristic
145C2×Dic73C22×C411yescharacteristic
146D292—22no—
147D292—22no—
148D292—41no—
149C4×D73—21no—
150C4×D73—21no—
151C4×D73—21no—
152C4×D73—21no—
153C4×D73—22no—
154C4×D73—41no—
155C4×D73C2×D412yes—
156C4×D73#4112yes—
157Dic146—22no—
158Dic146—22no—
159C8×C73—21no—
160C8×C73—21no—
161C8×C73—21no—
162C8×C73C2×D412yes—
163#10596831—21no—
164#10596831—21no—
165#10596831—21no—
166#10596831C2×D412yes—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73C23×C411yescharacteristic
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—21no—
181C2×D73—21no—
182C2×D73C4×D412yes—
183C4×C73—21no—
184C4×C73—21no—
185C4×C73—21no—
186C4×C73—21no—
187C4×C73C22×D411yescharacteristic
188C4×C73C2×#4111yescharacteristic
189Dic73—21no—
190Dic73—21no—
191Dic73—21no—
192Dic73C4×D412yes—
193Dic73#13112yescomplemented
194C2×C73—41no—
195C2×C73—41no—
196C2×C73C2×C4×D411yescharacteristic
197C2×C73C2×#13111yescharacteristic
198C2×C73#56811yescharacteristic
199D73—22no—
200D73—41no—
201D73—41no—
202#2935—731nomaximal, Sylow
203C73#293511yescharacteristic, complemented, Sylow
204C2×#131—731no—
205C2×#131—731no—
206#532—731no—
207#436—731no—
208#436—731no—
209#435—731no—
210#435—731no—
211#435—731no—
212#435D7311yescharacteristic, complemented
213C8×D4—731no—
214C8×D4—731no—
215C2×C4⋊C8—731no—
216#408—731no—
217#408—731no—
218C4×M16—731no—
219C2×#41—731no—
220C2×#41—731no—
221#131—1464no—
222#131—1464no—
223C2×M16—731no—
224C2×M16—731no—
225C2×M16—731no—
226C2×M16—731no—
227C2×M16—731no—
228C2×M16C2×D7311yescharacteristic
229C22×C8—731no—
230C22×C8—731no—
231C22×C8—731no—
232C22×C8—731no—
233C22×C8—731no—
234C22×C8C2×D7311yescharacteristic
235C4⋊Q8—731no—
236#127—731no—
237#124—731no—
238#124—731no—
239#121—731no—
240#121—731no—
241#121—731no—
242#121—731no—
243C4×D4—731no—
244C4×D4—731no—
245C4×D4—731no—
246C4×D4C2×D7311yescharacteristic
247C2×C42—731no—
248C4⋊C8—731no—
249C4⋊C8—731no—
250C4⋊C8—731no—
251C4⋊C8C2×D7311yescharacteristic
252C22⋊C8—731no—
253C22⋊C8—731no—
254C22⋊C8—731no—
255C22⋊C8—731no—
256C22⋊C8—731no—
257C22⋊C8—731no—
258C22⋊C8C2×D7311yescharacteristic
259C22⋊C8C2×D7311yescharacteristic
260#97—731no—
261#97C2×D7311yescharacteristic
262C4×C8—731no—
263C4×C8—731no—
264#41—1462no—
265#41—1462no—
266#41—1462no—
267#41—1462no—
268C2×Q8—731no—
269C2×Q8—731no—
270C2×D4—731no—
271C2×D4—731no—
272C2×D4—731no—
273C2×D4—731no—
274C2×D4—731no—
275C2×D4—731no—
276C2×D4—731no—
277C2×D4—731no—
278C2×D4—731no—
279C2×D4C4×D7311yescharacteristic
280C22×C4—731no—
281C22×C4—731no—
282C22×C4—731no—
283C22×C4—731no—
284C22×C4—731no—
285C22×C4C22×D7311yescharacteristic
286C22×C4C22×D7311yescharacteristic
287M16—22no—
288M16—734no—
289M16—1462no—
290M16—1462no—
291M16—1462no—
292M16—1462no—
293C2×C8—22no—
294C2×C8—731no—
295C2×C8—731no—
296C2×C8—731no—
297C2×C8—731no—
298C2×C8—1462no—
299C2×C8—1462no—
300C2×C8—1462no—
301C2×C8—1462no—
302C2×C8—1462no—
303C2×C8C22×D7311yescharacteristic
304C2×C8C22×D7311yescharacteristic
305C2×C8C22×D7311yescharacteristic
306C2×C8C22×D7311yescharacteristic
307C4⋊C4—731no—
308C4⋊C4—731no—
309C4⋊C4—731no—
310C4⋊C4C4×D7311yescharacteristic
311C22⋊C4—731no—
312C22⋊C4—731no—
313C22⋊C4—731no—
314C22⋊C4—731no—
315C22⋊C4—731no—
316C22⋊C4—731no—
317C22⋊C4C4×D7311yescharacteristic
318C22⋊C4C4×D7311yescharacteristic
319C42—731no—
320C42—731no—
321C42—731no—
322C42C22×D7311yescharacteristic
323C23—731no—
324C23—731no—
325C23—731no—
326C23C2×C4×D7311yescharacteristic
327C23C2×C4×D7311yescharacteristic
328Q8—1462no—
329Q8—1462no—
330D4—41no—
331D4—2921no—
332D4—1462no—
333D4—1462no—
334D4—1462no—
335D4—1462no—
336D4—1462no—
337D4—1462no—
338D4—1462no—
339D4—1462no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—2921no—
345C2×C4—731no—
346C2×C4—731no—
347C2×C4—732no—
348C2×C4—732no—
349C2×C4—731no—
350C2×C4—731no—
351C2×C4—731no—
352C2×C4—1462no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4C2×C4×D7311yescharacteristic
358C2×C4C2×C4×D7311yescharacteristic
359C2×C4C2×C4×D7311yescharacteristic
360C2×C4C2×C4×D7311yescharacteristic
361C2×C4C23×D7311yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—732no—
366C8—1461no—
367C8—1461no—
368C8—1461no—
369C8D4×D7312yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—732no—
377C22—1461no—
378C22—1461no—
379C22—1461no—
380C22—1461no—
381C22—1461no—
382C22—1461no—
383C22—1461no—
384C22—1461no—
385C22C22×C4×D7311yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—732no—
391C4—732no—
392C4—1461no—
393C4—1461no—
394C4—1461no—
395C4C2×D4×D7311yescharacteristic
396C4#41×D7311yescharacteristic
397C2—41no—
398C2—41no—
399C2—2921no—
400C2—2921no—
401C2—1462no—
402C2C4×D4×D7311yescharacteristic
403C2#131×D7311yescharacteristic
404C2#1798935311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D73
commutator, socleC22×C73C23×C4
Fitting#435×C73C2
hypercenter#435D73
hypocenterC73#2935
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#14556599C2semidirect
2. C2×#14556597C2semidirect
4. #17988663C2semidirect
5. #17988662C2semidirect
6. #17988660C2semidirect
7. #17988659C2semidirect
8. #17988657C2semidirect
9. C8×C22⋊D73C2semidirect
10. #17988650C2semidirect
11. C4⋊C8×D73C2semidirect
12. #17988552C2semidirect
13. #17988552C2semidirect
14. #17988539C2semidirect
15. #435×C73C2semidirect
85. #11924011D4semidirect
193. Dic73#131semidirect
203. C73#2935semidirect
212. #435D73semidirect