Finite Group Databasebeta

← #29579538

Subgroups — #29579538

Order 15616.

510 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#16840001C211yesmaximal, characteristic
2#21446804C211yesmaximal, characteristic
3#21445842C211yesmaximal, characteristic
4#21445597C211yesmaximal, characteristic
5#21444391C211yesmaximal, characteristic
6#21444390C211yesmaximal, characteristic
7C61×#1996C211yesmaximal, characteristic
8C22×#11758202C411yescharacteristic, complemented
9C23×#92418C2211yescharacteristic
10C2×#14519756C2211yescharacteristic
11#16840001—21no—
12#16840001—21no—
13#16840001—21no—
14#16840001—21no—
15C2×#14519710C411yescharacteristic, complemented
16C2×#14519708—21no—
17C2×#14519701C411yescharacteristic, complemented
18C2×#14519700C411yescharacteristic, complemented
19C2×C22⋊#92418C2211yescharacteristic
20C2×#14519688—21no—
21#16839622C2211yescharacteristic
22#16839528—22no—
23#16839524—21no—
24#16839517—21no—
25#16839499—22no—
26#16839498—22no—
27C2×C22⋊Q8×C61C2211yescharacteristic
28C61×#380C2211yescharacteristic
29C4×C22⋊C4×C61C2211yescharacteristic
30C61×#342—22no—
31C22×Dic122C2×C411yescharacteristic
32C2×#11758202—21no—
33C2×#11758202—21no—
34C2×#11758202—42no—
35C22×#92418—21no—
36C22×#92418—42no—
37C22×#92418C2×C411yescharacteristic
38C22×#92418C2×C411yescharacteristic
39C22×#92418D411yescharacteristic
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42C22×#92418D411yescharacteristic
43#14519756—21no—
44#14519756—21no—
45#14519756—21no—
46#14519756—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758196—21no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—21no—
52#14519710—21no—
53#14519710—21no—
54#14519708—42no—
55#14519701—21no—
56#14519701—21no—
57#14519700—21no—
58#14519700—21no—
59C22⋊#92418—21no—
60C22⋊#92418D412yes—
61#14519688—42no—
62#14519684—21no—
63C22×Q8×C61C2×C411yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C22⋊Q8×C61—21no—
66C22⋊Q8×C61—21no—
67C22⋊Q8×C61—21no—
68C22⋊Q8×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61D412yes—
75C2×C42×C61—21no—
76#95×C61—21no—
77#95×C61—21no—
78C24×C61C2×D411yescharacteristic
79C2×Q8×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—41no—
82C2×Q8×C61—41no—
83C22×C4×C61—22no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—41no—
98C2×Dic122—21no—
99C2×Dic122—21no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C22⋊C4×C61—22no—
109C22⋊C4×C61—22no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—42no—
113C42×C61—41no—
114C42×C61—41no—
115C22⋊Dic61—41no—
116C22⋊Dic61—41no—
117C22⋊Dic61—42no—
118#11758202—42no—
119#11758202—42no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124#11758196—41no—
125#11758196—41no—
126C2×#92418—22no—
127C2×#92418—22no—
128C2×#92418—22no—
129C2×#92418—22no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135C2×#92418C22⋊C411yescharacteristic
136C2×#92418C22⋊C411yescharacteristic
137C2×#92418C22⋊C411yescharacteristic
138C2×#92418C22⋊C411yescharacteristic
139C23×C61—41no—
140C23×C61—41no—
141C23×C61C4×D411yescharacteristic
142C23×C61#12111yescharacteristic
143C23×C61#12711yescharacteristic
144C23×C61#13712yes—
145C23×C61#13712yes—
146Q8×C61—41no—
147Q8×C61—41no—
148Q8×C61—81no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61C2×C22⋊C411yescharacteristic
169C2×C4×C61C4×D411yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12411yescharacteristic
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—81no—
175C2×Dic61—81no—
176C2×Dic61—81no—
177C2×Dic61—81no—
178C2×Dic61—81no—
179Dic122—41no—
180Dic122—41no—
181Dic122—81no—
182#92418—21no—
183#92418—21no—
184#92418—21no—
185#92418—42no—
186#92418#9912yes—
187#9784—611nomaximal, Sylow
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—42no—
195C22×C61—42no—
196C22×C61#39011yescharacteristic
197C22×C61#44112yes—
198C22×C61#47012yes—
199C22×C61#49711yescharacteristic
200C22×C61#49711yescharacteristic
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—82no—
205C4×C61—81no—
206C4×C61—81no—
207C4×C61—161no—
208C4×C61C2×#9911yescharacteristic
209C4×C61#41011yescharacteristic
210Dic61—81no—
211Dic61—81no—
212Dic61—161no—
213C2×#467—611no—
214#1996—611no—
215#1996D6111yescharacteristic
216#1807—611no—
217#1752—611no—
