Finite Group Databasebeta

← #30596980

Subgroups — #30596980

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C211yesmaximal, characteristic
2C2×#16840733C211yesmaximal, characteristic
3#21460702C214yesmaximal, complemented
4C2×C22⋊C8×D61C211yesmaximal, characteristic
5C22×#11758213—21no—
6C22×#11758213C412yes—
7#16840733—21no—
8#16840733—21no—
9#16840733—21no—
10#16840733—21no—
11#16840733C412yes—
12#16840733C412yes—
13#16840733C412yes—
14#16840733C2212yes—
15C2×#14519834—21no—
16C2×#14519834C2212yes—
17C2×C22⋊#92420—21no—
18C2×C22⋊#92420—21no—
19C23×C4×D61C2211yescharacteristic
20C22×C8×D61—21no—
21C2×C22⋊#92418C411yescharacteristic
22C2×#14519689—21no—
23C22⋊C8×D61—21no—
24C22⋊C8×D61—21no—
25C22⋊C8×D61C412yes—
26C22⋊C8×D61C2212yes—
27C2×C22⋊C8×C61C411yescharacteristic
28C2×#11758213—22no—
29C2×#11758213—22no—
30C2×#11758213—22no—
31C2×#11758213—44no—
32C2×#11758213—44no—
33C2×#11758213C2×C414yes—
34C22×#92420—22no—
35C22×#92420—22no—
36#14519834—22no—
37#14519834—22no—
38#14519834—22no—
39#14519834C2×C414yes—
40C22⋊#92420—22no—
41C22⋊#92420—22no—
42C22⋊#92420—22no—
43C22⋊#92420—22no—
44C24×D61Q811yescharacteristic
45C23×Dic61D411yescharacteristic
46C22×C4×D61—44no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C22×#92418—21no—
60C2×C8×D61—22no—
61C2×C8×D61—22no—
62C2×C8×D61—44no—
63C22⋊#92418—21no—
64C22⋊#92418C2×C412yes—
65#14519689—22no—
66#14519689—22no—
67C23×C4×C61C2×C411yescharacteristic
68C22×C8×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61C2×C412yes—
71C24×C61C4⋊C411yescharacteristic
72C23×D61—22no—
73C23×D61—22no—
74C23×D61—42no—
75C23×D61—42no—
76C23×D61C4⋊C411yescharacteristic
77C23×D61C4⋊C411yescharacteristic
78C23×D61C4⋊C411yescharacteristic
79C23×D61C4⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C2×Q811yescharacteristic
82C22×C4×C61—42no—
83C22×C4×C61C4211yescharacteristic
84C22×C4×C61C4211yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C4⋊C411yescharacteristic
88C22×C4×C61C22×C411yescharacteristic
89C22×Dic61—42no—
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C4⋊C411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C2×C4×D61—24no—
97C2×C4×D61—24no—
98C2×C4×D61—24no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×C4×D61—42no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
104C2×C4×D61—42no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—42no—
108C2×C4×D61C4211yescharacteristic
109C2×C4×D61C4211yescharacteristic
110C2×C4×D61C22⋊C411yescharacteristic
111C2×C4×D61C22⋊C411yescharacteristic
112C2×C4×D61C22⋊C411yescharacteristic
113C2×C4×D61C22⋊C411yescharacteristic
114C2×C4×D61C22⋊C411yescharacteristic
115C2×C4×D61C22⋊C411yescharacteristic
116C2×C4×D61C4⋊C411yescharacteristic
117C2×C4×D61C4⋊C411yescharacteristic
118C2×C4×D61C4⋊C411yescharacteristic
119C2×C4×D61C4⋊C411yescharacteristic
120C2×C4×D61C22×C411yescharacteristic
121C2×C4×D61C22×C411yescharacteristic
122C2×C4×D61C2×D411yescharacteristic
123C2×C4×D61C2×D411yescharacteristic
124C2×#92420—24no—
125C2×#92420—24no—
126C2×#92420—44no—
127C2×#92420—44no—
128#11758213—44no—
129#11758213—44no—
130#11758213—44no—
131#11758213—44no—
132C2×C8×C61—22no—
133C2×C8×C61—42no—
134C2×#92418—22no—
135C2×#92418—42no—
136C8×D61—44no—
137C8×D61—44no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61#9511yescharacteristic
141C23×C61#9511yescharacteristic
