Finite Group Databasebeta

← #21450892

Subgroups — #21450892

Order 7808.

696 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519764C211yesmaximal, characteristic, complemented
2C2×#14519763C211yesmaximal, characteristic, complemented
3C2×#14519749C211yesmaximal, characteristic, complemented
4#16839682C211yesmaximal, characteristic, complemented
5#16839676C211yesmaximal, characteristic, complemented
6#16839670C211yesmaximal, characteristic, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839662C211yesmaximal, characteristic, complemented
9#16839652C211yesmaximal, characteristic, complemented
10#16839650C211yesmaximal, characteristic, complemented
11#16839642C211yesmaximal, characteristic, complemented
12#16839641C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
15C2×#121×C61C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C23×Dic61C2211yescharacteristic
21#14519764—24no—
22#14519763—24no—
23#14519749—24no—
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×C4×Dic61C2211yescharacteristic
39C2×C4×Dic61C2211yescharacteristic
40C2×C4×Dic61C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47C22×D4×C61C2211yescharacteristic
48C22×D4×C61C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50C23×C4×C61C2211yescharacteristic
51#121×C61—24no—
52C2×C4⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C24×C61C2311yescharacteristic
58C23×D61C2311yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61—22no—
62C2×D4×C61—22no—
63C2×D4×C61—22no—
64C2×D4×C61—22no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—41no—
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C2×C22⋊D61—22no—
76C2×C22⋊D61—22no—
77C2×C22⋊D61—22no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C22×Dic61—22no—
85C22×Dic61—22no—
86C22×Dic61—41no—
87C22×Dic61C2311yescharacteristic
88C22×Dic61C2311yescharacteristic
89C22×Dic61C2311yescharacteristic
90C22×Dic61C2311yescharacteristic
91C22×Dic61C2311yescharacteristic
92C22×Dic61C2311yescharacteristic
93C22×Dic61C2311yescharacteristic
94C2×Dic122—22no—
95C2×Dic122—22no—
96C2×Dic122—41no—
97C4⋊C4×C61—22no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61D414yescomplemented
100C22⋊Dic61—22no—
101C22⋊Dic61—22no—
102C22⋊Dic61—22no—
103C22⋊Dic61—22no—
104C22⋊Dic61—22no—
105C22⋊Dic61—22no—
106C22⋊Dic61—22no—
107C22⋊Dic61D414yescomplemented
108#11758198—22no—
109#11758198—22no—
110#11758198—22no—
111#11758198—22no—
112#11758196—22no—
113#11758196—41no—
114C4×Dic61—22no—
115C4×Dic61—22no—
116C4×Dic61—41no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61C2×D412yes—
137C23×C61C2×D412yes—
138C23×C61C2411yescharacteristic
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146D4×C61—44no—
147D4×C61—44no—
148D4×C61—44no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—44no—
159C2×C4×C61C2×D412yes—
160C2×C4×C61C2×D412yes—
161C2×C4×C61#4112yes—
162C22⋊D61—44no—
163C22⋊D61—44no—
164C22⋊D61—44no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—44no—
183C2×Dic61C2×D412yes—
184C2×Dic61C2×D412yes—
185C2×Dic61#4112yes—
186C2×Dic61#4112yes—
187Dic122—44no—
188C22×C61—22no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61—22no—
192C22×C61—22no—
193C22×C61—22no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61C22×D411yescharacteristic
210C22×C61C22×D411yescharacteristic
211C22×C61C2×#4111yescharacteristic
212C22×C61C2×#4111yescharacteristic
213C22×C61C2×#4111yescharacteristic
214C22×C61H(5,𝔽2)11yescharacteristic
215C22×C61H(5,𝔽2)11yescharacteristic
216C2×D61—41no—
217C2×D61—41no—
218C2×D61—41no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—41no—
223C4×C61—22no—
224C4×C61—22no—
225C4×C61—22no—
226C4×C61—41no—
227Dic61—22no—
228Dic61—22no—
229Dic61—22no—
230Dic61—22no—
231Dic61—41no—
232Dic61—41no—
233Dic61—41no—
234#2555—611nomaximal, Sylow
235C2×C61—42no—
236C2×C61—42no—
237C2×C61—81no—
238C2×C61#53211yescharacteristic
239C2×C61#53211yescharacteristic
240C2×C61#53811yescharacteristic
241C2×C61D4211yescharacteristic
242C2×C61#54611yescharacteristic
243C2×C61#54611yescharacteristic
244C2×C61#55511yescharacteristic
245D61—81no—
246C2×#124—611no—
247C2×#124—611no—
248C2×#121—611no—
