Finite Group Databasebeta

← #30600688

Subgroups — #30600688

Order 15616.

594 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 90 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#21462327C211yesmaximal, characteristic, complemented
2#21461958C211yesmaximal, characteristic
3#21461722C211yesmaximal, characteristic, complemented
4#21461255C211yesmaximal, characteristic
5#21460682C211yesmaximal, characteristic, complemented
6#21460661C211yesmaximal, characteristic, complemented
7C2×#16840074C211yesmaximal, characteristic
8C2×#14519856—21no—
9C2×#14519835—21no—
10C2×#14519835—21no—
11D61⋊(C22⋊C8)C2211yescharacteristic
12#16840713—21no—
13#16840711—22no—
14#16840705—21no—
15#16840704C2211yescharacteristic
16#16840704C2211yescharacteristic
17C4⋊C4×#6923—21no—
18C4×C22⋊#6923C2211yescharacteristic
19#16840635—21no—
20#16840635—21no—
21#16840613—22no—
22C2×#14519748C2211yescharacteristic
23C2×C4⋊C4×D61C2211yescharacteristic
24#16840074—21no—
25#16840074—21no—
26#16840074—21no—
27#16840074—21no—
28C2×#14519711C411yescharacteristic, complemented
29C2×#14519710C411yescharacteristic, complemented
30C2×#14519698C411yescharacteristic, complemented
31C2×#14519689C2211yescharacteristic
32C2×#102×C61C411yescharacteristic, complemented
33C2×D61⋊C8—21no—
34#14519856—42no—
35#14519856—42no—
36C2×C4⋊#6923—22no—
37C2×C4⋊#6923—21no—
38C2×C4⋊#6923—21no—
39C2×C22⋊#6923—21no—
40C2×C22⋊#6923—21no—
41C2×C22⋊#6923D411yescharacteristic
42C2×C22⋊#6923D411yescharacteristic
43C2×C4×#6923—22no—
44C2×C4×#6923—21no—
45#14519835—42no—
46#14519835—42no—
47#14519834—21no—
48C22⋊#92420—21no—
49(C2×#6923)⋊C4—22no—
50(C2×#6923)⋊C4—22no—
51(C2×#6923)⋊C4—21no—
52(C2×#6923)⋊C4—21no—
53(C2×#6923)⋊C4D412yes—
54C22×C22⋊D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61C2311yescharacteristic
57C22×#92418C2×C411yescharacteristic
58#14519748—21no—
59#14519748—21no—
60#14519748—21no—
61#14519748—21no—
62C2×C4⋊Dic61C2×C411yescharacteristic
63C2×C4⋊Dic61C2×C411yescharacteristic
64C2×#11758196—21no—
65C4⋊C4×D61—21no—
66C4⋊C4×D61—21no—
67C4⋊C4×D61D411yescharacteristic
68C4⋊C4×D61D411yescharacteristic
69C4⋊C4×D61D411yescharacteristic
70C4⋊C4×D61D411yescharacteristic
71C2×C22⋊Dic61—21no—
72#14519711—21no—
73#14519711—21no—
74#14519710—21no—
75#14519710—21no—
76#14519698—21no—
77#14519698—21no—
78#14519689—21no—
79#14519689—21no—
80C22×D4×C61C2×C411yescharacteristic
81C22×C8×C61C2×C411yescharacteristic
82C2×C4⋊C4×C61C2×C411yescharacteristic
83#102×C61—21no—
84#102×C61—21no—
85C24×C61—21no—
86C23×D61C2×D411yescharacteristic
87C22×#6923—21no—
88C22×#6923—21no—
89C22×#6923—22no—
90C22×#6923—41no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C22×C4×C61—21no—
96C22×C4×C61C22×C411yescharacteristic
97C2×C22⋊D61—41no—
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61#4111yescharacteristic
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
116C2×C4×D61C2×D411yescharacteristic
117C2×C4×D61C2×D411yescharacteristic
118C2×C4×D61C2×D411yescharacteristic
119C2×C4×D61#4111yescharacteristic
120C22⋊#6923—21no—
121C22⋊#6923—21no—
122C22⋊#6923—21no—
123C22⋊#6923—41no—
124C22⋊#6923—41no—
125C22⋊#6923—41no—
126C22⋊#6923—41no—
127C22⋊#6923D812yes—
128C2×#92420—41no—
129C4⋊#6923—41no—
130C4⋊#6923—41no—
131C4⋊#6923—41no—
132C4⋊#6923—41no—
133C4⋊#6923—44no—
134C4×#6923—41no—
135C4×#6923—41no—
136C4×#6923—44no—
137D61⋊C8—41no—
138D61⋊C8—41no—
139C2×C8×C61—21no—
140C2×C8×C61—41no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61C22⋊C411yescharacteristic
143C4⋊C4×C61C22⋊C411yescharacteristic
144C22⋊Dic61—41no—
145C22⋊Dic61—41no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61C22⋊C411yescharacteristic
