Finite Group Databasebeta

← #29576485

Subgroups — #29576485

Order 15616.

478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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#21456600C211yesmaximal, characteristic
2#21454873C211yesmaximal, characteristic
3#21444321C211yesmaximal, characteristic
4#21444183C211yesmaximal, characteristic, complemented
5#21443707C211yesmaximal, characteristic, complemented
6#21443662C211yesmaximal, characteristic, complemented
7C2×C61×#328C211yesmaximal, characteristic, complemented
8#16840273C2211yescharacteristic
9#16840100—21no—
10#16840092C411yescharacteristic, complemented
11#16840075C411yescharacteristic, complemented
12#16840001—21no—
13#16839993—21no—
14#16839922—21no—
15#16839918C411yescharacteristic, complemented
16#16839901C411yescharacteristic, complemented
17#16839833—21no—
18#16839830—21no—
19C8×C22⋊D61—21no—
20#16839825—21no—
21#16839820—21no—
22#16839727—21no—
23#16839726C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26#16839498—21no—
27#16839495—21no—
28#16839488—21no—
29#16839488—21no—
30C2×C22⋊Q8×C61C2211yescharacteristic
31C2×C22⋊C8×C61C2211yescharacteristic
32C2×#95×C61C2211yescharacteristic
33C61×#328—21no—
34C61×#328—21no—
35C2×#11758222D411yescharacteristic
36C2×#11758202—21no—
37C2×#11758201—21no—
38C2×#11758194—21no—
39C2×#11758189—21no—
40C22×#92418—21no—
41C22×#92418—21no—
42C2×C8×D61—21no—
43#14519760—21no—
44#14519756C2×C411yescharacteristic
45#14519756D411yescharacteristic
46#14519751C2×C411yescharacteristic
47#14519751D411yescharacteristic
48#14519746—21no—
49C4×C22⋊D61—21no—
50C4×C22⋊D61—21no—
51#14519736D411yescharacteristic
52#14519710—21no—
53#14519708—21no—
54#14519706—21no—
55#14519706—21no—
56#14519701—21no—
57#14519701—21no—
58#14519700—21no—
59#14519697—21no—
60C22⋊#92418—21no—
61C22⋊#92418—21no—
62C22⋊#92418—21no—
63C22⋊#92418—21no—
64C22⋊#92418C2×C411yescharacteristic
65C22⋊#92418C2×C411yescharacteristic
66C22⋊#92418D411yescharacteristic
67C22⋊#92418D411yescharacteristic
68#14519689—21no—
69#14519689—21no—
70#14519687—21no—
71C8×Dic61—21no—
72C22×Q8×C61C2×C411yescharacteristic
73C23×C4×C61—21no—
74C23×C4×C61C2311yescharacteristic
75C22×C8×C61—21no—
76C22⋊Q8×C61—21no—
77C22⋊Q8×C61—21no—
78C22⋊Q8×C61—21no—
79C22⋊Q8×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61C2×C411yescharacteristic
82C2×C22⋊C4×C61—21no—
83C22⋊C8×C61—21no—
84C22⋊C8×C61D411yescharacteristic
85C22⋊C8×C61D411yescharacteristic
86#95×C61—21no—
87#95×C61—21no—
88C24×C61#4111yescharacteristic
89C2×Q8×C61—21no—
90C2×Q8×C61—21no—
91C2×Q8×C61—81no—
92C22×C4×C61—21no—
93C22×C4×C61—22no—
94C22×C4×C61—21no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—81no—
98C22×C4×C61—81no—
99C22×C4×C61—81no—
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61#4111yescharacteristic
106C2×C22⋊D61—21no—
107C2×C22⋊D61—21no—
108C2×C22⋊D61—21no—
109#11758222—81no—
110C2×D244C22⋊C411yescharacteristic
111C2×C4×D61—21no—
112C2×Dic122C22⋊C411yescharacteristic
113C2×C8×C61—21no—
114C2×C8×C61—21no—
115C2×C8×C61—81no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊Dic61—21no—
123C22⋊Dic61—21no—
124C22⋊Dic61—21no—
125#11758202—81no—
126#11758201—81no—
127#11758198—21no—
128#11758198—21no—
129C4⋊Dic61C22⋊C411yescharacteristic
130C4⋊Dic61C22⋊C411yescharacteristic
131#11758196—21no—
132#11758196—21no—
133C4×Dic61—21no—
134#11758194—81no—
135C2×#92418—21no—
136C2×#92418—21no—
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418—41no—
140C2×#92418—81no—
141C2×#92418—81no—
142#11758189—81no—
143C8×D61—81no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—41no—
149C23×C61C4×D411yescharacteristic
150C23×C61#12111yescharacteristic
151C23×C61#12311yescharacteristic
152C22×D61—21no—
153Q8×C61—41no—
154Q8×C61—41no—
155Q8×C61—81no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—81no—
168C2×C4×C61—82no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61—82no—
172C2×C4×C61C2×C22⋊C411yescharacteristic
173C2×C4×C61C4×D411yescharacteristic
174C2×C4×C61#12011yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C22⋊D61—41no—
177C22⋊D61—41no—
178C22⋊D61—41no—
179C22⋊D61—41no—
180C22⋊D61—81no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184D244—41no—
185C4×D61—41no—
186C4×D61—41no—
187Dic122—41no—
188C8×C61—41no—
189C8×C61—41no—
190#92418—41no—
191#92418—41no—
192#92418—41no—
193#92418—41no—
194#92418—81no—
195#9263—611nomaximal, Sylow
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61—41no—
207C22×C61#38611yescharacteristic
208C22×C61#44311yescharacteristic
209C22×C61#44411yescharacteristic
210C22×C61#47111yescharacteristic
211C22×C61#47311yescharacteristic
212C2×D61—41no—
213C2×D61—41no—
214C2×D61—41no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—82no—
