Finite Group Databasebeta

← #21457572

Subgroups — #21457572

Order 7808.

504 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519798C211yesmaximal, characteristic, complemented
2C2×#14519797C211yesmaximal, characteristic, complemented
3#16840431C211yesmaximal, characteristic, complemented
4#16840430C211yesmaximal, characteristic, complemented
5#16840137C211yesmaximal, characteristic, complemented
6#16839997C211yesmaximal, characteristic, complemented
7#16839996C211yesmaximal, characteristic, complemented
8#16839961C211yesmaximal, characteristic, complemented
9#16839960C211yesmaximal, characteristic, complemented
10#16839910C211yesmaximal, characteristic, complemented
11#16839909C211yesmaximal, characteristic, complemented
12#16839904C211yesmaximal, characteristic, complemented
13#16839854C211yesmaximal, characteristic, complemented
14#16839825C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758224C2211yescharacteristic
19#14519798—24no—
20#14519797—24no—
21C2×#11758202C2211yescharacteristic
22C2×#11758190C2211yescharacteristic
23C2×#11758200C2211yescharacteristic
24C2×#11758201C2211yescharacteristic
25C2×D488C2211yescharacteristic
26C2×#11758199C2211yescharacteristic
27C2×#11758199C2211yescharacteristic
28C22×#92418C2211yescharacteristic
29C2×C8×D61C2211yescharacteristic
30#14519773—21no—
31#14519773—21no—
32#14519773C2211yescharacteristic
33#14519773C2211yescharacteristic
34#14519752C2211yescharacteristic
35#14519751—21no—
36#14519751C2211yescharacteristic
37#14519750—21no—
38#14519749—21no—
39#14519748—21no—
40#14519748C2211yescharacteristic
41Q8×Dic61C2211yescharacteristic
42#14519742C2211yescharacteristic
43C4×C22⋊D61—21no—
44C4×C22⋊D61C2211yescharacteristic
45#14519737—21no—
46#14519710C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519698C2211yescharacteristic
51#14519697C2211yescharacteristic
52#14519689C2211yescharacteristic
53C8×Dic61C2211yescharacteristic
54C2×#41×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56C2×D8×C61C2211yescharacteristic
57#121×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59#102×C61C2211yescharacteristic
60C22⋊C8×C61C2211yescharacteristic
61#41×C61—22no—
62#41×C61—41no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61C2311yescharacteristic
67C2×D4×C61C2311yescharacteristic
68C22×C4×C61—21no—
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61D411yescharacteristic
79C22×Dic61—21no—
80#11758226—22no—
81#11758226—41no—
82#11758224—22no—
83#11758224—41no—
84#11758222—22no—
85#11758222—41no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244C2311yescharacteristic
89C2×D244C2311yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61C2311yescharacteristic
93C2×Dic122C2311yescharacteristic
94SD16×C61—22no—
95D8×C61—41no—
96C2×C8×C61C2311yescharacteristic
97C2×C8×C61C2311yescharacteristic
98C4⋊C4×C61C2311yescharacteristic
99C22⋊C4×C61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61D411yescharacteristic
102#11758202D414yescomplemented
103#11758201—22no—
104#11758200—22no—
105#11758199—22no—
106#11758199—22no—
107#11758198—21no—
108#11758198—21no—
109#11758198D411yescharacteristic
110C4⋊Dic61—21no—
111C4⋊Dic61C2311yescharacteristic
112#11758196—21no—
113#11758196D411yescharacteristic
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61C2311yescharacteristic
117C2×#92418—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120D488—41no—
121#11758190—22no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61C2×D411yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61C2×D411yescharacteristic
129Q8×C61—21no—
130Q8×C61C2×D412yes—
131D4×C61—21no—
132D4×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—42no—
136D4×C61—81no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—42no—
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2411yescharacteristic
144C22⋊D61—22no—
145C22⋊D61—42no—
146C22⋊D61—42no—
147C22⋊D61—42no—
148C22⋊D61—42no—
149C22⋊D61—81no—
150C22⋊D61—81no—
151C22⋊D61—81no—
152C22⋊D61—81no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—42no—
156C2×Dic61C2×D411yescharacteristic
157C2×Dic61C2×D411yescharacteristic
158C2×Dic61C2×D411yescharacteristic
159D244—21no—
160D244—21no—
161D244—21no—
162D244—21no—
163D244—42no—
164D244—81no—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—42no—
168C4×D61—42no—
169Dic122—21no—
170Dic122C2×D412yes—
171C8×C61—21no—
172C8×C61—21no—
173#92418—21no—
174#92418C2×D412yes—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61C22×D411yescharacteristic
