Finite Group Databasebeta

← #21455109

Subgroups — #21455109

Order 7808.

700 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519825C211yesmaximal, characteristic
2C2×#14519809C211yesmaximal, characteristic, complemented
3C2×Q16×D61C211yesmaximal, characteristic, complemented
4#16840335C211yesmaximal, characteristic, complemented
5#16839927C211yesmaximal, characteristic, complemented
6#16839926C211yesmaximal, characteristic, complemented
7#16839923C211yesmaximal, characteristic, complemented
8#16839922C211yesmaximal, characteristic, complemented
9#16839919C211yesmaximal, characteristic, complemented
10#16839918C211yesmaximal, characteristic, complemented
11#16839916C211yesmaximal, characteristic, complemented
12#16839769C211yesmaximal, characteristic, complemented
13#16839757C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#451C211yesmaximal, characteristic, complemented
16#14519825—24no—
17#14519825—24no—
18C2×#11758226—21no—
19C2×#11758226C2211yescharacteristic
20C2×#11758226C2211yescharacteristic
21C2×#11758222—21no—
22C2×#11758222—21no—
23C2×#11758222C2211yescharacteristic
24C2×#11758222C2211yescharacteristic
25C2×Q8×D61—21no—
26C2×Q8×D61C2211yescharacteristic
27C2×Q8×D61C2211yescharacteristic
28C2×Q8×D61C2211yescharacteristic
29#14519809—24no—
30C2×Dic244C2211yescharacteristic
31C2×#11758202C2211yescharacteristic
32C2×#11758202C2211yescharacteristic
33C2×#11758202C2211yescharacteristic
34Q16×D61—24no—
35C2×#11758190C2211yescharacteristic
36C2×#11758201C2211yescharacteristic
37C2×#11758189C2211yescharacteristic
38C2×C8×D61C2211yescharacteristic
39#14519776—21no—
40#14519763—21no—
41#14519762—21no—
42#14519759—21no—
43#14519757C2211yescharacteristic
44#14519756C2211yescharacteristic
45#14519753C2211yescharacteristic
46#14519735C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519701C2211yescharacteristic
49#14519701C2211yescharacteristic
50#14519700C2211yescharacteristic
51#14519699C2211yescharacteristic
52#14519697C2211yescharacteristic
53C22⋊#92418C2211yescharacteristic
54#14519689C2211yescharacteristic
55#14519689C2211yescharacteristic
56C22×Q8×C61C2211yescharacteristic
57C2×Q16×C61C2211yescharacteristic
58C2×Q16×C61C2211yescharacteristic
59C22⋊Q8×C61C2211yescharacteristic
60#103×C61C2211yescharacteristic
61#103×C61C2211yescharacteristic
62C22⋊C8×C61C2211yescharacteristic
63C2×Q8×C61—22no—
64C2×Q8×C61—22no—
65C2×Q8×C61—21no—
66C2×Q8×C61C2311yescharacteristic
67C2×Q8×C61C2311yescharacteristic
68C2×Q8×C61C2311yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61C2311yescharacteristic
71C2×C22⋊D61—21no—
72C2×C22⋊D61D411yescharacteristic
73C2×C22⋊D61D411yescharacteristic
74#11758226—28no—
75#11758226—22no—
76#11758226—22no—
77#11758226—22no—
78#11758226D414yes—
79Q8×D61—28no—
80Q8×D61—22no—
81Q8×D61—22no—
82Q8×D61—22no—
83Q8×D61—22no—
84Q8×D61—22no—
85Q8×D61D414yes—
86#11758222—28no—
87#11758222—28no—
88#11758222—22no—
89#11758222—22no—
90#11758222—22no—
91#11758222—22no—
92C2×D244—21no—
93C2×D244—21no—
94C2×D244D411yescharacteristic
95C2×D244C2311yescharacteristic
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61C2311yescharacteristic
103C2×C4×D61C2311yescharacteristic
104C2×Dic122—21no—
105C2×Dic122—21no—
106C2×Dic122—21no—
107C2×Dic122D411yescharacteristic