220C4×C61—81no—
221C4×C61—81no—
222Dic61—41no—
223Dic61—41no—
224Dic61—41no—
225#3190—611no—
226#2977—611no—
227#1504—611no—
228C2×#328D6111yescharacteristic, complemented
229#1472—611no—
230#1298—611no—
231#1280—611no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—21no—
235C2×C61—21no—
236C2×C61—41no—
237C2×C61#187611yescharacteristic
238C2×C61#190811yescharacteristic
239C2×C61#191311yescharacteristic
240D61—81no—
241#525—611no—
242C2×C22⋊Q8C2×D6111yescharacteristic
243#485—1221no—
244#483—611no—
245#480—611no—
246#467—1221no—
247#465—1221no—
248#452—1221no—
249#451—611no—
250#448—611no—
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⋊C8C2×D6111yescharacteristic
261C2×#95C2×D6111yescharacteristic
262#328—21no—
263#328—21no—
264#328—1221no—
265#327—1221no—
266#324—1221no—
267#324—1221no—
268C61#926311yescharacteristic, complemented, Sylow
269C2×#41—611no—
270C22×Q8C4×D6111yescharacteristic
271C23×C4—21no—
272C23×C4C22×D6111yescharacteristic
273C2×Q16—1221no—
274C2×SD16—1221no—
275C2×M16—1221no—
276C2×M16—1221no—
277C22×C8—21no—
278C22×C8—1221no—
279C22×C8—1221no—
280C22×C8—1221no—
281#123—1221no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—611no—
287C22⋊Q8—611no—
288#121—611no—
289#121—611no—
290#120—1221no—
291C4×D4—1221no—
292C4×D4—1221no—
293#117—611no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4C4×D6111yescharacteristic
296C2×C22⋊C4—21no—
297#107—1221no—
298#106—1221no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301#103—1221no—
302#103—1221no—
303#103—1221no—
304#102—1221no—
305C22⋊C8—21no—
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⋊C8C22⋊D6111yescharacteristic
317C22⋊C8C22⋊D6111yescharacteristic
318#97—1221no—
319C4×C8—1221no—
320#95—21no—
321#95—21no—
322C24#1175822411yescharacteristic
323#41—4881no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—81no—
327C2×Q8—611no—
328C2×D4—611no—
329C2×D4—1221no—
330C2×D4—1221no—
331C2×D4—1221no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—81no—
338C22×C4—81no—
339C22×C4—81no—
340C22×C4—1221no—
341C22×C4C2×C4×D6111yescharacteristic
342C22×C4#1175822211yescharacteristic
343C22×C4D4×D6111yescharacteristic
344C22×C4D4×D6111yescharacteristic
345C22×C4D4×D6111yescharacteristic
346C22×C4C2×C22⋊D6111yescharacteristic
347Q16—4881no—
348SD16—4881no—
349M16—4881no—
350M16—4881no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—81no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8—1221no—
357C2×C8—1221no—
358C2×C8—4881no—
359C2×C8—4881no—
360C2×C8—4881no—
361C2×C8—2441no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—611no—
367C4⋊C4—611no—
368C4⋊C4—1221no—
369C4⋊C4—1221no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—1221no—
373C22⋊C4—1221no—
374C22⋊C4—1221no—
375C22⋊C4—1221no—
376C22⋊C4—1221no—
377C42—1221no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—41no—
383C23—1221no—
384C23#1451973711yescharacteristic
385C23#1451974811yescharacteristic
386C23#1451975911yescharacteristic
387Q8—41no—
388Q8—41no—
389Q8—81no—
390Q8—2441no—
391D4—4881no—
392D4—2441no—
393D4—2441no—
394D4—2441no—
395D4—2441no—
396D4—2441no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—81no—
409C2×C4—82no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—82no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4C22⋊C4×D6111yescharacteristic
419C2×C4C4×C22⋊D6111yescharacteristic
420C2×C4#1451974511yescharacteristic
421C2×C4#1451975011yescharacteristic
422C8—41no—
423C8—41no—
424C8—4881no—
425C8—2441no—
426C8—2441no—
427C8—2441no—
428C8—2441no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—2441no—
441C22—2441no—
442C22—2441no—
443C22#1683963811yescharacteristic
444C22#1683987611yescharacteristic
445C22#1683988111yescharacteristic
446C22#1684002211yescharacteristic
447C22#1684003411yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—82no—
453C4—81no—
454C4—81no—
455C4—2441no—
456C4—2441no—
457C4—2441no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—41no—
463C2—4881no—
464C2#2144614311yescharacteristic
465C2#2144633711yescharacteristic
466C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#328C2
socleC22×C61#386
prime radical#16840273C22
cosocleC23×C4×C61C23
hypercenterC2×#328D61
hypocenterC61#9263
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. #21444183C2semidirect
5. #21443707C2semidirect
6. #21443662C2semidirect
7. C2×C61×#328C2semidirect
10. #16840092C4semidirect
11. #16840075C4semidirect
15. #16839918C4semidirect
16. #16839901C4semidirect
228. C2×#328D61semidirect
268. C61#9263semidirect

Maximal subgroups

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

subgroupindex
#214566002
#214548732
#214443212
#214441832
#214437072
#214436622
C2×C61×#3282
#926361