249C2×#121D6111yescharacteristic, complemented
250#395—611no—
251#394—611no—
252#392—611no—
253#392—611no—
254#390—611no—
255#388—611no—
256#388—611no—
257#386—611no—
258#386—611no—
259C4×C22⋊C4—611no—
260C4×C22⋊C4—611no—
261C61#255511yescharacteristic, complemented, Sylow
262C22×Q8—611no—
263C22×D4—611no—
264C22×D4—611no—
265C22×D4—611no—
266C22×D4C2×D6111yescharacteristic
267C22×D4C2×D6111yescharacteristic
268C22×D4C2×D6111yescharacteristic
269C23×C4—611no—
270C23×C4C2×D6111yescharacteristic
271#124—1224no—
272#124—1224no—
273#121—24no—
274#121—1224no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4C2×D6111yescharacteristic
278C2×C22⋊C4—611no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4—611no—
289C2×C22⋊C4—611no—
290C2×C22⋊C4C2×D6111yescharacteristic
291C2×C22⋊C4C2×D6111yescharacteristic
292C2×C42—611no—
293C2×C42—611no—
294C2×C42—611no—
295#95—611no—
296#95—611no—
297#95—611no—
298#95—611no—
299#95—611no—
300#95—611no—
301C24—611no—
302C24C22×D6111yescharacteristic
303C24C22×D6111yescharacteristic
304C24C22×D6111yescharacteristic
305C2×Q8—1222no—
306C2×Q8—1222no—
307C2×Q8—2441no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—1222no—
318C2×D4—1222no—
319C2×D4—1222no—
320C2×D4—1222no—
321C2×D4—1222no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—41no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—611no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—611no—
336C22×C4—1222no—
337C22×C4—1222no—
338C22×C4—2441no—
339C22×C4C22×D6111yescharacteristic
340C22×C4C22×D6111yescharacteristic
341C22×C4C22×D6111yescharacteristic
342C22×C4C22×D6111yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—1222no—
345C4⋊C4—2441no—
346C22⋊C4—22no—
347C22⋊C4—614no—
348C22⋊C4—1222no—
349C22⋊C4—1222no—
350C22⋊C4—1222no—
351C22⋊C4—1222no—
352C22⋊C4—1222no—
353C22⋊C4—1222no—
354C22⋊C4—1222no—
355C22⋊C4—1222no—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C22⋊C4—1222no—
359C22⋊C4C22⋊D6114yescomplemented
360C42—1222no—
361C42—1222no—
362C42—2441no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—1221no—
383C23—1221no—
384C23—1221no—
385C23—1221no—
386C23—1221no—
387C23—1221no—
388C23—1221no—
389C23D4×D6112yes—
390C23C2×C22⋊D6112yes—
391C23C23×D6111yescharacteristic
392Q8—2444no—
393D4—44no—
394D4—44no—
395D4—44no—
396D4—2444no—
397D4—2444no—
398D4—2444no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—44no—
409C2×C4—612no—
410C2×C4—612no—
411C2×C4—612no—
412C2×C4—612no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—1221no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—1221no—
420C2×C4—1221no—
421C2×C4—1221no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—2444no—
431C2×C4#1175822412yes—
432C2×C4C2×C22⋊D6112yes—
433C2×C4C2×C22⋊D6112yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—2441no—
456C22—2441no—
457C22—2441no—
458C22—2441no—
459C22—2441no—
460C22—2441no—
461C22—2441no—
462C22C2×D4×D6111yescharacteristic
463C22C22×C22⋊D6111yescharacteristic
464C22#41×D6111yescharacteristic
465C22#41×D6111yescharacteristic
466C22C2×#1175822411yescharacteristic
467C22#1451982211yescharacteristic
468C22#1451982211yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—1222no—
474C4—1222no—
475C4—1222no—
476C4—1222no—
477C4—2441no—
478C4—2441no—
479C4—2441no—
480C2—42no—
481C2—42no—
482C2—81no—
483C2—4881no—
484C2#1684030711yescharacteristic
485C2#1684030811yescharacteristic
486C2#1684034411yescharacteristic
487C2D4×C22⋊D6111yescharacteristic
488C2#1684040111yescharacteristic
489C2#1684040611yescharacteristic
490C2#1684047611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2555
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519764C2semidirect
2. C2×#14519763C2semidirect
3. C2×#14519749C2semidirect
4. #16839682C2semidirect
5. #16839676C2semidirect
6. #16839670C2semidirect
7. #16839670C2semidirect
8. #16839662C2semidirect
9. #16839652C2semidirect
10. #16839650C2semidirect
11. #16839642C2semidirect
12. #16839641C2semidirect
13. C22⋊C4×Dic61C2semidirect
14. C4×C22⋊Dic61C2semidirect
15. C2×#121×C61C2semidirect
99. C22⋊C4×C61D4semidirect
107. C22⋊Dic61D4semidirect
249. C2×#121D61semidirect
261. C61#2555semidirect
359. C22⋊C4C22⋊D61semidirect