Finite Group Databasebeta

← #21452813

Subgroups — #21452813

Order 7808.

548 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519763C211yesmaximal, characteristic, complemented
2C2×#14519755C211yesmaximal, characteristic, complemented
3#16839698C211yesmaximal, characteristic, complemented
4#16839691C211yesmaximal, characteristic, complemented
5#16839684C211yesmaximal, characteristic, complemented
6#16839678C211yesmaximal, characteristic, complemented
7#16839677C211yesmaximal, characteristic, complemented
8#16839671C211yesmaximal, characteristic
9#16839668C211yesmaximal, characteristic, complemented
10#16839664C211yesmaximal, characteristic, complemented
11#16839651C211yesmaximal, characteristic, complemented
12#16839645C211yesmaximal, characteristic, complemented
13#16839640C211yesmaximal, characteristic, complemented
14#16839638C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519763—24no—
22#14519755—24no—
23C2×C4⋊Dic61C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×C4×Dic61C2211yescharacteristic
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
50C2×C42×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—41no—
65C2×C22⋊D61—41no—
66C2×C22⋊D61—41no—
67C2×C22⋊D61—41no—
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C2×D244—22no—
75C2×D244—22no—
76C2×D244—41no—
77C2×C4×D61—22no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122D414yescomplemented
83C4⋊C4×C61—22no—
84C22⋊C4×C61—22no—
85C22⋊C4×C61—22no—
86C22⋊C4×C61—41no—
87C42×C61—41no—
88C22⋊Dic61—22no—
89C22⋊Dic61—41no—
90#11758198—22no—
91#11758198—22no—
92#11758198—22no—
93#11758198—22no—
94#11758198—22no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98#11758198—41no—
99C4⋊Dic61—22no—
100C4⋊Dic61—41no—
101#11758196—22no—
102#11758196—22no—
103#11758196—41no—
104C4×Dic61—22no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
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×D61—21no—
125C22×D61—21no—
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×C61C2×D412yes—
144C2×C4×C61#4112yes—
145C22⋊D61—44no—
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—21no—
163C2×Dic61C2×D412yes—
164C2×Dic61C2×D412yes—
165D244—44no—
166C4×D61—44no—
167Dic122—44no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61C22×D411yescharacteristic
176C22×C61C2×#4111yescharacteristic
177C22×C61C2×#4111yescharacteristic
178C22×C61H(5,𝔽2)11yescharacteristic
179C22×C61H(5,𝔽2)11yescharacteristic
180C22×C61H(5,𝔽2)11yescharacteristic
181C22×C612−1+411yescharacteristic
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C4×C61—22no—
197C4×C61—22no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61—41no—
201C4×C61—41no—
202Dic61—22no—
203Dic61—22no—
204Dic61—41no—
205Dic61—41no—
206Dic61—41no—
207Dic61—41no—
208#2730—611nomaximal, Sylow
209C2×C61—81no—
210C2×C61#53411yescharacteristic
211C2×C61#53811yescharacteristic
212C2×C61#54211yescharacteristic
213C2×C61#54811yescharacteristic
214C2×C61#55011yescharacteristic
215C2×C61#55111yescharacteristic
216C2×C61#56211yescharacteristic
217D61—42no—
218D61—81no—
219C2×#124—611no—
220C2×C22⋊Q8—611no—
221#399—611no—
222#397—611no—
223#396—611no—
224#394—611no—
225#394—611no—
226#392—611no—
227#391—611no—
228#390—611no—
229#388—611no—
230#388D6111yescharacteristic, complemented
231#387—611no—
232#386—611no—
233#386—611no—
234C61#273011yescharacteristic, complemented, Sylow
235C22×Q8—611no—
236C22×D4—611no—
237C22×D4—611no—
238C22×D4—611no—
239C23×C4—611no—
240#124—1224no—
241C22⋊Q8—1224no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4C2×D6111yescharacteristic
248C2×C22⋊C4—611no—
249C2×C22⋊C4—611no—
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⋊C4—611no—
259C2×C22⋊C4C2×D6111yescharacteristic
260C2×C22⋊C4C2×D6111yescharacteristic
261C2×C22⋊C4C2×D6111yescharacteristic
262C2×C42—611no—
263C2×C42C2×D6111yescharacteristic
264#95—611no—
265#95—611no—
266#95—611no—
267#95—611no—
268#95—611no—
269#95—611no—
270#95C2×D6111yescharacteristic
271#95C2×D6111yescharacteristic
272C24—611no—
273C24—611no—
274C24C22×D6111yescharacteristic
275C2×Q8—614no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C2×D4—1222no—
279C2×D4—1222no—
280C2×D4—1222no—
281C2×D4—1222no—
282C2×D4—2441no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4—2441no—
286C2×D4—2441no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—1222no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4C22×D6111yescharacteristic
297C22×C4C22×D6111yescharacteristic
298C22×C4C22×D6111yescharacteristic
299C22×C4C22×D6111yescharacteristic
300C22×C4C22×D6111yescharacteristic
301C22×C4C22×D6111yescharacteristic
302C4⋊C4—22no—
303C4⋊C4—1222no—
304C4⋊C4—1222no—
305C4⋊C4—1222no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—41no—
311C22⋊C4—1222no—
312C22⋊C4—1222no—
313C22⋊C4—1222no—
314C22⋊C4—1222no—
315C22⋊C4—1222no—
316C22⋊C4—1222no—
317C22⋊C4—2441no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C42—41no—
323C42—1222no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—612no—
332C23—1221no—
333C23—1221no—
334C23—1221no—
335C23—1221no—
336C23—1221no—
337C23—1221no—
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23—1221no—
345C23C23×D6111yescharacteristic
346Q8—2444no—
347D4—2444no—
348D4—2444no—
349D4—2444no—
350C2×C4—21no—
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—612no—
367C2×C4—612no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
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—2444no—
385C2×C4#1175822212yes—
386C2×C4D4×D6112yes—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—1222no—
395C22—1222no—
396C22—1222no—
397C22—2441no—
398C22—2441no—
399C22—2441no—
400C22—2441no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22C2×D4×D6111yescharacteristic
409C22#41×D6111yescharacteristic
410C22C2×#1175822211yescharacteristic
411C22#1451982211yescharacteristic
412C22#1451982311yescharacteristic
413C22#1451982311yescharacteristic
414C22#1451982411yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—1222no—
422C4—1222no—
423C4—2441no—
424C4—2441no—
425C4—2441no—
426C4—2441no—
427C2—81no—
428C2—4881no—
429C2—2442no—
430C2#1684032011yescharacteristic
431C2#1684035111yescharacteristic
432C2#1684038311yescharacteristic
433C2#1684042011yescharacteristic
434C2#1684043311yescharacteristic
435C2#1684044111yescharacteristic
436C2#1684050911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#388C2
hypercenter#388D61
hypocenterC61#2730
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14519763C2semidirect
2. C2×#14519755C2semidirect
3. #16839698C2semidirect
4. #16839691C2semidirect
5. #16839684C2semidirect
6. #16839678C2semidirect
7. #16839677C2semidirect
9. #16839668C2semidirect
10. #16839664C2semidirect
11. #16839651C2semidirect
12. #16839645C2semidirect
13. #16839640C2semidirect
14. #16839638C2semidirect
15. C61×#388C2semidirect
82. C2×Dic122D4semidirect
230. #388D61semidirect
234. C61#2730semidirect