Finite Group Databasebeta

← #22621584

Subgroups — #22621584

Order 9344.

476 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556622C211yesmaximal, characteristic, complemented
2C2×#14556621C211yesmaximal, characteristic, complemented
3#17989246C211yesmaximal, characteristic, complemented
4#17988969C211yesmaximal, characteristic, complemented
5#17988835C211yesmaximal, characteristic, complemented
6#17988831C211yesmaximal, characteristic, complemented
7#17988809C211yesmaximal, characteristic, complemented
8#17988806C211yesmaximal, characteristic, complemented
9#17988743C211yesmaximal, characteristic, complemented
10#17988742C211yesmaximal, characteristic, complemented
11#17988732C211yesmaximal, characteristic, complemented
12#17988730C211yesmaximal, characteristic, complemented
13C4×#11924018C211yesmaximal, characteristic, complemented
14#17988665C211yesmaximal, characteristic, complemented
15#548×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18#14556622—24no—
19#14556621—24no—
20C2×#11924018C2211yescharacteristic
21C2×#11924018C2211yescharacteristic
22C2×#11924018C2211yescharacteristic
23C2×#11924018C2211yescharacteristic
24C2×#11924016C2211yescharacteristic
25C2×#11924016C2211yescharacteristic
26C2×#11924015C2211yescharacteristic
27C2×#11924015C2211yescharacteristic
28C2×#11924013C2211yescharacteristic
29C2×#11924012C2211yescharacteristic
30C2×#11924012C2211yescharacteristic
31#14556579C2211yescharacteristic
32#14556577—21no—
33#14556570C2211yescharacteristic
34#14556569—21no—
35#14556565C2211yescharacteristic
36#14556563—21no—
37C4×Dic146C2211yescharacteristic
38#14556551—21no—
39#14556524C2211yescharacteristic
40C4⋊#10596831C2211yescharacteristic
41#14556515C2211yescharacteristic
42#14556515C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556512C2211yescharacteristic
46#14556511C2211yescharacteristic
47C22⋊#10596831C2211yescharacteristic
48C22⋊#10596831C2211yescharacteristic
49C4×#10596831C2211yescharacteristic
50C2×#41×C73C2211yescharacteristic
51C22×Q8×C73C2211yescharacteristic
52#124×C73—21no—
53#124×C73C2211yescharacteristic
54C22⋊Q8×C73—21no—
55C22⋊Q8×C73C2211yescharacteristic
56#121×C73—21no—
57#121×C73C2211yescharacteristic
58C4×Q8×C73C2211yescharacteristic
59C4×D4×C73—21no—
60C4×D4×C73C2211yescharacteristic
61#11924028—22no—
62#11924028—41no—
63C2×Dic146—22no—
64C2×Dic146—21no—
65C2×Dic146—41no—
66C2×Dic146C2311yescharacteristic
67C2×Dic146C2311yescharacteristic
68C2×D292C2311yescharacteristic
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C22×Dic73—21no—
72C2×C4×D73—21no—
73#11924018—22no—
74#11924018—22no—
75#11924018—41no—
76#11924018D414yescomplemented
77#11924016—22no—
78#11924016—22no—
79#11924015—22no—
80#11924015—22no—
81#11924013—41no—
82#11924012—22no—
83#11924012—22no—
84C2×#10596831C2311yescharacteristic
85C2×#10596831C2311yescharacteristic
86C2×#10596831C2311yescharacteristic
87C2×#10596831C2311yescharacteristic
88C4⋊Dic73C2311yescharacteristic
89#11924007—21no—
90#11924007—21no—
91C22⋊Dic73—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95C4×Dic73—21no—
96#41×C73—22no—
