Finite Group Databasebeta

← #29577053

Subgroups — #29577053

Order 15616.

520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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#21456621C211yesmaximal, characteristic
2#21448985C211yesmaximal, characteristic, complemented
3#21446655C211yesmaximal, characteristic
4#21444349C211yesmaximal, characteristic
5#21443724C211yesmaximal, characteristic, complemented
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1508C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9#16840095C412yescomplemented
10#16840075—21no—
11#16840010—22no—
12#16839912C412yescomplemented
13#16839901—21no—
14C2×#14519691—21no—
15C2×#14519691—21no—
16#16839726C2211yescharacteristic
17#16839669—21no—
18#16839661—21no—
19#16839655—21no—
20#16839655—21no—
21#16839648—21no—
22#16839648—21no—
23#16839625C2211yescharacteristic
24#16839622C2211yescharacteristic
25#16839497—21no—
26#16839497—21no—
27C2×C22⋊Q8×C61C2211yescharacteristic
28C61×#407C2211yescharacteristic
29C4×C22⋊C4×C61C2211yescharacteristic
30C61×#328—22no—
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C2×#11758201—22no—
34C2×#11758194—21no—
35#14519751—21no—
36#14519751—21no—
37#14519751—21no—
38#14519751—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×C22⋊Dic61D411yescharacteristic
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49#14519710—22no—
50#14519701—22no—
51#14519697—22no—
52#14519691—42no—
53#14519691—42no—
54C22⋊#92418—21no—
55C22⋊#92418C2×C412yes—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684D411yescharacteristic
63#14519684D411yescharacteristic
64C22×Q8×C61D411yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C2×M16×C61—21no—
67C22⋊Q8×C61—21no—
68C22⋊Q8×C61—21no—
69C22⋊Q8×C61C2×C412yes—
70C22⋊Q8×C61D412yes—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61D411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C42×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78#95×C61—21no—
79C24×C61C2×D411yescharacteristic
80C23×D61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61—81no—
83C2×Q8×C61C22⋊C412yes—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—41no—
87C22×C4×C61—81no—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C2×C22⋊D61—41no—
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—41no—
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C22×Dic61—21no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C2×D244—21no—
106C2×D244—21no—
107C2×D244—81no—
108M16×C61—81no—
109C2×C8×C61—41no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—22no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61C22⋊C412yes—
114C22⋊C4×C61—22no—
115C22⋊C4×C61—22no—
116C22⋊C4×C61—22no—
117C22⋊C4×C61—41no—
118C42×C61—81no—
119C22⋊Dic61—41no—
120C22⋊Dic61—41no—
121C22⋊Dic61—81no—
122#11758201—82no—
123#11758198—41no—
124#11758198—41no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—81no—
128C4⋊Dic61—81no—
129C4⋊Dic61—81no—
130C4×Dic61—81no—
131C4×Dic61—81no—
132#11758194—81no—
133C2×#92418—22no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61C4×D411yescharacteristic
139C23×C61#12011yescharacteristic
140C23×C61#12111yescharacteristic
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61—81no—
145C22×D61—81no—
146Q8×C61—42no—
147Q8×C61—81no—
148C2×C4×C61—22no—
149C2×C4×C61—22no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12311yescharacteristic
167C22⋊D61—81no—
168C22⋊D61—81no—
169C22⋊D61—81no—
170C22⋊D61—81no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186D244—42no—
187D244—81no—
188C8×C61—81no—
189#92418—42no—
190#9344—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61#38611yescharacteristic
202C22×C61#45311yescharacteristic
203C22×C61#45411yescharacteristic
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—161no—
208C2×D61—161no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—42no—
214C4×C61—42no—
215C4×C61—82no—
216Dic61—81no—
217Dic61—81no—
218Dic61—81no—
219Dic61—81no—
220Dic61—81no—
221#3193—611no—
222#2378—611no—
223#1964—611no—
224#1510—611no—
225#1508D6111yescharacteristic, complemented