150C4⋊Dic61C22⋊C411yescharacteristic
151#11758196—21no—
152#11758196—21no—
153#11758196—21no—
154#11758196—21no—
155C2×#92418—21no—
156C2×#92418—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—81no—
161C23×C61—81no—
162C23×C61C4×D411yescharacteristic
163C22×D61—41no—
164C22×D61—41no—
165C22×D61#12011yescharacteristic
166C22×D61#12111yescharacteristic
167C22×D61C2×D811yescharacteristic
168C22×D61#13511yescharacteristic
169C22×D61AGL(1,ℤ/8)11yescharacteristic
170C22×D61AGL(1,ℤ/8)11yescharacteristic
171C2×#6923—22no—
172C2×#6923—41no—
173C2×#6923—41no—
174C2×#6923—41no—
175C2×#6923—42no—
176C2×#6923—41no—
177C2×#6923—42no—
178C2×#6923—42no—
179C2×#6923—41no—
180C2×#6923—81no—
181C2×#6923—81no—
182C2×#6923—81no—
183D4×C61—41no—
184D4×C61—41no—
185D4×C61—81no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61C2×C22⋊C411yescharacteristic
193C2×C4×C61C4×D411yescharacteristic
194C22⋊D61—81no—
195C22⋊D61—81no—
196C22⋊D61—81no—
197C22⋊D61—81no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61#12111yescharacteristic
207C2×Dic61#12311yescharacteristic
208C4×D61—21no—
209C4×D61—21no—
210C4×D61—21no—
211C4×D61—21no—
212C4×D61—41no—
213C4×D61—41no—
214C4×D61—41no—
215C4×D61—41no—
216C4×D61—41no—
217C4×D61—41no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61—41no—
222#92420—81no—
223C8×C61—41no—
224#92418—41no—
225#9260—611nomaximal, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—81no—
229C22×C61—81no—
230C22×C61—81no—
231C22×C61—161no—
232C22×C61—161no—
233C22×C61#38611yescharacteristic
234C22×C61C4×D811yescharacteristic
235C22×C61#44211yescharacteristic
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61#44711yescharacteristic
245C2×D61#44911yescharacteristic
246C2×D61#45911yescharacteristic
247C2×D61#46311yescharacteristic
248#6923—42no—
249#6923—82no—
250#6923—81no—
251#6923—161no—
252C4×C61—21no—
253C4×C61—41no—
254C4×C61—41no—
255C4×C61#41011yescharacteristic
256C4×C61#41011yescharacteristic
257Dic61—21no—
258Dic61—21no—
259Dic61—41no—
260Dic61—41no—
261Dic61—81no—
262C2×#480—611no—
263#2344—611no—
264#1964—611no—
265#1823—611no—
266#1519—611no—
267#1289—611no—
268#1282—611no—
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—161no—
272C2×C61#187911yescharacteristic
273C2×C61#189911yescharacteristic
274C2×C61#190511yescharacteristic
275D61—21no—
276D61—21no—
277D61—21no—
278D61—21no—
279C2×#121—611no—
280C2×#117—1221no—
281C22×C4⋊C4—611no—
282#480—1221no—
283#480—1221no—
284#480—1221no—
285#480—1221no—
286C2×#107—611no—
287C2×#107—611no—
288C2×#102—611no—
289C2×#102#692311yescharacteristic, complemented
290C2×#99—1221no—
291C2×#99—1221no—
292C2×C22⋊C8—611no—
293C2×C22⋊C8—611no—
294#389—1221no—
295#387—1222no—
296#381—1221no—
297#380—611no—
298#380—611no—
299C4×C4⋊C4—1221no—
300C4×C22⋊C4—611no—
301#340—1221no—
302#340—1221no—
303#327—1222no—
304C61#926011yescharacteristic, complemented, Sylow
305C22×D4—1221no—
306C22×D4C2×#692311yescharacteristic
307C23×C4—611no—
308C23×C4—1221no—
309C22×C8—611no—
310C22×C8—1221no—
311C22×C8C2×#692311yescharacteristic
312#121—1221no—
313#121—1221no—
314#121—1221no—
315#121—1221no—
316#117—2442no—
317#117—2442no—
318C2×C4⋊C4—611no—
319C2×C4⋊C4—611no—
320C2×C4⋊C4—611no—
321C2×C4⋊C4—611no—
322C2×C4⋊C4—611no—
323C2×C4⋊C4—611no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4—1221no—
326C2×C4⋊C4—1221no—
327C2×C4⋊C4—1221no—
328C2×C4⋊C4—1221no—
329C2×C4⋊C4—1222no—
330C2×C4⋊C4C2×#692311yescharacteristic
331C2×C22⋊C4—611no—
332C2×C22⋊C4—611no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4—1221no—
335C2×C22⋊C4—1221no—
336C2×C42—1221no—
337C2×C42—1222no—
338#107—1221no—
339#107—1221no—
340#107—1221no—
