Finite Group Databasebeta

← #29597549

Subgroups — #29597549

Order 15616.

702 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#101×D61C211yesmaximal, characteristic, complemented
2#21449474C211yesmaximal, characteristic
3C2×#16839559C211yesmaximal, characteristic, complemented
4#21445741C211yesmaximal, characteristic, complemented
5#21443945C211yesmaximal, characteristic, complemented
6#21443945C211yesmaximal, characteristic, complemented
7C2×C61×#355C211yesmaximal, characteristic, complemented
8C22×Q8×D61C2211yescharacteristic
9C2×M16×D61—21no—
10C2×#14519764C411yescharacteristic
11C2×#14519748C411yescharacteristic
12C2×#14519696C2211yescharacteristic
13C2×#14519696C2211yescharacteristic
14C2×#14519695—21no—
15C2×#14519695—21no—
16#101×D61—22no—
17#101×D61—22no—
18#16839725—21no—
19#16839674—21no—
20#16839674—21no—
21#16839669C2211yescharacteristic
22#16839668C411yescharacteristic
23#16839638—21no—
24#16839638—21no—
25C4×#11758198C411yescharacteristic
26#16839559—22no—
27C2×#124×C61C2211yescharacteristic
28C2×#101×C61C2211yescharacteristic
29C2×#101×C61C2211yescharacteristic
30C61×#355—22no—
31C22×Dic122C2×C411yescharacteristic
32C22×Dic122D411yescharacteristic
33C22×Dic122D411yescharacteristic
34C2×Q8×D61—21no—
35C2×Q8×D61—21no—
36C2×Q8×D61—21no—
37C2×Q8×D61—21no—
38C2×Q8×D61—42no—
39C2×Q8×D61—41no—
40C2×Q8×D61—41no—
41C22×C22⋊D61—21no—
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C2×#11758194—21no—
46C2×#11758194—21no—
47C2×#11758189—41no—
48M16×D61—24no—
49M16×D61—42no—
50C2×C8×D61—41no—
51#14519764—42no—
52#14519748—41no—
53#14519748—41no—
54C2×C4⋊Dic61C2×C411yescharacteristic
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×C22⋊Dic61—21no—
58C2×#11758198—21no—
59C2×C4×Dic61C2×C411yescharacteristic
60#14519696—21no—
61#14519696—21no—
62#14519696—21no—
63#14519696D412yescomplemented
64#14519695—24no—
65#14519695—42no—
66#14519689—41no—
67#14519689—41no—
68#14519684—21no—
69#14519684—21no—
70#14519684—21no—
71#14519684—21no—
72#14519684—21no—
73C22×Q8×C61C2311yescharacteristic
74C22×D4×C61C2×C411yescharacteristic
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77#124×C61—21no—
78#124×C61—21no—
79#124×C61—21no—
80#124×C61—21no—
81C2×C22⋊C4×C61—21no—
82C2×C22⋊C4×C61—21no—
83C2×C42×C61C2×C411yescharacteristic
84#101×C61—21no—
85#101×C61—21no—
86#101×C61—21no—
87#101×C61D412yescomplemented
88C24×C61—21no—
89C23×D61C22⋊C411yescharacteristic
90C2×Q8×C61—41no—
91C2×Q8×C61—41no—
92C2×Q8×C61C2×D411yescharacteristic
93C2×Q8×C61C2×D411yescharacteristic
94C2×Q8×C61#4111yescharacteristic
95C2×Q8×C61#4111yescharacteristic
96C2×D4×C61—21no—
97C2×D4×C61—21no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C22×C4×C61—21no—
101C22×C4×C61C22×C411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C2×C22⋊D61—44no—
105C2×C22⋊D61—41no—
106C2×C22⋊D61—41no—
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61C22⋊C411yescharacteristic
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C411yescharacteristic
112Q8×D61—42no—
113Q8×D61—42no—
114Q8×D61—42no—
115Q8×D61—42no—
116Q8×D61—42no—
117Q8×D61—42no—
118Q8×D61—42no—
119Q8×D61—42no—
120C2×C4×D61—21no—
121C2×C4×D61—21no—
122C2×C4×D61—21no—
123C2×C4×D61—21no—
124C2×C4×D61—22no—
125C2×C4×D61—21no—
126C2×C4×D61—21no—
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×C4×D61—21no—
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×Dic122—21no—
136C2×Dic122—21no—
137C2×Dic122—21no—
138C2×Dic122—21no—
139C2×Dic122—21no—
140C2×Dic122—21no—
141C2×Dic122—22no—
142C2×Dic122—22no—
143C2×Dic122—41no—
144C2×Dic122—41no—
145C2×Dic122—41no—
146C2×Dic122—41no—
147M16×C61—22no—
148M16×C61—41no—
149M16×C61—41no—
150M16×C61—41no—
151C2×C8×C61—41no—
152C2×C8×C61—41no—
153C22⋊C4×C61—41no—
154C22⋊C4×C61—41no—
155C22⋊C4×C61—41no—
156C22⋊C4×C61—41no—
157C42×C61—21no—
158C42×C61—21no—
