Finite Group Databasebeta

← #30599653

Subgroups — #30599653

Order 15616.

702 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 94 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
1#21462308C211yesmaximal, characteristic
2#21461806C211yesmaximal, characteristic
3#21461768C211yesmaximal, characteristic, complemented
4#21461007C211yesmaximal, characteristic, complemented
5#21460693C211yesmaximal, characteristic, complemented
6#21460656C211yesmaximal, characteristic, complemented
7#327×D61C211yesmaximal, characteristic
8C2×D4×#6923—21no—
9C22×C4⋊#6923—21no—
10C22×C4⋊#6923C2211yescharacteristic
11C2×#14519846—21no—
12C2×#14519839—21no—
13D61⋊(C22⋊C8)C2211yescharacteristic
14#16840712—21no—
15#16840711—21no—
16#16840710—21no—
17#16840710—21no—
18#16840709—21no—
19#16840704C2211yescharacteristic
20C2×(C2×#6923)⋊C4—21no—
21C2×(C2×#6923)⋊C4C2211yescharacteristic
22#16840636—21no—
23#16840635—21no—
24#121×D61C2211yescharacteristic
25C22⋊C8×D61C2211yescharacteristic
26#95×D61C2211yescharacteristic
27#16839497C411yescharacteristic, complemented
28#16839496C411yescharacteristic, complemented
29#16839495C411yescharacteristic, complemented
30C61×#327C411yescharacteristic, complemented
31C23×#6923—21no—
32C23×#6923—21no—
33C23×#6923D411yescharacteristic
34C23×#6923D411yescharacteristic
35C2×D61⋊C8—21no—
36D4×#6923—42no—
37D4×#6923—42no—
38C2×C4⋊#6923—21no—
39C2×C4⋊#6923—21no—
40C2×C4⋊#6923—21no—
41C2×C4⋊#6923—42no—
42C2×C4⋊#6923—42no—
43C2×C4⋊#6923—42no—
44C2×C4⋊#6923—42no—
45C2×C4⋊#6923D411yescharacteristic
46C2×C4⋊#6923D411yescharacteristic
47C2×C22⋊#6923—21no—
48C2×C22⋊#6923—21no—
49C2×C22⋊#6923—21no—
50C2×C22⋊#6923—21no—
51C2×C4×#6923—21no—
52#14519846—42no—
53#14519839—42no—
54#14519834—21no—
55C22⋊#92420—21no—
56(C2×#6923)⋊C4—21no—
57(C2×#6923)⋊C4—21no—
58(C2×#6923)⋊C4—21no—
59(C2×#6923)⋊C4—21no—
60(C2×#6923)⋊C4—21no—
61(C2×#6923)⋊C4—42no—
62C2×D4×D61—21no—
63C2×D4×D61D411yescharacteristic
64C22×C4×D61—21no—
65C22×C4×D61C2311yescharacteristic
66C2×C8×D61—21no—
67#14519752Q811yescharacteristic
68#14519751C2×C411yescharacteristic
69#14519750—21no—
70#14519749—21no—
71#14519748Q811yescharacteristic
72C4⋊C4×D61D411yescharacteristic
73C22⋊C4×D61—21no—
74C22⋊#92418C2×C411yescharacteristic, complemented
75#14519689—21no—
76#14519684—21no—
77#14519684C2×C411yescharacteristic, complemented
78#121×C61C2×C411yescharacteristic
79C22⋊C8×C61C2×C411yescharacteristic, complemented
80#95×C61C2×C411yescharacteristic, complemented
81C23×D61—21no—
82C23×D61C2×D411yescharacteristic
83C22×#6923—21no—
84C22×#6923—21no—
85C22×#6923—22no—
86C22×#6923—21no—
87C22×#6923—21no—
88C22×#6923—21no—
89C22×#6923—21no—
90C22×#6923—21no—
91C22×#6923—42no—
92C22×#6923—41no—
93C22×#6923—41no—
94C22×#6923—41no—
95C22×#6923—41no—
96C22×#6923—41no—
97C22×#6923—41no—
98C22×#6923—41no—
99C22×#6923—41no—
100C22×#6923—41no—
101C22×#6923—41no—
102C22×#6923—81no—
103C22×#6923—81no—
104C22×#6923D812yes—
105C2×D4×C61—21no—
106C2×D4×C61C4⋊C411yescharacteristic, complemented
107C22×C4×C61—21no—
108C22×C4×C61C22×C411yescharacteristic
109C2×C22⋊D61—21no—
110C2×C22⋊D61—21no—
111C2×C22⋊D61—21no—
112C22×Dic61—21no—
113C22×Dic61#4111yescharacteristic