97#41×C73—41no—
98C2×Q8×C73—21no—
99C2×Q8×C73—22no—
100C2×Q8×C73—41no—
101C2×Q8×C73C2311yescharacteristic
102C2×Q8×C73C2311yescharacteristic
103C2×D4×C73—21no—
104C2×D4×C73—21no—
105C2×D4×C73D411yescharacteristic
106C2×D4×C73C2311yescharacteristic
107C22×C4×C73—21no—
108C22×C4×C73—21no—
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111C4⋊C4×C73—21no—
112C4⋊C4×C73—21no—
113C4⋊C4×C73D411yescharacteristic
114C4⋊C4×C73C2311yescharacteristic
115C22⋊C4×C73—21no—
116C22⋊C4×C73—21no—
117C22⋊C4×C73—21no—
118C22⋊C4×C73—21no—
119C22⋊C4×C73D411yescharacteristic
120C22⋊C4×C73D411yescharacteristic
121C42×C73—21no—
122C42×C73C2311yescharacteristic
123C23×C73—21no—
124C23×C73C2×D411yescharacteristic
125C23×C73C2×D411yescharacteristic
126C22×D73—21no—
127Q8×C73—21no—
128Q8×C73—21no—
129Q8×C73—21no—
130Q8×C73—42no—
131Q8×C73C2×D412yes—
132D4×C73—21no—
133D4×C73—21no—
134D4×C73—41no—
135D4×C73—42no—
136D4×C73—42no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—42no—
145C2×C4×C73—42no—
146C2×C4×C73C2×D411yescharacteristic
147C2×C4×C73C2×D411yescharacteristic
148C2×C4×C73C2×D411yescharacteristic
149C2×C4×C73C2×D411yescharacteristic
150C2×C4×C73C2411yescharacteristic
151C22⋊D73—42no—
152C22⋊D73—42no—
153C2×Dic73—21no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73—42no—
157D292—21no—
158D292—21no—
159C4×D73—42no—
160Dic146—21no—
161Dic146—21no—
162Dic146—21no—
163Dic146—42no—
164Dic146C2×D412yes—
165#10596831—21no—
166#10596831—21no—
167#10596831—21no—
168#10596831C2×D412yes—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—21no—
175C22×C73—41no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73C22×D411yescharacteristic
179C2×D73—41no—
180C2×D73—41no—
181C2×D73—41no—
182C4×C73—21no—
183C4×C73—21no—
184C4×C73—22no—
185C4×C73—21no—
186C4×C73—21no—
187C4×C73—41no—
188C4×C73—41no—
189C4×C73C22×D411yescharacteristic
190C4×C73H(5,𝔽2)11yescharacteristic
191Dic73—22no—
192Dic73—41no—
193Dic73—41no—
194C2×C73—41no—
195C2×C73—41no—
196C2×C73—81no—
197C2×C73D4211yescharacteristic
198C2×C73#57511yescharacteristic
199C2×C73#57811yescharacteristic
200D73—81no—
201#3277—731nomaximal, Sylow
202C73#327711yescharacteristic, complemented, Sylow
203C2×#137—731no—
204C2×#137—731no—
205#548—731no—
206#548D7311yescharacteristic, complemented
207#495—731no—
208#468—731no—
209#468—731no—
210#464—731no—
211#464—731no—
212#451—731no—
213#451—731no—
214#449—731no—
215#449—731no—
216C4×Q16—731no—
217#436—731no—
218C2×#41—731no—
219C2×#41C2×D7311yescharacteristic
220C22×Q8—731no—
221C22×Q8C2×D7311yescharacteristic
222#137—1464no—
223#137—1464no—
224C2×Q16—731no—
225C2×Q16—731no—
226C2×Q16—731no—
227C2×Q16—731no—
228C2×SD16—731no—
229C2×SD16—731no—
230C2×SD16—731no—
231C2×SD16—731no—
232C2×D8—731no—
233C2×M16—731no—
234C2×M16—731no—
235#124—21no—
236#124—731no—
237#124—1461no—
238#124C2×D7311yescharacteristic
239C22⋊Q8—21no—
240C22⋊Q8—731no—
241C22⋊Q8—1461no—
242C22⋊Q8C2×D7311yescharacteristic
243#121—21no—
244#121—731no—
245#121—1461no—
246#121C2×D7311yescharacteristic
247C4×Q8—731no—
248C4×Q8C2×D7311yescharacteristic
249C4×D4—21no—
250C4×D4—1461no—
