Finite Group Databasebeta

← #21449564

Subgroups — #21449564

Order 7808.

610 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519750C211yesmaximal, characteristic
2C2×#14519737C211yesmaximal, characteristic, complemented
3#16839703C211yesmaximal, characteristic, complemented
4#16839691C211yesmaximal, characteristic, complemented
5#16839677C211yesmaximal, characteristic, complemented
6#16839652C211yesmaximal, characteristic, complemented
7#16839644C211yesmaximal, characteristic, complemented
8#16839640C211yesmaximal, characteristic, complemented
9#16839640C211yesmaximal, characteristic, complemented
10#16839639C211yesmaximal, characteristic, complemented
11#16839638C211yesmaximal, characteristic, complemented
12#16839633C211yesmaximal, characteristic, complemented
13#16839623C211yesmaximal, characteristic, complemented
14#95×D61C211yesmaximal, characteristic, complemented
15C61×#397C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic
23#14519750—24no—
24#14519737—24no—
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×C4×Dic61C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C23×D61C2311yescharacteristic
55C23×D61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—22no—
63C2×C22⋊D61—22no—
64C2×C22⋊D61—22no—
65C2×C22⋊D61—22no—
66C2×C22⋊D61—41no—
67C2×C22⋊D61D414yes—
68C22×Dic61—22no—
69C22×Dic61—22no—
70C22×Dic61—41no—
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C2×D244—22no—
78C2×D244—22no—
79C2×D244—22no—
80C2×C4×D61—22no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—22no—
91C22⋊C4×C61—22no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—41no—
94#11758198—22no—
95#11758198—22no—
96#11758198—22no—
97#11758198—22no—
98#11758198—41no—
99#11758198—41no—
100#11758198—41no—
101#11758196—22no—
102#11758196—22no—
103#11758196—22no—
104C4×Dic61—22no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61C2×D412yes—
112C23×C61C2411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61C2×D412yes—
125C22×D61#4112yes—
126C22×D61#4112yes—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C22⋊D61—28no—
146C22⋊D61—44no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—44no—
163C2×Dic61C2×D412yes—
164C2×Dic61#4112yes—
165C2×Dic61#4112yes—
166D244—44no—
167C4×D61—44no—
168C4×D61—44no—
169C4×D61—44no—
170C22×C61—22no—
171C22×C61—22no—
172C22×C61—22no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61C22×D411yescharacteristic
178C22×C61C2×#4111yescharacteristic
179C22×C61C2×#4111yescharacteristic
180C22×C61C2×#4111yescharacteristic
181C22×C61C2×#4111yescharacteristic
182C22×C61H(5,𝔽2)11yescharacteristic
183C22×C61H(5,𝔽2)11yescharacteristic
184C2×D61—22no—
185C2×D61—22no—
186C2×D61—22no—
187C2×D61—22no—
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61#12314yes—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—41no—
201C4×C61—41no—
202C4×C61—41no—
203C4×C61—41no—
204Dic61—22no—
205Dic61—22no—
206Dic61—22no—
207Dic61—41no—
208Dic61—41no—
209Dic61—41no—
210#2444—611nomaximal, Sylow
211C2×C61—42no—
212C2×C61C2×#12311yescharacteristic
213C2×C61#52911yescharacteristic
214C2×C61#53811yescharacteristic
215C2×C61#54611yescharacteristic
216C2×C61#54611yescharacteristic
217C2×C61#55311yescharacteristic
218C2×C61#55311yescharacteristic
219D61—24no—
220D61—81no—
221C2×#121—611no—
222C2×C4×D4—611no—
223#400—611no—
224#397—611no—
225#397D6111yescharacteristic, complemented
226#394—611no—
227#388—611no—
228#387—611no—
229#386—611no—
230#386—611no—
231#386—611no—
232#386—611no—
233#385—611no—
234#381—611no—
235C2×#95—611no—
236C61#244411yescharacteristic, complemented, Sylow
237C22×D4—611no—