114D4×D61—41no—
115D4×D61—41no—
116D4×D61—41no—
117D4×D61—41no—
118D4×D61—41no—
119D4×D61—41no—
120C2×D244—21no—
121C2×D244C4⋊C411yescharacteristic, complemented
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—21no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×C4×D61—41no—
128C2×C4×D61—41no—
129C2×C4×D61—41no—
130C2×C4×D61—41no—
131C2×C4×D61C2×D411yescharacteristic
132C2×C4×D61C2×D411yescharacteristic
133C2×C4×D61C2×Q811yescharacteristic
134C2×C4×D61#4111yescharacteristic
135C22⋊#6923—42no—
136C22⋊#6923—41no—
137C22⋊#6923—41no—
138C22⋊#6923—81no—
139C22⋊#6923—81no—
140C2×#92420—41no—
141C4⋊#6923—22no—
142C4⋊#6923—22no—
143C4⋊#6923—41no—
144C4⋊#6923—41no—
145C4⋊#6923—41no—
146C4⋊#6923—41no—
147C4⋊#6923—42no—
148C4⋊#6923—48no—
149C4×#6923—42no—
150D61⋊C8—41no—
151D61⋊C8—41no—
152C2×C8×C61—21no—
153C4⋊C4×C61C4⋊C411yescharacteristic, complemented
154C22⋊C4×C61—21no—
155C22⋊Dic61—21no—
156#11758198—21no—
157#11758198—21no—
158C4⋊Dic61C4⋊C411yescharacteristic, complemented
159#11758196—21no—
160C2×#92418—21no—
161C8×D61—41no—
162C8×D61—41no—
163C23×C61—21no—
164C23×C61C4×D411yescharacteristic
165C22×D61—21no—
166C22×D61—21no—
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61#12011yescharacteristic
177C22×D61C22⋊Q811yescharacteristic
178C22×D61C2×D811yescharacteristic
179C22×D61#13511yescharacteristic
180C22×D61AGL(1,ℤ/8)11yescharacteristic
181C22×D61#13711yescharacteristic
182C2×#6923—22no—
183C2×#6923—41no—
184C2×#6923—41no—
185C2×#6923—42no—
186C2×#6923—42no—
187C2×#6923—42no—
188C2×#6923—42no—
189C2×#6923—41no—
190C2×#6923—41no—
191C2×#6923—41no—
192C2×#6923—41no—
193C2×#6923—41no—
194C2×#6923—41no—
195C2×#6923—42no—
196C2×#6923—41no—
197C2×#6923—41no—
198C2×#6923—41no—
199C2×#6923—81no—
200C2×#6923—84no—
201C2×#6923—81no—
202C2×#6923—81no—
203C2×#6923—81no—
204C2×#6923—81no—
205C2×#6923—81no—
206D4×C61—41no—
207D4×C61—41no—
208D4×C61—41no—
209C2×C4×C61—22no—
210C2×C4×C61—21no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61C2×C4⋊C411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C22⋊D61—41no—
217C22⋊D61—41no—
218C22⋊D61—41no—
219C22⋊D61—41no—
220C22⋊D61—81no—
221C2×Dic61—22no—
222C2×Dic61—21no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61C22⋊Q811yescharacteristic
227C2×Dic61#12311yescharacteristic
228D244—41no—
229D244—41no—
230D244—41no—
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—21no—
234C4×D61—21no—
235C4×D61—41no—
236C4×D61—41no—
237C4×D61—42no—
238C4×D61—42no—
239C4×D61—42no—
240C4×D61—42no—
241C4×D61—41no—
242C4×D61—41no—
243#92420—81no—
244C8×C61—41no—
245#92418—41no—
246#8866—611nomaximal, Sylow
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61#38511yescharacteristic
253C22×C61C4×D811yescharacteristic
254C22×C61#44011yescharacteristic
255C2×D61—21no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—81no—
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C2×D61#44711yescharacteristic
273C2×D61#45211yescharacteristic
274C2×D61#45311yescharacteristic
275C2×D61#45611yescharacteristic
276C2×D61B(4,𝔽2)11yescharacteristic
277C2×D61#45811yescharacteristic
278C2×D61#47411yescharacteristic
279C2×D61#47811yescharacteristic
280#6923—42no—
281#6923—82no—