251C4×D4C2×D7311yescharacteristic
252#107—731no—
253C4⋊C8—731no—
254#103—731no—
255#103—731no—
256#103—731no—
257#103—731no—
258#102—731no—
259#102—731no—
260C22⋊C8—731no—
261C22⋊C8—731no—
262C4×C8—731no—
263#41—22no—
264#41—41no—
265#41—2921no—
266#41—1462no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—2921no—
271C2×Q8—731no—
272C2×Q8—731no—
273C2×Q8—1462no—
274C2×Q8—1461no—
275C2×Q8C22×D7311yescharacteristic
276C2×Q8C22×D7311yescharacteristic
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—731no—
280C2×D4—1461no—
281C2×D4—1461no—
282C2×D4C22⋊D7311yescharacteristic
283C2×D4C22×D7311yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—1461no—
287C22×C4—1461no—
288C22×C4C22×D7311yescharacteristic
289C22×C4C22×D7311yescharacteristic
290Q16—2921no—
291Q16—734no—
292Q16—1462no—
293Q16—1462no—
294SD16—1462no—
295SD16—1462no—
296SD16—1462no—
297SD16—1462no—
298D8—2921no—
299M16—1462no—
300M16—1462no—
301C2×C8—731no—
302C2×C8—731no—
303C2×C8—731no—
304C2×C8—731no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—731no—
308C4⋊C4—1461no—
309C4⋊C4—1461no—
310C4⋊C4C22⋊D7311yescharacteristic
311C4⋊C4C22×D7311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—1461no—
317C22⋊C4—1461no—
318C22⋊C4—1461no—
319C22⋊C4—1461no—
320C22⋊C4C22⋊D7311yescharacteristic
321C22⋊C4C22⋊D7311yescharacteristic
322C42—21no—
323C42—1461no—
324C42C22×D7311yescharacteristic
325C23—21no—
326C23—1461no—
327C23C2×C22⋊D7311yescharacteristic
328C23C2×C22⋊D7311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—2922no—
334Q8—732no—
335Q8—1461no—
336Q8—1461no—
337Q8—1461no—
338Q8D4×D7312yes—
339D4—21no—
340D4—21no—
341D4—41no—
342D4—42no—
343D4—42no—
344D4—2922no—
345D4—2922no—
346D4—1461no—
347D4—1461no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—2922no—
358C2×C4—2922no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4C2×C22⋊D7311yescharacteristic
363C2×C4C2×C22⋊D7311yescharacteristic
364C2×C4C2×C22⋊D7311yescharacteristic
365C2×C4C2×C22⋊D7311yescharacteristic
366C2×C4C23×D7311yescharacteristic
367C8—732no—
368C8—1461no—
369C8—1461no—
370C8—1461no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—2921no—
381C22—2921no—
382C22—2921no—
383C22C22×C22⋊D7311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—2921no—
392C4—2921no—
393C4—1462no—
394C4C2×D4×D7311yescharacteristic
395C4#1455663611yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—5841no—
400C2D4×C22⋊D7311yescharacteristic
401C2#1798938511yescharacteristic
402C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#548×C73C2
socleC22×C73C22×D4
hypercenter#548D73
hypocenterC73#3277
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14556622C2semidirect
2. C2×#14556621C2semidirect
3. #17989246C2semidirect
4. #17988969C2semidirect
5. #17988835C2semidirect
6. #17988831C2semidirect
7. #17988809C2semidirect
8. #17988806C2semidirect
9. #17988743C2semidirect
10. #17988742C2semidirect
11. #17988732C2semidirect
12. #17988730C2semidirect
13. C4×#11924018C2semidirect
14. #17988665C2semidirect
15. #548×C73C2semidirect
76. #11924018D4semidirect
202. C73#3277semidirect
206. #548D73semidirect