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C4×C61—21no—
195C4×C61—22no—
196C4×C61—41no—
197C4×C61C22×D411yescharacteristic
198C4×C61H(5,𝔽2)11yescharacteristic
199Dic61—22no—
200Dic61—21no—
201Dic61—21no—
202Dic61—41no—
203Dic61#13512yescomplemented
204#3287—611nomaximal, Sylow
205C2×C61—41no—
206C2×C61—81no—
207C2×C61—81no—
208C2×C61D4211yescharacteristic
209C2×C61C2×#13511yescharacteristic
210C2×C61#57611yescharacteristic
211D61—41no—
212D61—81no—
213D61—81no—
214C2×#135—611no—
215C2×#135—611no—
216#550—611no—
217#550—611no—
218#493—611no—
219#466—611no—
220#466—611no—
221#460—611no—
222#460—611no—
223#449—611no—
224#449—611no—
225#449—611no—
226#449D6111yescharacteristic, complemented
227C4×Q16—611no—
228C8×D4—611no—
229C61#328711yescharacteristic, complemented, Sylow
230C2×#41—611no—
231C2×#41—611no—
232C2×#41—611no—
233C2×#41C2×D6111yescharacteristic
234#135—1224no—
235#135—1224no—
236C2×Q16—611no—
237C2×SD16—611no—
238C2×SD16—611no—
239C2×SD16—611no—
240C2×SD16C2×D6111yescharacteristic
241C2×D8—611no—
242C2×D8—611no—
243C2×D8—611no—
244C2×D8C2×D6111yescharacteristic
245C22×C8—611no—
246C22×C8—611no—
247#127—611no—
248#127—611no—
249#127—1221no—
250#127—1221no—
251#121—611no—
252#121—611no—
253#121—611no—
254#121—1221no—
255#121—1221no—
256#121—1221no—
257#121—1221no—
258#121C2×D6111yescharacteristic
259C4×Q8—611no—
260C4×Q8—611no—
261C4×D4—611no—
262C4×D4—1221no—
263C4×D4—1221no—
264#107—611no—
265C4⋊C8—611no—
266#103—611no—
267#103C2×D6111yescharacteristic
268#102—611no—
269#102—611no—
270#102—611no—
271#102C2×D6111yescharacteristic
272C22⋊C8—611no—
273C22⋊C8C2×D6111yescharacteristic
274C4×C8—611no—
275#41—22no—
276#41—41no—
277#41—1222no—
278#41—1222no—
279#41—1222no—
280#41—2441no—
281#41—2441no—
282#41—2441no—
283C2×Q8—611no—
284C2×Q8C22×D6111yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—611no—
288C2×D4—611no—
289C2×D4—611no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4C22×D6111yescharacteristic
301C2×D4C22×D6111yescharacteristic
302C22×C4—21no—
303C22×C4—611no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4C22×D6111yescharacteristic
308Q16—614no—
309SD16—22no—
310SD16—1222no—
311SD16—1222no—
312SD16—1222no—
313D8—41no—
314D8—1222no—
315D8—1222no—
316D8—2441no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8—1222no—
320C2×C8—1222no—
321C2×C8C22×D6111yescharacteristic
322C2×C8C22×D6111yescharacteristic
323C4⋊C4—611no—
324C4⋊C4—611no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4C22×D6111yescharacteristic
328C22⋊C4—21no—
329C22⋊C4—611no—
330C22⋊C4—611no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C42—611no—
335C42—1221no—
336C42—1221no—
337C23—21no—
338C23—21no—
339C23—611no—
340C23—1221no—
341C23—1221no—
342C23D4×D6111yescharacteristic
343Q8—21no—
344Q8—612no—
345Q8—1221no—
346Q8D4×D6112yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—1222no—
354D4—1221no—
355D4—1221no—
356D4—1221no—
357D4—1221no—
358D4—4881no—
359D4—4881no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—2442no—
364D4—2442no—
365D4—2442no—
366D4—2442no—
367D4—2442no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—611no—
374C2×C4—611no—
375C2×C4—611no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4D4×D6111yescharacteristic
384C2×C4C23×D6111yescharacteristic
385C8—21no—
386C8—21no—
387C8—612no—
388C8—1221no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—1221no—
399C22—1221no—
400C22—1221no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22C2×D4×D6111yescharacteristic
408C4—21no—
409C4—22no—
410C4—41no—
411C4—612no—
412C4—1221no—
413C4—1221no—
414C4—1222no—
415C4—2441no—
416C4C2×D4×D6111yescharacteristic
417C4#1451982211yescharacteristic
418C2—41no—
419C2—81no—
420C2—81no—
421C2—4881no—
422C2—4881no—
423C2—2441no—
424C2#1684039411yescharacteristic
425C2#135×D6111yescharacteristic
426C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3287
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#14519798C2semidirect
2. C2×#14519797C2semidirect
3. #16840431C2semidirect
4. #16840430C2semidirect
5. #16840137C2semidirect
6. #16839997C2semidirect
7. #16839996C2semidirect
8. #16839961C2semidirect
9. #16839960C2semidirect
10. #16839910C2semidirect
11. #16839909C2semidirect
12. #16839904C2semidirect
13. #16839854C2semidirect
14. #16839825C2semidirect
15. C61×#449C2semidirect
102. #11758202D4semidirect
203. Dic61#135semidirect
226. #449D61semidirect
229. C61#3287semidirect