341#107—1221no—
342#102—21no—
343#102—21no—
344#102—1221no—
345#102—1221no—
346#99—2442no—
347#99—2442no—
348C22⋊C8—1221no—
349C22⋊C8—1221no—
350C22⋊C8—1221no—
351C22⋊C8—1221no—
352#95—612no—
353#95—1221no—
354#95—1221no—
355#95—1222no—
356#95—1222no—
357C24—21no—
358C24—611no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—2441no—
364C2×D4—2441no—
365C2×D4—2441no—
366C2×D4—2441no—
367C2×D4—2441no—
368C2×D4—2441no—
369C22×C4—21no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—1221no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—1222no—
382C22×C4—1221no—
383C22×C4—1221no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4C22×#692311yescharacteristic
392C2×C8—21no—
393C2×C8—41no—
394C2×C8—1221no—
395C2×C8—2441no—
396C2×C8—2441no—
397C2×C8—2441no—
398C2×C8—2441no—
399C4⋊C4—21no—
400C4⋊C4—611no—
401C4⋊C4—611no—
402C4⋊C4—1221no—
403C4⋊C4—1221no—
404C4⋊C4—1221no—
405C4⋊C4—1221no—
406C4⋊C4—1221no—
407C4⋊C4—1221no—
408C4⋊C4—1221no—
409C4⋊C4—2441no—
410C4⋊C4—2441no—
411C4⋊C4—2444no—
412C4⋊C4—2441no—
413C4⋊C4—2441no—
414C4⋊C4C22⋊#692311yescharacteristic
415C4⋊C4C22⋊#692311yescharacteristic
416C22⋊C4—612no—
417C22⋊C4—1221no—
418C22⋊C4—1221no—
419C22⋊C4—1221no—
420C22⋊C4—2441no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C22⋊C4—2441no—
424C22⋊C4—2441no—
425C22⋊C4—2441no—
426C42—2444no—
427C42—2441no—
428C42—2441no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—81no—
433C23—81no—
434C23—611no—
435C23—611no—
436C23—611no—
437C23—611no—
438C23—611no—
439C23—611no—
440C23—2441no—
441C23—2441no—
442C23D4×#692311yescharacteristic
443D4—41no—
444D4—41no—
445D4—81no—
446D4—4881no—
447D4—4881no—
448D4—4881no—
449D4—4881no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—611no—
457C2×C4—611no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—1221no—
461C2×C4—1221no—
462C2×C4—1222no—
463C2×C4—1221no—
464C2×C4—1221no—
465C2×C4—4881no—
466C2×C4—4881no—
467C2×C4—4881no—
468C2×C4—2441no—
469C2×C4—2441no—
470C2×C4—2441no—
471C2×C4—2441no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2442no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4C2×C22⋊#692311yescharacteristic
493C2×C4D4×#692311yescharacteristic
494C8—41no—
495C8—4881no—
496C8—2441no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—161no—
503C22—161no—
504C22—611no—
505C22—611no—
506C22—611no—
507C22—611no—
508C22—1221no—
509C22—1221no—
510C22—1221no—
511C22—1221no—
512C22—2441no—
513C22—2441no—
514C22—2441no—
515C22—2441no—
516C22#1684071011yescharacteristic
517C22D8×#692311yescharacteristic
518C22#1684080311yescharacteristic
519C4—21no—
520C4—41no—
521C4—41no—
522C4—1221no—
523C4—1221no—
524C4—9761no—
525C4—4882no—
526C4—4881no—
527C4—4881no—
528C4—2442no—
529C4—2441no—
530C4—2441no—
531C4#1684074111yescharacteristic
532C4#1684074211yescharacteristic
533C2—21no—
534C2—21no—
535C2—161no—
536C2—1221no—
537C2—1221no—
538C2—1221no—
539C2—1221no—
540C2#2146181411yescharacteristic
541C2#2146184211yescharacteristic
542C2#2146185511yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#102×C61C4
socleC22×C61#386
prime radicalC2×#14519748C22
cosocleC22×C4×D61C23
hypercenterC2×#102#6923
hypocenterC61#9260
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #21462327C2semidirect
3. #21461722C2semidirect
5. #21460682C2semidirect
6. #21460661C2semidirect
28. C2×#14519711C4semidirect
29. C2×#14519710C4semidirect
30. C2×#14519698C4semidirect
32. C2×#102×C61C4semidirect
289. C2×#102#6923semidirect
304. C61#9260semidirect

Maximal subgroups

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

subgroupindex
#214623272
#214619582
#214617222
#214612552
#214606822
#214606612
C2×#168400742
#926061