Finite Group Databasebeta

← #30600682

Subgroups — #30600682

Order 15616.

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

normal subgroups only

This group has 524 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#21462328C211yesmaximal, characteristic
2#21462009C211yesmaximal, characteristic
3#21461723C211yesmaximal, characteristic
4#21461258C211yesmaximal, characteristic
5#21460682C211yesmaximal, characteristic
6#21460661C211yesmaximal, characteristic
7C2×#16840099C211yesmaximal, characteristic
8D61⋊(C22⋊C8)C2211yescharacteristic
9#16840713—21no—
10#16840711—22no—
11#16840704—21no—
12#16840704C2211yescharacteristic
13#16840704C2211yescharacteristic
14C4⋊C4×#6923—21no—
15C4×C22⋊#6923—21no—
16C4×C22⋊#6923C2211yescharacteristic
17#16840640—21no—
18#16840640—21no—
19#16840635—21no—
20#16840635—21no—
21#16840615—22no—
22C2×#14519757C2211yescharacteristic
23C2×C4⋊C4×D61C2211yescharacteristic
24#16840099—21no—
25#16840099—21no—
26#16840099—21no—
27#16840099—21no—
28C2×#14519710C411yescharacteristic, complemented
29C2×#14519702C411yescharacteristic, complemented
30C2×#14519700C411yescharacteristic, complemented
31C2×#14519689C2211yescharacteristic
32C2×#107×C61C411yescharacteristic, complemented
33C2×D61⋊C8—21no—
34C2×C4⋊#6923—21no—
35C2×C4⋊#6923—21no—
36C2×C4⋊#6923—22no—
37C2×C22⋊#6923—21no—
38C2×C22⋊#6923—21no—
39C2×C22⋊#6923D411yescharacteristic
40C2×C22⋊#6923D411yescharacteristic
41C2×C4×#6923—21no—
42C2×C4×#6923—22no—
43#14519834—21no—
44C22⋊#92420—21no—
45(C2×#6923)⋊C4—22no—
46(C2×#6923)⋊C4—22no—
47(C2×#6923)⋊C4—21no—
48(C2×#6923)⋊C4—21no—
49(C2×#6923)⋊C4D412yes—
50C22×Dic122C2×C411yescharacteristic
51C22×C4×D61—21no—
52C22×C4×D61C2311yescharacteristic
53C22×#92418C2×C411yescharacteristic
54#14519757—21no—
55#14519757—21no—
56#14519757—21no—
57#14519757—21no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61C2×C411yescharacteristic
60C2×#11758196—21no—
61C4⋊C4×D61—21no—
62C4⋊C4×D61—21no—
63C4⋊C4×D61D411yescharacteristic
64C4⋊C4×D61D411yescharacteristic
65C4⋊C4×D61D411yescharacteristic
66C4⋊C4×D61D411yescharacteristic
67C2×#11758198—21no—
68#14519710—21no—
69#14519710—21no—
70#14519702—21no—
71#14519702—21no—
72#14519700—21no—
73#14519700—21no—
74#14519689—21no—
75#14519689—21no—
76C22×C8×C61C2×C411yescharacteristic
77C2×C4⋊C4×C61C2×C411yescharacteristic
78C2×C4⋊C4×C61C2×C411yescharacteristic
79#107×C61—21no—
80#107×C61—21no—
81C23×D61C2×D411yescharacteristic
82C22×#6923—21no—
83C22×#6923—21no—
84C22×#6923—22no—
85C22×#6923—41no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61C22×C411yescharacteristic
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61#4111yescharacteristic
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—82no—
99C2×C4×D61C2×D411yescharacteristic
100C2×C4×D61C2×D411yescharacteristic
101C2×C4×D61C2×D411yescharacteristic
102C2×C4×D61#4111yescharacteristic
103C2×Dic122—21no—
104C2×Dic122—21no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107C22⋊#6923—21no—
108C22⋊#6923—21no—
109C22⋊#6923—21no—
110C22⋊#6923—41no—
111C22⋊#6923—41no—
112C22⋊#6923—41no—
113C22⋊#6923—41no—
114C22⋊#6923Q1612yes—
115C2×#92420—41no—
116C4⋊#6923—41no—
117C4⋊#6923—41no—
118C4⋊#6923—41no—
119C4⋊#6923—41no—
120C4⋊#6923—82no—
121C4×#6923—41no—
122C4×#6923—41no—
123C4×#6923—82no—
124D61⋊C8—41no—
125D61⋊C8—41no—
126C2×C8×C61—21no—
127C2×C8×C61—41no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61C22⋊C411yescharacteristic
132C4⋊C4×C61C22⋊C411yescharacteristic
133#11758198—41no—
134#11758198—41no—