108C2×Dic122C2311yescharacteristic
109C2×Dic122C2311yescharacteristic
110Q16×C61—22no—
111Q16×C61—22no—
112C2×C8×C61C2311yescharacteristic
113C2×C8×C61C2311yescharacteristic
114C4⋊C4×C61—21no—
115C4⋊C4×C61C2311yescharacteristic
116C22⋊C4×C61—21no—
117C22⋊Dic61—21no—
118#11758202—22no—
119#11758202—22no—
120#11758202—22no—
121#11758201—22no—
122#11758198—21no—
123#11758198—21no—
124#11758198—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61C2311yescharacteristic
127#11758196—21no—
128#11758196—21no—
129C4×Dic61—21no—
130C2×#92418C2311yescharacteristic
131C2×#92418C2311yescharacteristic
132Dic244—22no—
133#11758190—22no—
134#11758189—22no—
135C8×D61—22no—
136C23×C61C2×D411yescharacteristic
137C22×D61—21no—
138C22×D61C2×D411yescharacteristic
139C22×D61C2×D411yescharacteristic
140Q8×C61—24no—
141Q8×C61—21no—
142Q8×C61—21no—
143Q8×C61—21no—
144Q8×C61—21no—
145Q8×C61C2×D412yes—
146Q8×C61C2×D412yes—
147C2×C4×C61—24no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61C2×D411yescharacteristic
155C2×C4×C61C2411yescharacteristic
156C22⋊D61—24no—
157C22⋊D61—22no—
158C22⋊D61—22no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61C2×D411yescharacteristic
163C2×Dic61C2×D411yescharacteristic
164D244—24no—
165D244—24no—
166D244—22no—
167D244—21no—
168D244C2×D412yes—
169C4×D61—24no—
170C4×D61—24no—
171C4×D61—24no—
172C4×D61—24no—
173C4×D61—21no—
174C4×D61—21no—
175C4×D61—24no—
176C4×D61—42no—
177C4×D61C2×D412yes—
178C4×D61C2×D412yes—
179Dic122—24no—
180Dic122—21no—
181Dic122—24no—
182Dic122—22no—
183Dic122—21no—
184Dic122—21no—
185Dic122—42no—
186Dic122C2×D412yes—
187C8×C61—21no—
188C8×C61—21no—
189#92418—21no—
190#92418—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61C22×D411yescharacteristic
195C2×D61—21no—
196C2×D61—21no—
197C2×D61—21no—
198C2×D61—22no—
199C2×D61—21no—
200C2×D61—21no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61#12012yes—
204C4×C61—22no—
205C4×C61—22no—
206C4×C61—21no—
207C4×C61—41no—
208C4×C61—41no—
209C4×C61C22×D411yescharacteristic
210C4×C61C22×D411yescharacteristic
211Dic61—21no—
212Dic61—22no—
213Dic61—41no—
214Dic61—41no—
215Dic61#12012yes—
216#3011—611nomaximal, Sylow
217C2×C61—41no—
218C2×C61C2×#12011yescharacteristic
219C2×C61#57811yescharacteristic
220C2×C61#57811yescharacteristic
221D61—22no—
222D61—41no—
223D61—42no—
224C2×2−1+4—611no—
225C2×#137—611no—
226C22×Q16—611no—
227#536—611no—
228#452—611no—
229#452—611no—
230#452—611no—
231#452—611no—
232#451—611no—
233#451—611no—
234#451—611no—
235#451D6111yescharacteristic, complemented
236#419—611no—
237#416—611no—
238#408—611no—
239C61#301111yescharacteristic, complemented, Sylow
2402−1+4—1224no—
2412−1+4—1224no—
242C2×#41—611no—
243C2×#41—611no—
244C2×#41—611no—
245C2×#41—611no—
246C2×#41—1221no—
247C2×#41—1221no—
248C2×#41—1221no—
249C22×Q8—611no—
250C22×Q8—611no—
251C22×Q8—611no—
252C22×Q8—1221no—
253C22×Q8C2×D6111yescharacteristic
254#137—1224no—
255C2×Q16—611no—
256C2×Q16—611no—
257C2×Q16—611no—
258C2×Q16—611no—
259C2×Q16—1224no—
260C2×Q16C2×D6111yescharacteristic
261C2×Q16C2×D6111yescharacteristic
262C2×SD16—611no—
263C2×SD16—611no—
264C2×M16—611no—
265C22×C8—611no—
266C4⋊Q8—1221no—
267#124—1221no—
268#123—1221no—
269#123—1221no—
270C22⋊Q8—611no—
271C22⋊Q8—611no—
272C22⋊Q8—611no—
273C22⋊Q8C2×D6111yescharacteristic