159C22⋊Dic61—42no—
160C22⋊Dic61—42no—
161C22⋊Dic61—42no—
162#11758198—42no—
163C4⋊Dic61—41no—
164C4×Dic61—41no—
165#11758194—22no—
166#11758194—41no—
167#11758194—41no—
168#11758194—41no—
169C2×#92418—41no—
170C2×#92418—41no—
171#11758189—44no—
172C8×D61—44no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—41no—
176C23×C61—41no—
177C23×C61—41no—
178C23×C61C2×C22⋊C411yescharacteristic
179C22×D61—21no—
180C22×D61—21no—
181C22×D61—22no—
182C22×D61—41no—
183C22×D61#9911yescharacteristic
184C22×D61#9911yescharacteristic
185Q8×C61—41no—
186Q8×C61—41no—
187Q8×C61—41no—
188Q8×C61—41no—
189D4×C61—81no—
190D4×C61—81no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61C4×D411yescharacteristic
201C2×C4×C61C4×D411yescharacteristic
202C2×C4×C61#12011yescharacteristic
203C2×C4×C61#12111yescharacteristic
204C2×C4×C61#12111yescharacteristic
205C2×C4×C61#12311yescharacteristic
206C22⋊D61—82no—
207C22⋊D61—82no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—21no—
213C2×Dic61—21no—
214C2×Dic61—21no—
215C2×Dic61—21no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61—42no—
219C2×Dic61—41no—
220C2×Dic61—41no—
221C2×Dic61#9912yes—
222C4×D61—22no—
223C4×D61—22no—
224C4×D61—22no—
225C4×D61—22no—
226C4×D61—41no—
227C4×D61—41no—
228C4×D61—41no—
229C4×D61—41no—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—41no—
233C4×D61—41no—
234Dic122—42no—
235Dic122—42no—
236Dic122—42no—
237Dic122—42no—
238Dic122—42no—
239Dic122—42no—
240C8×C61—42no—
241C8×C61—81no—
242#92418—42no—
243#92418—81no—
244#13092—611nomaximal, Sylow
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—82no—
248C22×C61—82no—
249C22×C61—81no—
250C22×C61—81no—
251C22×C61—81no—
252C22×C61#38611yescharacteristic
253C22×C61C2×#9911yescharacteristic
254C22×C61C2×#9911yescharacteristic
255C2×D61—21no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—21no—
260C2×D61—42no—
261C2×D61—42no—
262C2×D61#35512yescomplemented
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—81no—
270Dic61—22no—
271Dic61—41no—
272Dic61—41no—
273Dic61—81no—
274Dic61—81no—
275C22×#101—611no—
276#2436—611no—
277C2×#355—611no—
278C2×#355D6111yescharacteristic, complemented
279#1784—611no—
280#1394—611no—
281#1394—611no—
282C2×C61—21no—
283C2×C61—21no—
284C2×C61—161no—
285C2×C61#189811yescharacteristic
286C2×C61C2×#35511yescharacteristic
287C2×C61#213311yescharacteristic
288D61—22no—
289D61—41no—
290C23×Q8—611no—
291C22×M16—1221no—
292C2×#124—611no—
293C2×#124C2×D6111yescharacteristic
294C2×#121—611no—
295C2×#101—611no—
296C2×#101—611no—
297C2×#101—1222no—
298C2×#101—1221no—
299C2×#101—1222no—
300C2×#101—1221no—
301C2×#101C2×D6111yescharacteristic
302C2×#101C2×D6111yescharacteristic
303#407—1221no—
304#393—1221no—
305#393—1221no—
306#391—611no—
307#391—611no—
308#386—1221no—
309#386—1221no—
310C4×C22⋊C4—611no—
311#355—22no—
312#355—1222no—
313C61#1309211yescharacteristic, complemented, Sylow
314C22×Q8—611no—
315C22×Q8—611no—
316C22×Q8—611no—
317C22×Q8—1221no—
318C22×Q8—1221no—
319C22×Q8—1221no—
320C22×Q8—1221no—
321C22×Q8—2441no—
322C22×Q8—2441no—
323C22×Q8—2442no—
324C22×Q8C22×D6111yescharacteristic
325C22×D4—1221no—
326C22×D4C4×D6111yescharacteristic
327C23×C4—611no—
328C23×C4—611no—
329C23×C4—611no—
330C2×M16—21no—
331C2×M16—21no—
332C2×M16—1224no—
333C2×M16—1221no—
334C2×M16—1221no—
335C2×M16—2441no—
336C2×M16—2442no—
337C22×C8—2441no—
338#124—21no—
339#124—21no—
340#124—21no—
341#124—21no—
342#124—2442no—
343#121—2441no—
344#121—2441no—
345C2×C4⋊C4—611no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—1221no—
349C2×C22⋊C4—1221no—
350C2×C22⋊C4—1221no—
351C2×C22⋊C4—1221no—
352C2×C42—611no—
353C2×C42C4×D6111yescharacteristic
354#101—21no—
355#101—21no—
356#101—21no—
357#101—612no—
358#101—1224no—
359#101—1221no—
360#101—1221no—
361#101—1221no—
362#101—2442no—
363#101C22⋊D6112yescomplemented