135C4⋊Dic61—21no—
136C4⋊Dic61—41no—
137C4⋊Dic61—41no—
138C4⋊Dic61C22⋊C411yescharacteristic
139C4⋊Dic61C22⋊C411yescharacteristic
140#11758196—21no—
141#11758196—21no—
142#11758196—21no—
143#11758196—21no—
144C2×#92418—21no—
145C2×#92418—41no—
146C23×C61C4×D411yescharacteristic
147C22×D61—41no—
148C22×D61—41no—
149C22×D61#12011yescharacteristic
150C22×D61#12111yescharacteristic
151C22×D61C2×Q1611yescharacteristic
152C22×D61#13511yescharacteristic
153C22×D61#13711yescharacteristic
154C22×D61#13711yescharacteristic
155C2×#6923—22no—
156C2×#6923—41no—
157C2×#6923—41no—
158C2×#6923—41no—
159C2×#6923—42no—
160C2×#6923—42no—
161C2×#6923—41no—
162C2×#6923—41no—
163C2×#6923—42no—
164C2×#6923—81no—
165C2×#6923—81no—
166C2×#6923—81no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—41no—
172C2×C4×C61—81no—
173C2×C4×C61—81no—
174C2×C4×C61C2×C22⋊C411yescharacteristic
175C2×C4×C61C4×D411yescharacteristic
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—81no—
181C2×Dic61—81no—
182C2×Dic61#12111yescharacteristic
183C2×Dic61#12311yescharacteristic
184C4×D61—21no—
185C4×D61—21no—
186C4×D61—21no—
187C4×D61—21no—
188C4×D61—41no—
189C4×D61—41no—
190C4×D61—42no—
191C4×D61—42no—
192C4×D61—81no—
193C4×D61—81no—
194Dic122—41no—
195Dic122—41no—
196Dic122—81no—
197#92420—81no—
198C8×C61—41no—
199#92418—41no—
200#9257—611nomaximal, Sylow
201C22×C61—21no—
202C22×C61—21no—
203C22×C61#38611yescharacteristic
204C22×C61C4×Q1611yescharacteristic
205C22×C61#44111yescharacteristic
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—21no—
209C2×D61—21no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61—41no—
214C2×D61#45111yescharacteristic
215C2×D61#45211yescharacteristic
216C2×D61#46211yescharacteristic
217C2×D61#46411yescharacteristic
218#6923—42no—
219#6923—81no—
220#6923—82no—
221#6923—161no—
222C4×C61—21no—
223C4×C61—41no—
224C4×C61—41no—
225C4×C61—81no—
226C4×C61#41011yescharacteristic
227C4×C61#41011yescharacteristic
228Dic61—21no—
229Dic61—21no—
230Dic61—41no—
231Dic61—41no—
232Dic61—81no—
233C2×#484—611no—
234#2345—611no—
235#1996—611no—
236#1824—611no—
237#1520—611no—
238#1289—611no—
239#1282—611no—
240C2×C61—21no—
241C2×C61—21no—
242C2×C61#187811yescharacteristic
243C2×C61#189911yescharacteristic
244C2×C61#190411yescharacteristic
245D61—21no—
246D61—21no—
247D61—21no—
248D61—21no—
249C2×C22⋊Q8—611no—
250C22×C4⋊C4—611no—
251#484—1221no—
252#484—1221no—
253#484—1221no—
254#484—1221no—
255C2×#107—611no—
256C2×#107#692311yescharacteristic, complemented
257C2×#103—611no—
258C2×#103—611no—
259C2×C22⋊C8—611no—
260C2×C22⋊C8—611no—
261#389—1221no—
262#387—1222no—
263#380—611no—
264#380—611no—
265#380—1221no—
266C4×C4⋊C4—1221no—
267C4×C22⋊C4—611no—
268C4×C22⋊C4—1221no—
269#342—1221no—
270#342—1221no—
271#340—1221no—
272#340—1221no—
273#328—1222no—
274C61#925711yescharacteristic, complemented, Sylow
275C22×Q8—611no—
276C23×C4—611no—
277C23×C4—1221no—
278C22×C8—611no—
279C22×C8—1221no—
280C22×C8C2×#692311yescharacteristic
281C22⋊Q8—1221no—
282C22⋊Q8—1221no—
283C22⋊Q8—1221no—
284C22⋊Q8—1221no—
285C2×C4⋊C4—611no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—611no—
289C2×C4⋊C4—611no—
290C2×C4⋊C4—1221no—
291C2×C4⋊C4—1221no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1222no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—1221no—
297C2×C4⋊C4C2×#692311yescharacteristic
298C2×C4⋊C4C2×#692311yescharacteristic
299C2×C22⋊C4—611no—
300C2×C22⋊C4—611no—
301C2×C22⋊C4—1221no—
302C2×C22⋊C4—1221no—
303C2×C22⋊C4—1221no—
304C2×C42—1222no—
305C2×C42—1221no—