274#117—611no—
275#103—611no—
276#103—611no—
277#103—611no—
278#103—611no—
279#103C2×D6111yescharacteristic
280#103C2×D6111yescharacteristic
281#102—611no—
282#102—611no—
283C22⋊C8—611no—
284C22⋊C8—611no—
285C22⋊C8—611no—
286C22⋊C8C2×D6111yescharacteristic
287#41—614no—
288#41—1222no—
289#41—1222no—
290#41—1222no—
291#41—1222no—
292#41—1228no—
293#41—1228no—
294#41—1222no—
295#41—1222no—
296#41—1228no—
297#41—1222no—
298C2×Q8—22no—
299C2×Q8—22no—
300C2×Q8—21no—
301C2×Q8—611no—
302C2×Q8—614no—
303C2×Q8—611no—
304C2×Q8—611no—
305C2×Q8—1221no—
306C2×Q8—1221no—
307C2×Q8—1221no—
308C2×Q8—1222no—
309C2×Q8—1222no—
310C2×Q8—1222no—
311C2×Q8—1222no—
312C2×Q8—1228no—
313C2×Q8—1222no—
314C2×Q8C22×D6111yescharacteristic
315C2×Q8C22×D6111yescharacteristic
316C2×Q8C22×D6111yescharacteristic
317C2×D4—611no—
318C2×D4—611no—
319C2×D4—611no—
320C2×D4—611no—
321C2×D4—1221no—
322C2×D4—1221no—
323C2×D4—1221no—
324C22×C4—21no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4C22×D6111yescharacteristic
334Q16—22no—
335Q16—22no—
336Q16—1222no—
337Q16—1222no—
338Q16—1222no—
339Q16—1222no—
340SD16—1222no—
341SD16—1222no—
342M16—1222no—
343C2×C8—611no—
344C2×C8—611no—
345C2×C8—1222no—
346C2×C8C22×D6111yescharacteristic
347C2×C8C22×D6111yescharacteristic
348C4⋊C4—21no—
349C4⋊C4—611no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C4⋊C4C22×D6111yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C42—1221no—
360C23—611no—
361C23—611no—
362C23—1221no—
363C23D4×D6111yescharacteristic
364Q8—24no—
365Q8—21no—
366Q8—21no—
367Q8—21no—
368Q8—21no—
369Q8—612no—
370Q8—1224no—
371Q8—1222no—
372Q8—1224no—
373Q8—1221no—
374Q8—1221no—
375Q8—1221no—
376Q8—2442no—
377Q8D4×D6112yes—
378Q8D4×D6112yes—
379D4—612no—
380D4—1222no—
381D4—1224no—
382D4—1224no—
383D4—1222no—
384D4—1222no—
385D4—1224no—
386D4—1221no—
387C2×C4—24no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—611no—
395C2×C4—612no—
396C2×C4—612no—
397C2×C4—611no—
398C2×C4—1224no—
399C2×C4—1224no—
400C2×C4—1224no—
401C2×C4—1224no—
402C2×C4—1224no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—2442no—
409C2×C4D4×D6111yescharacteristic
410C2×C4C23×D6111yescharacteristic
411C8—21no—
412C8—21no—
413C8—1221no—
414C8—1221no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—612no—
419C22—1221no—
420C22—1221no—
421C22—1222no—
422C22—1221no—
423C22—1221no—
424C22—1221no—
425C22—2441no—
426C22—2441no—
427C22C2×D4×D6111yescharacteristic
428C4—22no—
429C4—22no—
430C4—21no—
431C4—41no—
432C4—41no—
433C4—612no—
434C4—1221no—
435C4—1222no—
436C4—2441no—
437C4—2441no—
438C4C2×D4×D6111yescharacteristic
439C4C2×D4×D6111yescharacteristic
440C2—41no—
441C2—1222no—
442C2—2441no—
443C2—2442no—
444C2#120×D6111yescharacteristic
445C2#1684057511yescharacteristic
446C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61#3011
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×#14519809C2semidirect
3. C2×Q16×D61C2semidirect
4. #16840335C2semidirect
5. #16839927C2semidirect
6. #16839926C2semidirect
7. #16839923C2semidirect
8. #16839922C2semidirect
9. #16839919C2semidirect
10. #16839918C2semidirect
11. #16839916C2semidirect
12. #16839769C2semidirect
13. #16839757C2semidirect
14. #16839727C2semidirect
15. C61×#451C2semidirect
235. #451D61semidirect
239. C61#3011semidirect