226#1305—611no—
227#1284—611no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—41no—
231C2×C61—41no—
232C2×C61#188311yescharacteristic
233C2×C61#190511yescharacteristic
234C2×C61#191311yescharacteristic
235D61—161no—
236C2×C22⋊Q8C2×D6111yescharacteristic
237C2×#121—611no—
238#484—612no—
239#480—1221no—
240#468—1222no—
241#450—612no—
242#448—1221no—
243C2×#99—1221no—
244C2×#99—1221no—
245#407—611no—
246#407C2×D6111yescharacteristic
247#391—1221no—
248#389—1221no—
249#388—1221no—
250#388—1221no—
251#387—1221no—
252#387—1221no—
253#381—611no—
254#380—611no—
255C4×C22⋊C4C2×D6111yescharacteristic
256#328—22no—
257#327—1221no—
258#327—1221no—
259C61#934411yescharacteristic, complemented, Sylow
260C22×Q8D24411yescharacteristic
261C22×D4—611no—
262C22×D4—1221no—
263C23×C4C22×D6111yescharacteristic
264C2×SD16—1222no—
265C2×M16—21no—
266C2×M16—1221no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8C4×D6112yes—
270C22⋊Q8C22⋊D6112yes—
271#121—1221no—
272#121—1221no—
273#121—1221no—
274#121—1221no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4D24411yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C42—21no—
288C2×C42—1221no—
289C2×C42—1221no—
290#107—1222no—
291#103—1222no—
292#102—1222no—
293#99—2442no—
294#99—2442no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—612no—
298C22⋊C8—1221no—
299#95—21no—
300#95—611no—
301#95—611no—
302#95—1221no—
303#95—1221no—
304#95—1221no—
305#95—1221no—
306#95—1221no—
307#95—1221no—
308C24—1221no—
309C24D4×D6111yescharacteristic
310C2×Q8—21no—
311C2×Q8—81no—
312C2×Q8#1175819812yes—
313C2×D4—1221no—
314C2×D4—1221no—
315C2×D4—4881no—
316C2×D4—2441no—
317C2×D4—2441no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2441no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—81no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4C2×C4×D6111yescharacteristic
332C22×C4C2×D24411yescharacteristic
333C22×C4D4×D6111yescharacteristic
334C22×C4#1175822411yescharacteristic
335C22×C4#1175822411yescharacteristic
336C22×C4C2×C22⋊D6111yescharacteristic
337SD16—4882no—
338M16—81no—
339M16—4881no—
340C2×C8—41no—
341C2×C8—1222no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—4881no—
348C4⋊C4—4881no—
349C4⋊C4—4881no—
350C4⋊C4#1175819812yes—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—41no—
355C22⋊C4—4881no—
356C22⋊C4—2441no—
357C22⋊C4—2441no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C42—81no—
361C42—4881no—
362C42—4881no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—4881no—
368C23—4881no—
369C23—2441no—
370C23—2441no—
371C23—2441no—
372C23#1451973711yescharacteristic
373C23#1451974711yescharacteristic
374C23#1451974911yescharacteristic
375Q8—42no—
376Q8—81no—
377D4—4881no—
378D4—4881no—
379D4—4881no—
380D4—4881no—
381D4—4881no—
382D4—2442no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4C2×#1175819811yescharacteristic
414C2×C4#1451973711yescharacteristic
415C2×C4#1451974911yescharacteristic
416C2×C4#1451976111yescharacteristic
417C8—81no—
418C8—2442no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—9761no—
430C22—9761no—
431C22—4881no—
432C22—4881no—
433C22—4881no—
434C22#1683963911yescharacteristic
435C22#1683993111yescharacteristic
436C22#1683993611yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—42no—
443C4—82no—
444C4—4881no—
445C4—4881no—
446C4—4881no—
447C4—4881no—
448C4—4881no—
449C2—21no—
450C2—21no—
451C2—41no—
452C2—41no—
453C2—9761no—
454C2#2144619311yescharacteristic
455C2#2144631111yescharacteristic
456C2#2144635911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1508C2
socleC22×C61#386
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1508D61
hypocenterC61#9344
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
2. #21448985C2semidirect
5. #21443724C2semidirect
6. #21443672C2semidirect
7. C61×#1508C2semidirect
9. #16840095C4semidirect
12. #16839912C4semidirect
225. #1508D61semidirect
259. C61#9344semidirect

Maximal subgroups

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

subgroupindex
#214566212
#214489852
#214466552
#214443492
#214437242
#214436722
C61×#15082
#934461