218#1520—611no—
219#1520—611no—
220C2×C61—21no—
221C2×C61—22no—
222C2×C61—21no—
223C2×C61—22no—
224C2×C61#196411yescharacteristic
225C2×C61#197111yescharacteristic
226C2×C61#197611yescharacteristic
227C22×Q16—611no—
228C23×C8—611no—
229C2×C22⋊Q8—611no—
230C2×C22⋊Q8C2×D6111yescharacteristic
231#467—1221no—
232#467—1221no—
233#467—1221no—
234#467—1221no—
235C2×#107—611no—
236C2×#106—1221no—
237C2×#103—611no—
238C2×#103—611no—
239C2×C22⋊C8—611no—
240C2×#97—1221no—
241#380—611no—
242#380C2×D6111yescharacteristic
243C4×C22⋊C4C2×D6111yescharacteristic
244#342—22no—
245#342—1222no—
246#340—1221no—
247#336—1221no—
248#328—1222no—
249#328—1222no—
250C61#978411yescharacteristic, complemented, Sylow
251C22×Q8—611no—
252C22×Q8C4×D6111yescharacteristic
253C23×C4C22×D6111yescharacteristic
254C2×Q16—1221no—
255C2×Q16—1221no—
256C2×Q16—2442no—
257C22×C8—611no—
258C22×C8—611no—
259C22×C8—611no—
260C22×C8—611no—
261C22×C8—611no—
262C22×C8—611no—
263C22×C8—1221no—
264C22×C8—2442no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—1221no—
270C22⋊Q8—1221no—
271C22⋊Q8—1221no—
272C22⋊Q8—1221no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4C4×D6111yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—1221no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4C22⋊D6112yes—
284C2×C42—21no—
285#107—1221no—
286#107—1221no—
287#106—2442no—
288#103—1221no—
289#103—1221no—
290#103—1221no—
291#103—1221no—
292C22⋊C8—612no—
293C22⋊C8—1221no—
294#97—2442no—
295#95—21no—
296#95—21no—
297#95—1221no—
298C24C2×C22⋊D6111yescharacteristic
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—1221no—
304C2×Q8—1221no—
305C2×Q8—2441no—
306C2×Q8—2441no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—2441no—
316C22×C4C2×C4×D6111yescharacteristic
317C22×C4#1175822211yescharacteristic
318C22×C4D4×D6111yescharacteristic
319C22×C4D4×D6111yescharacteristic
320C22×C4D4×D6111yescharacteristic
321C22×C4#1175822411yescharacteristic
322Q16—2442no—
323Q16—2442no—
324C2×C8—611no—
325C2×C8—611no—
326C2×C8—611no—
327C2×C8—611no—
328C2×C8—1222no—
329C2×C8—1222no—
330C2×C8—1222no—
331C2×C8—1222no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8—2441no—
335C2×C8—2441no—
336C2×C8—2441no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—1221no—
344C4⋊C4—1221no—
345C4⋊C4—2441no—
346C4⋊C4—2441no—
347C4⋊C4—2441no—
348C4⋊C4—2441no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—42no—
354C22⋊C4—2442no—
355C22⋊C4—2441no—
356C22⋊C4—2441no—
357C42—41no—
358C42—41no—
359C23—41no—
360C23—41no—
361C23C4×C22⋊D6111yescharacteristic
362C23#1451974911yescharacteristic
363C23#1451977311yescharacteristic
364C23#1451980712yes—
365C23#1451980812yes—
366Q8—41no—
367Q8—41no—
368Q8—81no—
369Q8—4881no—
370Q8—2441no—
371Q8—2441no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—4881no—
394C2×C4—4881no—
395C2×C4—4881no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4C22⋊C4×D6111yescharacteristic
399C2×C4#1451973711yescharacteristic
400C2×C4#1451975011yescharacteristic
401C2×C4#1451976311yescharacteristic
402C8—612no—
403C8—1221no—
404C8—1221no—
405C8—1221no—
406C8—2442no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—42no—
414C22—42no—
415C22#1683966211yescharacteristic
416C22#1683986712yes—
417C22#1684001812yes—
418C22#1684015411yescharacteristic
419C22#1684015711yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—82no—
424C4—81no—
425C4—81no—
426C4—161no—
427C4—9761no—
428C4—4881no—
429C4—4881no—
430C4#99×D6111yescharacteristic
431C4#1683973411yescharacteristic
432C2—22no—
433C2—21no—
434C2—21no—
435C2—22no—
436C2#2144665311yescharacteristic
437C2#2144668911yescharacteristic
438C2#2144671411yescharacteristic
subgroupG/H
centerC22#16839662
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1996C2
socleC22×C61#390
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1996D61
hypocenterC61#9784
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
8. C22×#11758202C4semidirect
15. C2×#14519710C4semidirect
17. C2×#14519701C4semidirect
18. C2×#14519700C4semidirect
250. C61#9784semidirect

Maximal subgroups

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

subgroupindex
C2×#168400012
#214468042
#214458422
#214455972
#214443912
#214443902
C61×#19962
#978461