282#6923—81no—
283#6923—81no—
284#6923—81no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—42no—
288C4×C61—41no—
289Dic61—21no—
290Dic61—21no—
291Dic61—42no—
292Dic61—41no—
293#2325—611no—
294#1874—611no—
295#1852—611no—
296C2×#327—611no—
297#1444—611no—
298#1294—611no—
299#1280—611no—
300C2×C61—21no—
301C2×C61—21no—
302C2×C61—81no—
303C2×C61#185911yescharacteristic
304C2×C61#186211yescharacteristic
305C2×C61#186711yescharacteristic
306D61—21no—
307D61—21no—
308D61—81no—
309D61#159511yescharacteristic
310D61#160311yescharacteristic
311D61#161011yescharacteristic
312D61#161811yescharacteristic
313C2×#121—611no—
314C2×C4×D4—1221no—
315C22×C4⋊C4—611no—
316C22×C4⋊C4—1221no—
317C2×#107—1221no—
318C2×#102—1221no—
319C2×C22⋊C8—611no—
320C2×C22⋊C8—611no—
321#388—1221no—
322#387—1221no—
323#386—1221no—
324#386—1221no—
325#385—1221no—
326#380—611no—
327C2×#95—611no—
328C2×#95—611no—
329C2×#95—1221no—
330#340—1221no—
331#340—1221no—
332#327—611no—
333#327—611no—
334#327—611no—
335#327#692311yescharacteristic, complemented
336C61#886611yescharacteristic, complemented, Sylow
337C22×D4—611no—
338C22×D4—1221no—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—1221no—
343C23×C4—1221no—
344C23×C4—1221no—
345C22×C8—1221no—
346C22×C8—1221no—
347#121—611no—
348#121—611no—
349#121—611no—
350#121—1221no—
351#121—1221no—
352#121C2×#692311yescharacteristic
353C4×D4—2442no—
354C4×D4—2442no—
355C2×C4⋊C4—611no—
356C2×C4⋊C4—611no—
357C2×C4⋊C4—611no—
358C2×C4⋊C4—1221no—
359C2×C4⋊C4—1221no—
360C2×C4⋊C4—1221no—
361C2×C4⋊C4—2442no—
362C2×C4⋊C4—2442no—
363C2×C4⋊C4—2442no—
364C2×C4⋊C4—2442no—
365C2×C22⋊C4—1221no—
366C2×C22⋊C4—1221no—
367C2×C22⋊C4—1221no—
368C2×C22⋊C4—1221no—
369C2×C22⋊C4—1221no—
370C2×C42—1221no—
371#107—2442no—
372#102—2442no—
373C22⋊C8—611no—
374C22⋊C8—1221no—
375C22⋊C8—1221no—
376C22⋊C8—1221no—
377C22⋊C8C2×#692311yescharacteristic, complemented
378#95—611no—
379#95—1221no—
380#95—1221no—
381#95—1221no—
382#95—1221no—
383#95—1221no—
384#95—1221no—
385#95—2442no—
386#95C2×#692311yescharacteristic, complemented
387C24—611no—
388C24—1221no—
389C2×D4—21no—
390C2×D4—611no—
391C2×D4—1221no—
392C2×D4—1221no—
393C2×D4—1221no—
394C2×D4—1221no—
395C2×D4—2441no—
396C2×D4—2441no—
397C2×D4—2441no—
398C2×D4—2441no—
399C2×D4—2441no—
400C2×D4—2441no—
401C2×D4C4⋊#692311yescharacteristic, complemented
402C22×C4—21no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—612no—
409C22×C4—1221no—
410C22×C4—1222no—
411C22×C4—1222no—
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—1222no—
421C22×C4—4881no—
422C22×C4—4881no—
423C22×C4—2441no—
424C22×C4—2441no—
425C22×C4—2441no—
426C22×C4—2441no—
427C22×C4—2441no—
428C22×C4—2441no—
429C22×C4—2442no—
430C22×C4—2441no—
431C22×C4—2441no—
432C22×C4—2441no—
433C22×C4—2441no—
434C22×C4—2441no—
435C22×C4—2441no—
436C22×C4—2441no—
437C22×C4—2441no—
438C22×C4—2441no—
439C22×C4—2441no—
440C22×C4C22×#692311yescharacteristic
441C2×C8—21no—
442C2×C8—1221no—
443C2×C8—2441no—
444C2×C8—2441no—
445C2×C8—2441no—
446C2×C8—2441no—
447C2×C8—2441no—
448C4⋊C4—611no—
449C4⋊C4—1221no—
450C4⋊C4—1222no—
451C4⋊C4—1222no—
452C4⋊C4—2441no—
453C4⋊C4—2441no—
454C4⋊C4—2441no—
455C4⋊C4—2441no—
456C4⋊C4—2442no—