238C22×D4—611no—
239C22×D4—611no—
240C23×C4—611no—
241C23×C4—611no—
242C23×C4—611no—
243C23×C4—611no—
244#121—1224no—
245C4×D4—1224no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4C2×D6111yescharacteristic
250C2×C22⋊C4—611no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—611no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—611no—
256C2×C22⋊C4—611no—
257C2×C22⋊C4—611no—
258C2×C22⋊C4C2×D6111yescharacteristic
259C2×C22⋊C4C2×D6111yescharacteristic
260C2×C22⋊C4C2×D6111yescharacteristic
261C2×C42—611no—
262#95—611no—
263#95—611no—
264#95—611no—
265#95—611no—
266#95—611no—
267#95—611no—
268#95—611no—
269#95—611no—
270#95—611no—
271#95C2×D6111yescharacteristic
272#95C2×D6111yescharacteristic
273#95C2×D6111yescharacteristic
274C24—611no—
275C24—611no—
276C24C22×D6111yescharacteristic
277C2×D4—614no—
278C2×D4—1222no—
279C2×D4—1222no—
280C2×D4—1222no—
281C2×D4—1222no—
282C2×D4—1222no—
283C2×D4—1222no—
284C2×D4—1222no—
285C2×D4—2441no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—1222no—
293C22×C4—1222no—
294C22×C4—1222no—
295C22×C4—1222no—
296C22×C4—1222no—
297C22×C4—1222no—
298C22×C4—1222no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4—2441no—
304C22×C4C22×D6111yescharacteristic
305C22×C4C22×D6111yescharacteristic
306C22×C4C22×D6111yescharacteristic
307C22×C4C22×D6111yescharacteristic
308C22×C4C22×D6111yescharacteristic
309C22×C4C22×D6111yescharacteristic
310C4⋊C4—41no—
311C4⋊C4—1222no—
312C4⋊C4—1222no—
313C4⋊C4—1222no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—41no—
317C22⋊C4—1222no—
318C22⋊C4—1222no—
319C22⋊C4—1222no—
320C22⋊C4—1222no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C22⋊C4—2441no—
325C42—1222no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—612no—
333C23—612no—
334C23—612no—
335C23—1221no—
336C23—1221no—
337C23—1221no—
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23—1221no—
345C23—1221no—
346C23D4×D6112yes—
347C23C23×D6111yescharacteristic
348D4—1228no—
349D4—2444no—
350D4—2444no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—612no—
370C2×C4—612no—
371C2×C4—612no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—2444no—
388C2×C4—2444no—
389C2×C4—2444no—
390C2×C4—2444no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—614no—
399C22—1222no—
400C22—1222no—
401C22—1222no—
402C22—1222no—
403C22—1222no—
404C22—1222no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22—2441no—
410C22—2441no—
411C22—2441no—
412C22C2×D4×D6111yescharacteristic
413C22#41×D6111yescharacteristic
414C22#41×D6111yescharacteristic
415C22#41×D6111yescharacteristic
416C22#41×D6111yescharacteristic
417C22#1451982211yescharacteristic
418C22#1451982311yescharacteristic
419C4—41no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—1222no—
426C4—1222no—
427C4—1222no—
428C4—2441no—
429C4—2441no—
430C4—2441no—
431C2—42no—
432C2—1224no—
433C2—4881no—
434C2#123×D6111yescharacteristic
435C2#1684029511yescharacteristic
436C2#1684034611yescharacteristic
437C2#1684040111yescharacteristic
438C2#1684040411yescharacteristic
439C2#1684045711yescharacteristic
440C2#1684046311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2444
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#14519737C2semidirect
3. #16839703C2semidirect
4. #16839691C2semidirect
5. #16839677C2semidirect
6. #16839652C2semidirect
7. #16839644C2semidirect
8. #16839640C2semidirect
9. #16839640C2semidirect
10. #16839639C2semidirect
11. #16839638C2semidirect
12. #16839633C2semidirect
13. #16839623C2semidirect
14. #95×D61C2semidirect
15. C61×#397C2semidirect
225. #397D61semidirect
236. C61#2444semidirect