142C23×C61#10812yes—
143C23×C61#10812yes—
144C23×C61C2×C4⋊C411yescharacteristic
145C22×D61—22no—
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—48no—
166C22×D61—48no—
167C22×D61#9511yescharacteristic
168C22×D61#9511yescharacteristic
169C22×D61C2×C4⋊C411yescharacteristic
170C22×D61C2×C4⋊C411yescharacteristic
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61#9511yescharacteristic
178C2×C4×C61#9511yescharacteristic
179C2×C4×C61C2×C4211yescharacteristic
180C2×C4×C61C2×C22⋊C411yescharacteristic
181C2×Dic61—22no—
182C2×Dic61—22no—
183C2×Dic61—22no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61#9511yescharacteristic
188C2×Dic61#9511yescharacteristic
189C2×Dic61C2×C22⋊C411yescharacteristic
190C2×Dic61C2×C22⋊C411yescharacteristic
191C4×D61—22no—
192C4×D61—22no—
193C4×D61—22no—
194C4×D61—22no—
195C4×D61—22no—
196C4×D61—22no—
197C4×D61—22no—
198C4×D61—22no—
199C4×D61—22no—
200C4×D61—41no—
201C4×D61—41no—
202C4×D61—41no—
203C4×D61—41no—
204C4×D61—41no—
205C4×D61—41no—
206C4×D61#9914yes—
207#92420—44no—
208#92420—44no—
209C8×C61—42no—
210#92418—42no—
211#8057—611nomaximal, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—42no—
219C22×C61—42no—
220C22×C61#34112yes—
221C22×C61#34112yes—
222C22×C61C2×#9511yescharacteristic
223C22×C61C2×#10811yescharacteristic
224C22×C61C2×#10811yescharacteristic
225C2×D61—28no—
226C2×D61—21no—
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—21no—
230C2×D61—21no—
231C2×D61—21no—
232C2×D61—21no—
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—44no—
237C2×D61—42no—
238C2×D61—42no—
239C2×D61—44no—
240C2×D61—42no—
241C2×D61—42no—
242C2×D61—44no—
243C2×D61#34212yes—
244C2×D61#43012yes—
245C4×C61—21no—
246C4×C61—21no—
247C4×C61—21no—
248C4×C61#34212yes—
249Dic61—21no—
250Dic61—21no—
251Dic61—21no—
252Dic61C2×#9912yes—
253C2×#407—611no—
254C2×#407—611no—
255C22×C22⋊C8—611no—
256#1298—614no—
257C2×C61—22no—
258C2×C61—22no—
259C2×C61—21no—
260C2×C61—21no—
261C2×C61C2×#34111yescharacteristic
262C2×C61#173811yescharacteristic
263C2×C61C2×#34211yescharacteristic
264D61—22no—
265D61—22no—
266D61—41no—
267D61—41no—
268C24×C4—611no—
269C22×M16—612no—
270C22×M16—1221no—
271C23×C8—1221no—
272#407—612no—
273#407—612no—
274#407—612no—
275#407—612no—
276#407—1221no—
277#407—1221no—
278#407—1221no—
279#407—1221no—
280C2×C22⋊C8—612no—
281C2×C22⋊C8—611no—
282C2×C22⋊C8—612no—
283C2×C22⋊C8—612no—
284C2×C22⋊C8—1221no—
285C2×C22⋊C8—1221no—
286C2×C22⋊C8—1221no—
287C2×C22⋊C8—1221no—
288C2×C22⋊C8—1221no—
289C2×C22⋊C8—1221no—
290C2×C22⋊C8#692311yescharacteristic
291C61#805711yescharacteristic, complemented, Sylow
292C25—611no—
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—611no—
296C23×C4—611no—
297C23×C4—611no—
298C23×C4—611no—
299C23×C4—611no—
300C23×C4—611no—
301C23×C4—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—611no—
306C23×C4—2444no—
307C23×C4C2×#692311yescharacteristic
308C2×M16—614no—
309C2×M16—1222no—
310C2×M16—1222no—
311C2×M16—1222no—
312C2×M16—2444no—
313C2×M16—2444no—
314C22×C8—21no—
315C22×C8—1222no—
316C22×C8—1222no—
317C22×C8—1222no—
318C22×C8—1222no—
319C22×C8—1221no—
320C22×C8—2444no—
321C22⋊C8—21no—
322C22⋊C8—614no—
323C22⋊C8—612no—
324C22⋊C8—1222no—
325C22⋊C8—1222no—
326C22⋊C8—1222no—
327C22⋊C8—1222no—
328C22⋊C8—1222no—
329C22⋊C8—1222no—
330C22⋊C8—1222no—
331C22⋊C8—1222no—
332C22⋊C8—1222no—
333C22⋊C8—1221no—