457C4⋊C4—2448no—
458C4⋊C4C4⋊#692311yescharacteristic, complemented
459C22⋊C4—21no—
460C22⋊C4—1221no—
461C22⋊C4—1221no—
462C22⋊C4—1221no—
463C22⋊C4—4881no—
464C22⋊C4—4881no—
465C22⋊C4—2442no—
466C22⋊C4—2441no—
467C22⋊C4—2441no—
468C42—2442no—
469C23—21no—
470C23—611no—
471C23—611no—
472C23—611no—
473C23—611no—
474C23—611no—
475C23—611no—
476C23—1221no—
477C23—1221no—
478C23—1221no—
479C23—1221no—
480C23—1221no—
481C23—2441no—
482C23—2441no—
483C23—2441no—
484C23—2441no—
485C23—2441no—
486C23—2441no—
487C23D4×#692311yescharacteristic
488D4—41no—
489D4—41no—
490D4—41no—
491D4—4881no—
492D4—2441no—
493D4—2441no—
494D4—2441no—
495D4—2441no—
496D4—2441no—
497D4—2441no—
498D4—2441no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—611no—
505C2×C4—611no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1222no—
511C2×C4—1222no—
512C2×C4—1221no—
513C2×C4—4881no—
514C2×C4—4881no—
515C2×C4—4881no—
516C2×C4—4881no—
517C2×C4—4884no—
518C2×C4—4881no—
519C2×C4—4881no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2442no—
525C2×C4—2442no—
526C2×C4—2442no—
527C2×C4—2442no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2442no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2442no—
547C2×C4C2×C4⋊#692311yescharacteristic
548C2×C4D4×#692311yescharacteristic
549C8—41no—
550C8—4881no—
551C8—2441no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—611no—
558C22—611no—
559C22—611no—
560C22—611no—
561C22—611no—
562C22—611no—
563C22—611no—
564C22—611no—
565C22—1221no—
566C22—1221no—
567C22—1221no—
568C22—1221no—
569C22—1221no—
570C22—1221no—
571C22—1221no—
572C22—1221no—
573C22—1221no—
574C22—1221no—
575C22—4881no—
576C22—4881no—
577C22—4881no—
578C22—4881no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22#1684070911yescharacteristic
583C22D8×#692311yescharacteristic
584C22#1684080111yescharacteristic
585C4—21no—
586C4—21no—
587C4—42no—
588C4—41no—
589C4—1221no—
590C4—1221no—
591C4—4882no—
592C4—4881no—
593C4—4881no—
594C4—4881no—
595C4—2442no—
596C4—2442no—
597C4—2441no—
598C2—21no—
599C2—21no—
600C2—81no—
601C2—611no—
602C2—611no—
603C2—611no—
604C2—611no—
605C2—1221no—
606C2—1221no—
607C2—4881no—
608C2#2146177811yescharacteristic
609C2#2146178211yescharacteristic
610C2#2146179011yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#327C4
socleC22×C61#385
prime radical#121×D61C22
cosocleC22×C4×D61C23
hypercenter#327#6923
hypocenterC61#8866
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
3. #21461768C2semidirect
4. #21461007C2semidirect
5. #21460693C2semidirect
6. #21460656C2semidirect
27. #16839497C4semidirect
28. #16839496C4semidirect
29. #16839495C4semidirect
30. C61×#327C4semidirect
74. C22⋊#92418C2×C4semidirect
77. #14519684C2×C4semidirect
79. C22⋊C8×C61C2×C4semidirect
80. #95×C61C2×C4semidirect
106. C2×D4×C61C4⋊C4semidirect
121. C2×D244C4⋊C4semidirect
153. C4⋊C4×C61C4⋊C4semidirect
158. C4⋊Dic61C4⋊C4semidirect
335. #327#6923semidirect
336. C61#8866semidirect
377. C22⋊C8C2×#6923semidirect
386. #95C2×#6923semidirect
401. C2×D4C4⋊#6923semidirect
458. C4⋊C4C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
#214623082
#214618062
#214617682
#214610072
#214606932
#214606562
#327×D612
#886661