306#107—21no—
307#107—21no—
308#107—1221no—
309#107—1221no—
310#103—1221no—
311#103—1221no—
312#103—1221no—
313#103—1221no—
314C22⋊C8—1221no—
315C22⋊C8—1221no—
316C22⋊C8—1221no—
317C22⋊C8—1221no—
318#95—612no—
319#95—1221no—
320#95—1221no—
321#95—1222no—
322#95—1222no—
323C24—611no—
324C2×Q8—1221no—
325C2×Q8—1221no—
326C2×Q8—2441no—
327C2×Q8—2441no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—611no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—1221no—
336C22×C4—1221no—
337C22×C4—1221no—
338C22×C4—1221no—
339C22×C4—1221no—
340C22×C4—1221no—
341C22×C4—1221no—
342C22×C4—1222no—
343C22×C4—1221no—
344C22×C4—4882no—
345C22×C4—2441no—
346C22×C4—2441no—
347C22×C4—2441no—
348C22×C4C22×#692311yescharacteristic
349C2×C8—21no—
350C2×C8—41no—
351C2×C8—1221no—
352C2×C8—2441no—
353C2×C8—2441no—
354C2×C8—2441no—
355C2×C8—2441no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—611no—
360C4⋊C4—611no—
361C4⋊C4—1221no—
362C4⋊C4—1221no—
363C4⋊C4—1221no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—4882no—
367C4⋊C4—2441no—
368C4⋊C4—2441no—
369C4⋊C4—2441no—
370C4⋊C4—2441no—
371C4⋊C4—2441no—
372C4⋊C4—2441no—
373C4⋊C4C22⋊#692311yescharacteristic
374C4⋊C4C22⋊#692311yescharacteristic
375C22⋊C4—612no—
376C22⋊C4—1221no—
377C22⋊C4—1221no—
378C22⋊C4—1221no—
379C22⋊C4—2441no—
380C22⋊C4—2441no—
381C22⋊C4—2441no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C42—4882no—
386C42—2441no—
387C42—2441no—
388C23—611no—
389C23—611no—
390C23—611no—
391C23—611no—
392C23—611no—
393C23—611no—
394C23—2441no—
395C23—2441no—
396C23D4×#692311yescharacteristic
397Q8—4881no—
398Q8—2441no—
399Q8—2441no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—611no—
408C2×C4—611no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1222no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—4881no—
417C2×C4—4881no—
418C2×C4—4881no—
419C2×C4—4881no—
420C2×C4—4881no—
421C2×C4—4881no—
422C2×C4—4881no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2442no—
430C2×C4—2442no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2442no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4C2×C22⋊#692311yescharacteristic
438C2×C4D4×#692311yescharacteristic
439C8—41no—
440C8—4881no—
441C8—2441no—
442C22—21no—
443C22—21no—
444C22—611no—
445C22—611no—
446C22—611no—
447C22—611no—
448C22—1221no—
449C22—1221no—
450C22—1221no—
451C22—1221no—
452C22—2441no—
453C22—2441no—
454C22—2441no—
455C22—2441no—
456C22#1684071011yescharacteristic
457C22Q16×#692311yescharacteristic
458C22#1684080211yescharacteristic
459C4—21no—
460C4—41no—
461C4—41no—
462C4—81no—
463C4—1221no—
464C4—1221no—
465C4—9761no—
466C4—4881no—
467C4—4882no—
468C4—4881no—
469C4—2442no—
470C4—2441no—
471C4—2441no—
472C4#1684074111yescharacteristic
473C4#1684074311yescharacteristic
474C2—21no—
475C2—21no—
476C2—1221no—
477C2—1221no—
478C2—1221no—
479C2—1221no—
480C2#2146181311yescharacteristic
481C2#2146184311yescharacteristic
482C2#2146185311yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#107×C61C4
socleC22×C61#386
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenterC2×#107#6923
hypocenterC61#9257
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
28. C2×#14519710C4semidirect
29. C2×#14519702C4semidirect
30. C2×#14519700C4semidirect
32. C2×#107×C61C4semidirect
256. C2×#107#6923semidirect
274. C61#9257semidirect

Maximal subgroups

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

subgroupindex
#214623282
#214620092
#214617232
#214612582
#214606822
#214606612
C2×#168400992
#925761