Finite Group Databasebeta

← #30600693

Subgroups — #30600693

Order 15616.

478 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 78 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#21462692C211yesmaximal, characteristic
2#21461204C211yesmaximal, characteristic
3C2×#16840616C211yesmaximal, characteristic, complemented
4#21461099C211yesmaximal, characteristic, complemented
5#21460702C211yesmaximal, characteristic, complemented
6#21460656C211yesmaximal, characteristic, complemented
7#21456597C211yesmaximal, characteristic
8#16840794—21no—
9#16840793—21no—
10#16840789—21no—
11D4×#92420—21no—
12#16840787—21no—
13#16840735—21no—
14#16840733C2211yescharacteristic
15C2×#14519834C2211yescharacteristic
16D61⋊(C22⋊C8)C2211yescharacteristic
17C2×(C2×#6923)⋊C4C2211yescharacteristic
18#16840616—21no—
19#16840616—21no—
20#16840615—21no—
21#16840613—21no—
22#16840608—21no—
23#16840608—21no—
24#16840272C2211yescharacteristic
25C2×#14519753C2211yescharacteristic
26#16840101—21no—
27#16840093C411yescharacteristic, complemented
28#16840073C411yescharacteristic, complemented
29#16840002—21no—
30#16839988—21no—
31#16839921—21no—
32#16839918C411yescharacteristic, complemented
33C22⋊C8×D61C2211yescharacteristic
34C61×#448C411yescharacteristic, complemented
35C23×#6923—21no—
36C2×#11758213—21no—
37C2×#11758217—21no—
38C2×D61⋊C8—21no—
39C22×#92420—21no—
40C22×#92420—21no—
41#14519844—21no—
42C4⋊#92420—21no—
43#14519834—21no—
44#14519834—21no—
45#14519834—21no—
46#14519834D411yescharacteristic
47#14519834D411yescharacteristic
48C22⋊#92420—21no—
49C22⋊#92420—21no—
50C22⋊#92420—21no—
51C22⋊#92420D411yescharacteristic
52C22⋊#92420D411yescharacteristic
53#14519832—21no—
54C4×#92420—21no—
55(C2×#6923)⋊C4—21no—
56(C2×#6923)⋊C4—21no—
57C2×#11758224D411yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C2×#11758202—21no—
60C2×C8×D61—21no—
61#14519759—21no—
62#14519757D411yescharacteristic
63#14519756C2×C411yescharacteristic
64#14519753—21no—
65#14519753—21no—
66#14519753—21no—
67#14519753—21no—
68#14519748D411yescharacteristic
69#14519745—21no—
70D4×Dic61—21no—
71#14519737—21no—
72#14519735D411yescharacteristic
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×#11758196—21no—
75C2×#11758198—21no—
76#14519710—21no—
77#14519709—21no—
78#14519702—21no—
79#14519701—21no—
80#14519698—21no—
81C22⋊#92418C2×C411yescharacteristic
82#14519689—21no—
83C22×Q8×C61C2×C411yescharacteristic
84C2×SD16×C61—21no—
85#121×C61C2×C411yescharacteristic
86#103×C61—21no—
87C22⋊C8×C61C2×C411yescharacteristic
88C23×D61#4111yescharacteristic
89C22×#6923—22no—
90C22×#6923—41no—
91C22×#6923—41no—
92C22×#6923—81no—
93C22×#6923—81no—
94C2×Q8×C61—21no—
95C2×Q8×C61—21no—
96C2×Q8×C61—81no—
97C2×D4×C61—21no—
98C2×D4×C61C22⋊C411yescharacteristic
99C22×C4×C61—21no—
100C22×C4×C61C22×C411yescharacteristic
101C2×C22⋊D61—21no—
102C2×C22⋊D61—21no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61C2×D411yescharacteristic
106#11758224—81no—
107C2×C4×D61—81no—
108C2×C4×D61C2×D411yescharacteristic
109C2×C4×D61C2×D411yescharacteristic
110C2×C4×D61C2×D411yescharacteristic
111C2×C4×D61#4111yescharacteristic
112C2×Dic122C22⋊C411yescharacteristic
113#11758217—81no—
114C2×#92420—21no—
115C2×#92420—21no—
116C2×#92420—21no—
117C2×#92420—21no—
118C2×#92420—41no—
119C2×#92420—81no—
120C2×#92420—81no—
121#11758213—81no—
122D61⋊C8—81no—
123SD16×C61—81no—