364C22⋊C8—2441no—
365C22⋊C8—2441no—
366#95—1221no—
367#95—1221no—
368#95—1221no—
369#95—1221no—
370#95—1221no—
371C24—21no—
372C24—611no—
373C2×Q8—41no—
374C2×Q8—41no—
375C2×Q8—1222no—
376C2×Q8—1222no—
377C2×Q8—1221no—
378C2×Q8—1221no—
379C2×Q8—1221no—
380C2×Q8—1221no—
381C2×Q8—1221no—
382C2×Q8—1221no—
383C2×Q8—2441no—
384C2×Q8—2441no—
385C2×Q8—2441no—
386C2×Q8—2441no—
387C2×Q8—2442no—
388C2×Q8—2442no—
389C2×Q8—2442no—
390C2×Q8—2442no—
391C2×Q8—2442no—
392C2×Q8—2442no—
393C2×Q8—2442no—
394C2×Q8—2442no—
395C2×Q8#1175822211yescharacteristic
396C2×Q8D4×D6111yescharacteristic
397C2×Q8#1175822411yescharacteristic
398C2×Q8C2×C22⋊D6111yescharacteristic
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—2441no—
404C2×D4—2441no—
405C2×D4—2444no—
406C22×C4—21no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—1222no—
411C22×C4—1221no—
412C22×C4—1221no—
413C22×C4—1221no—
414C22×C4—1221no—
415C22×C4—1221no—
416C22×C4—1221no—
417C22×C4—1221no—
418C22×C4—1221no—
419C22×C4—1221no—
420C22×C4—1221no—
421C22×C4—1221no—
422C22×C4—1221no—
423C22×C4—1221no—
424C22×C4—1221no—
425C22×C4—2441no—
426C22×C4—2441no—
427C22×C4C2×C4×D6111yescharacteristic
428C22×C4D4×D6111yescharacteristic
429C22×C4D4×D6111yescharacteristic
430M16—22no—
431M16—41no—
432M16—41no—
433M16—41no—
434M16—1222no—
435M16—2444no—
436M16—2441no—
437M16—2441no—
438M16—2441no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—2444no—
442C2×C8—2441no—
443C2×C8—2441no—
444C4⋊C4—2441no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—2442no—
450C22⋊C4—2442no—
451C22⋊C4—2442no—
452C22⋊C4—2442no—
453C42—21no—
454C42—21no—
455C42—2441no—
456C23—42no—
457C23—42no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—611no—
462C23—611no—
463C23—1222no—
464C23—1221no—
465C23—1221no—
466C23—2441no—
467C23C22⋊C4×D6111yescharacteristic
468Q8—41no—
469Q8—41no—
470Q8—41no—
471Q8—41no—
472Q8—2442no—
473Q8—2442no—
474Q8—2442no—
475Q8—2442no—
476Q8—2442no—
477Q8—2442no—
478D4—81no—
479D4—81no—
480D4—4882no—
481D4—4882no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—612no—
492C2×C4—1222no—
493C2×C4—1222no—
494C2×C4—1222no—
495C2×C4—1222no—
496C2×C4—1221no—
497C2×C4—1221no—
498C2×C4—1221no—
499C2×C4—1221no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2442no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4#1451973711yescharacteristic
518C2×C4C4×C22⋊D6111yescharacteristic
519C2×C4#1451974511yescharacteristic
520C2×C4#1451974811yescharacteristic
521C2×C4#1451975011yescharacteristic
522C2×C4#1451975911yescharacteristic
523C8—42no—
524C8—81no—
525C8—4881no—
526C8—2442no—
527C22—21no—
528C22—21no—
529C22—82no—
530C22—82no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—612no—
535C22—1221no—
536C22—1221no—
537C22—1221no—
538C22—1221no—
539C22—1221no—
540C22—2442no—
541C22—2442no—
542C22#1683963811yescharacteristic
543C22#99×D6111yescharacteristic
544C22#99×D6111yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—81no—
552C4—1222no—
553C4—4881no—
554C4—4881no—
555C4—2441no—
556C4—2441no—
557C2—21no—
558C2—21no—
559C2—161no—
560C2—1222no—
561C2—2441no—
562C2#2144626911yescharacteristic
563C2#355×D6111yescharacteristic
564C2#2144750511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC2×C61×#355C2
socleC22×C61C2×#99
prime radicalC2×#14519748C4
cosocleC22×Q8×C61C23
hypercenterC2×#355D61
hypocenterC61#13092
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
1. C2×#101×D61C2semidirect
3. C2×#16839559C2semidirect
4. #21445741C2semidirect
5. #21443945C2semidirect
6. #21443945C2semidirect
7. C2×C61×#355C2semidirect
63. #14519696D4semidirect
87. #101×C61D4semidirect
262. C2×D61#355semidirect
278. C2×#355D61semidirect
313. C61#13092semidirect
363. #101C22⋊D61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#101×D612
#214494742
C2×#168395592
#214457412
#214439452
C2×C61×#3552
#1309261