334C22⋊C8C2×#692312yes—
335C24—611no—
336C24—611no—
337C24—611no—
338C24—611no—
339C24—611no—
340C24—611no—
341C24—1222no—
342C24—1222no—
343C24—2442no—
344C24—2442no—
345C24C4⋊#692311yescharacteristic
346C22×C4—42no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—611no—
369C22×C4—1224no—
370C22×C4—1224no—
371C22×C4—1224no—
372C22×C4—2442no—
373C22×C4—2442no—
374C22×C4—2442no—
375C22×C4—2442no—
376C22×C4—2442no—
377C22×C4—2442no—
378C22×C4—2442no—
379C22×C4—2442no—
380C22×C4—2442no—
381C22×C4—2442no—
382C22×C4C4×#692311yescharacteristic
383C22×C4C4×#692311yescharacteristic
384C22×C4C4⋊#692311yescharacteristic
385C22×C4C22⋊#692311yescharacteristic
386C22×C4C22⋊#692311yescharacteristic
387C22×C4C22×#692311yescharacteristic
388M16—2444no—
389M16—2444no—
390M16—2444no—
391M16—2444no—
392C2×C8—22no—
393C2×C8—42no—
394C2×C8—1224no—
395C2×C8—1224no—
396C2×C8—1222no—
397C2×C8—2444no—
398C2×C8—2444no—
399C2×C8—2442no—
400C2×C8—2444no—
401C2×C8—2444no—
402C23—41no—
403C23—41no—
404C23—611no—
405C23—611no—
406C23—611no—
407C23—611no—
408C23—1222no—
409C23—1222no—
410C23—1222no—
411C23—1222no—
412C23—1222no—
413C23—1222no—
414C23—1222no—
415C23—1221no—
416C23—1221no—
417C23—1221no—
418C23—1221no—
419C23—1222no—
420C23—1222no—
421C23—1222no—
422C23—2441no—
423C23—2441no—
424C23—2441no—
425C23—2441no—
426C23—2441no—
427C23—2441no—
428C23—2448no—
429C23—2448no—
430C23(C2×#6923)⋊C411yescharacteristic
431C23(C2×#6923)⋊C411yescharacteristic
432C23#1451984712yes—
433C23#1451984812yes—
434C23C2×C4⋊#692311yescharacteristic
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—611no—
442C2×C4—614no—
443C2×C4—611no—
444C2×C4—611no—
445C2×C4—611no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—1222no—
450C2×C4—1222no—
451C2×C4—1222no—
452C2×C4—1222no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—1222no—
457C2×C4—1222no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4(C2×#6923)⋊C411yescharacteristic
468C2×C4(C2×#6923)⋊C411yescharacteristic
469C2×C4C2×C4×#692311yescharacteristic
470C2×C4C2×C22⋊#692311yescharacteristic
471C8—42no—
472C8—2442no—
473C8—2444no—
474C8—2444no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—42no—
482C22—42no—
483C22—612no—
484C22—612no—
485C22—1228no—
486C22—1221no—
487C22—1221no—
488C22—1221no—
489C22—1221no—
490C22—1221no—
491C22—1221no—
492C22—1221no—
493C22—1221no—
494C22—1221no—
495C22—1221no—
496C22—2442no—
497C22—2442no—
498C22—2442no—
499C22—2442no—
500C22—2444no—
501C22—2444no—
502C22—2444no—
503C22#1684063812yes—
504C22#1684063812yes—
505C22C2×(C2×#6923)⋊C411yescharacteristic
506C22C2×#1451984711yescharacteristic
507C22C2×#1451984811yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—612no—
512C4—1221no—
513C4—1221no—
514C4—1221no—
515C4#1684063912yes—
516C2—22no—
517C2—21no—
518C2—21no—
519C2—22no—
520C2—1222no—
521C2—1222no—
522C2—2441no—
523C2—2441no—
524C2C2×#1684063811yescharacteristic
525C2#2146151211yescharacteristic
526C2C2×#1684063911yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61C2×#95
prime radicalC24×D61Q8
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#8057
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #21460702C2semidirect
291. C61#8057semidirect

Maximal subgroups

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

subgroupindex
C2×#168407332
#214607022
C2×C22⋊C8×D612
#805761