124C2×C8×C61—21no—
125C4⋊C4×C61C22⋊C411yescharacteristic
126C22⋊C4×C61—21no—
127C22⋊Dic61—21no—
128C22⋊Dic61—21no—
129#11758202—81no—
130#11758198—21no—
131#11758198—21no—
132#11758198—41no—
133#11758198—41no—
134C4⋊Dic61—21no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137C4⋊Dic61C22⋊C411yescharacteristic
138#11758196—21no—
139#11758196—41no—
140#11758196—41no—
141C4×Dic61—21no—
142C2×#92418—21no—
143C8×D61—81no—
144C23×C61—21no—
145C23×C61C4×D411yescharacteristic
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—41no—
151C22×D61#12111yescharacteristic
152C22×D61#12311yescharacteristic
153C2×#6923—42no—
154C2×#6923—81no—
155C2×#6923—82no—
156C2×#6923—81no—
157C2×#6923—82no—
158Q8×C61—41no—
159Q8×C61—41no—
160Q8×C61—81no—
161D4×C61—41no—
162D4×C61—41no—
163D4×C61—41no—
164C2×C4×C61—21no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—81no—
168C2×C4×C61C2×C22⋊C411yescharacteristic
169C2×C4×C61C4×D411yescharacteristic
170C22⋊D61—41no—
171C22⋊D61—41no—
172C22⋊D61—81no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61#12011yescharacteristic
182C2×Dic61#12111yescharacteristic
183C4×D61—41no—
184C4×D61—41no—
185C4×D61—41no—
186C4×D61—41no—
187Dic122—41no—
188#92420—41no—
189#92420—41no—
190#92420—41no—
191#92420—41no—
192#92420—81no—
193C8×C61—41no—
194#92418—41no—
195#9263—611nomaximal, Sylow
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61#38611yescharacteristic
202C22×C61#44311yescharacteristic
203C22×C61#44411yescharacteristic
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—21no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61#47111yescharacteristic
214C2×D61#47311yescharacteristic
215#6923—82no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—41no—
219C4×C61—81no—
220Dic61—21no—
221Dic61—21no—
222Dic61—41no—
223Dic61—41no—
224Dic61—81no—
225#3190—611no—
226#2977—611no—
227#1504—611no—
228C2×#328—611no—
229#1472—611no—
230#1298—611no—
231#1280—611no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—81no—
235C2×C61#187611yescharacteristic
236C2×C61#190811yescharacteristic
237C2×C61#191311yescharacteristic
238D61—21no—
239D61—21no—
240D61—41no—
241#525—611no—
242C2×C22⋊Q8—611no—
243#485—1221no—
244#483—611no—
245#480—611no—
246#467—1221no—
247#465—1221no—
248#452—1221no—
249#451—611no—
250#448#692311yescharacteristic, complemented
251#435—1221no—
252#435—1221no—
253C8×D4—1221no—
254C8×D4—1221no—
255#433—1221no—
256#408—1221no—
257#407—611no—
258C2×C22⋊C8—611no—
259C2×C22⋊C8—611no—
260C2×C22⋊C8—611no—
261C2×#95—611no—
262#328—1221no—
263#328—1221no—
264#328—1221no—
265#327—1221no—
266#324—1221no—
267#324—1221no—
268C61#926311yescharacteristic, complemented, Sylow
269C2×#41—611no—
270C22×Q8C2×#692311yescharacteristic
271C23×C4—611no—
272C23×C4—1221no—
273C2×Q16—1221no—
274C2×SD16—21no—
275C2×M16—1221no—
276C2×M16—1221no—
277C22×C8—1221no—
278C22×C8—1221no—
279C22×C8—1221no—
280C22×C8—1221no—
281#123—1221no—
282C22⋊Q8—611no—
283C22⋊Q8—611no—
284C22⋊Q8—1221no—
285C22⋊Q8—1221no—
286C22⋊Q8—1221no—
287C22⋊Q8—1221no—
288#121—611no—
289#121C2×#692311yescharacteristic
290#120—1221no—
291C4×D4—1221no—
292C4×D4—1221no—
293#117—611no—
294C2×C4⋊C4—611no—
295C2×C4⋊C4—1221no—
296C2×C22⋊C4—1221no—
297#107—1221no—
298#106—1221no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301#103—21no—
302#103—1221no—
303#103—1221no—
304#102—1221no—
305C22⋊C8—611no—
306C22⋊C8—611no—
307C22⋊C8—611no—
308C22⋊C8—611no—
309C22⋊C8—611no—
310C22⋊C8—1221no—
311C22⋊C8—1221no—
312C22⋊C8—1221no—
313C22⋊C8—1221no—
314C22⋊C8—1221no—
315C22⋊C8—1221no—
316C22⋊C8—1221no—
317C22⋊C8C2×#692311yescharacteristic
318#97—1221no—
319C4×C8—1221no—
320#95—1221no—
321#95—1221no—
322C24—611no—
323#41—4881no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—81no—
327C2×Q8—611no—
328C2×D4—21no—
329C2×D4—1221no—
330C2×D4—1221no—
331C2×D4C22⋊#692311yescharacteristic
332C22×C4—21no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—611no—
336C22×C4—611no—
337C22×C4—611no—
338C22×C4—1221no—
339C22×C4—1222no—
340C22×C4—1221no—
341C22×C4—4881no—
342C22×C4—4881no—
343C22×C4—4881no—
344C22×C4—2441no—
345C22×C4—2441no—
346C22×C4C22×#692311yescharacteristic
347Q16—4881no—
348SD16—81no—
349M16—4881no—
350M16—4881no—
351C2×C8—21no—
352C2×C8—1221no—
353C2×C8—1221no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8—1221no—
357C2×C8—4881no—
358C2×C8—4881no—
359C2×C8—4881no—
360C2×C8—4881no—
361C2×C8—2441no—
362C4⋊C4—611no—
363C4⋊C4—1221no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—2441no—
368C4⋊C4—2441no—
369C4⋊C4C22⋊#692311yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—1221no—
372C22⋊C4—1221no—
373C22⋊C4—1221no—
374C22⋊C4—1221no—
375C22⋊C4—2441no—
376C22⋊C4—2441no—
377C42—1221no—
378C23—21no—
379C23—611no—
380C23—611no—
381C23—1221no—
382C23—1221no—
383C23—1221no—
384C23—1221no—
385C23—2441no—
386C23D4×#692311yescharacteristic
387Q8—41no—
388Q8—41no—
389Q8—81no—
390Q8—2441no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—4881no—
395D4—2441no—
396D4—2441no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—611no—
402C2×C4—611no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—4881no—
406C2×C4—4881no—
407C2×C4—4882no—
408C2×C4—4882no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2442no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4C2×C22⋊#692311yescharacteristic
421C2×C4D4×#692311yescharacteristic
422C8—41no—
423C8—4881no—
424C8—2441no—
425C8—2441no—
426C8—2441no—
427C8—2441no—
428C8—2441no—
429C22—21no—
430C22—21no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—611no—
435C22—611no—
436C22—1221no—
437C22—1221no—
438C22—1221no—
439C22—1221no—
440C22—1221no—
441C22—2441no—
442C22—2441no—
443C22—2441no—
444C22—2441no—
445C22#1684071011yescharacteristic
446C22#1684080511yescharacteristic
447C22#1684080711yescharacteristic
448C4—21no—
449C4—21no—
450C4—41no—
451C4—81no—
452C4—1221no—
453C4—1221no—
454C4—4882no—
455C4—4881no—
456C4—2441no—
457C4—2441no—
458C2—21no—
459C2—21no—
460C2—81no—
461C2—1221no—
462C2—1221no—
463C2—2441no—
464C2#2146180811yescharacteristic
465C2#2146185911yescharacteristic
466C2#2146186811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#448C4
socleC22×C61#386
prime radical#16840272C22
cosocleC22×C4×D61C23
hypercenter#448#6923
hypocenterC61#9263
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
3. C2×#16840616C2semidirect
4. #21461099C2semidirect
5. #21460702C2semidirect
6. #21460656C2semidirect
27. #16840093C4semidirect
28. #16840073C4semidirect
32. #16839918C4semidirect
34. C61×#448C4semidirect
250. #448#6923semidirect
268. C61#9263semidirect

Maximal subgroups

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

subgroupindex
#214626922
#214612042
C2×#168406162
#214610992
#214607022
#214606562
#214565972
#926361