Finite Group Databasebeta

← #29577669

Subgroups — #29577669

Order 15616.

568 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 91 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#21454847C211yesmaximal, characteristic, complemented
2#21450791C211yesmaximal, characteristic
3#21444443C211yesmaximal, characteristic, complemented
4#21444159C211yesmaximal, characteristic, complemented
5#21443676C211yesmaximal, characteristic, complemented
6#21443674C211yesmaximal, characteristic, complemented
7C61×#1533C211yesmaximal, characteristic, complemented
8C2×#14519773C411yescharacteristic
9C2×#14519766C411yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839835—22no—
12#16839832—22no—
13#16839819C2211yescharacteristic
14#16839819C2211yescharacteristic
15#16839724—21no—
16C22⋊C8×D61—21no—
17#16839678—21no—
18#16839678—21no—
19#16839669C411yescharacteristic
20#16839665C411yescharacteristic
21#16839638—21no—
22#16839638—21no—
23C4×C4⋊Dic61C2211yescharacteristic
24#16839502—22no—
25#16839485—21no—
26#16839485—21no—
27C2×#124×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C61×#432C2211yescharacteristic
30C61×#329—22no—
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61—21no—
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×#11758189—22no—
37C2×C8×D61—22no—
38#14519773—42no—
39#14519766—42no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198D411yescharacteristic
51C2×#11758198D411yescharacteristic
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61C2×C411yescharacteristic
54C4⋊#92418—21no—
55C4⋊#92418—21no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58#14519689—22no—
59#14519689—22no—
60#14519688—21no—
61#14519688D412yescomplemented
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65C22×Q8×C61C2×C411yescharacteristic
66C22×D4×C61C2×C411yescharacteristic
67#124×C61—21no—
68#124×C61—21no—
69#124×C61—21no—
70#124×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C4⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78#97×C61—21no—
79#97×C61D412yescomplemented
80C24×C61—21no—
81C23×D61C22⋊C411yescharacteristic
82C23×D61C22⋊C411yescharacteristic
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—41no—
86C2×Q8×C61—41no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C22×C4×C61—21no—
92C22×C4×C61C22×C411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C2×C22⋊D61—42no—
96C2×C22⋊D61—42no—
97C2×C22⋊D61—42no—
98C2×C22⋊D61—42no—
99C2×C22⋊D61—81no—
100C2×C22⋊D61—81no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C22⋊C411yescharacteristic
105C2×D244—22no—
106C2×D244—21no—
107C2×D244—21no—
108C2×D244—41no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—81no—
114C2×C4×D61—81no—
115C2×C8×C61—22no—
116C2×C8×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C42×C61#4111yescharacteristic
124C42×C61#4111yescharacteristic
125C22⋊Dic61—81no—
126C22⋊Dic61—81no—
127#11758198—21no—
128#11758198—21no—
129#11758198—21no—
130#11758198—21no—
131#11758198—42no—
132#11758198—42no—
133C4⋊Dic61—21no—
134C4⋊Dic61—21no—
135C4⋊Dic61—42no—
136C4×Dic61—41no—
137C4×Dic61—41no—
138C2×#92418—22no—
139C2×#92418—41no—
140#11758189—82no—
141C8×D61—82no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61C2×C22⋊C411yescharacteristic
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61#10012yes—
160Q8×C61—81no—
161Q8×C61—81no—
162D4×C61—81no—
163D4×C61—81no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61C4×D411yescharacteristic
172C2×C4×C61C4×D411yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12311yescharacteristic
177C22⋊D61—84no—
178C22⋊D61—84no—
179C2×Dic61—22no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189D244—42no—
190D244—42no—
191C4×D61—42no—
192C4×D61—42no—
193C4×D61—81no—
194C4×D61—81no—
195C8×C61—42no—
196C8×C61—81no—
197#92418—42no—
198#92418—81no—
199#9447—611nomaximal, Sylow
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—81no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61—81no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61#38611yescharacteristic
210C22×C61C2×#10011yescharacteristic
211C22×C61#41311yescharacteristic
212C2×D61—22no—
213C2×D61—41no—
214C2×D61—41no—
215C2×D61—42no—
216C2×D61—42no—
217C2×D61—41no—
218C2×D61—41no—
219C2×D61—41no—
220C2×D61—81no—
221C2×D61—81no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—81no—
229Dic61—42no—
230Dic61—41no—
231Dic61—41no—
232Dic61—81no—
233#2973—611no—
234#2544—611no—
235#1533—611no—
236#1533D6111yescharacteristic, complemented
237#1466—611no—
238#1285—611no—
239#1285—611no—
240C2×C61—21no—
241C2×C61—21no—
242C2×C61—161no—
243C2×C61#188411yescharacteristic
244C2×C61#190011yescharacteristic
245C2×C61#191111yescharacteristic
246D61—42no—
247D61—81no—
248C2×#127—611no—
249C2×#124—611no—
250C2×#124C2×D6111yescharacteristic
251C2×C4×D4—611no—
252#435—1222no—
253#435—1222no—
254#432—611no—
255#432—611no—
256#432C2×D6111yescharacteristic
257#432C2×D6111yescharacteristic
258#407—1221no—
259C2×C22⋊C8—1221no—
260#394—1221no—
261#394—1221no—
262#391—611no—
263#390—611no—
264#386—1221no—
265#386—1221no—
266C4×C4⋊C4—611no—
267#329—22no—
268#329—1222no—
269#323—1221no—
270#323—1221no—
271C61#944711yescharacteristic, complemented, Sylow
272C22×Q8C4×D6111yescharacteristic
273C22×D4—611no—
274C22×D4—1221no—
275C22×D4—1221no—
276C22×D4C4×D6111yescharacteristic
277C23×C4—611no—
278C23×C4—611no—
279C2×M16—1222no—
280C22×C8—1222no—
281#127—2442no—
282#124—21no—
283#124—21no—
284#124—21no—
285#124—21no—
286#124—2442no—
287C4×D4—1221no—
288C4×D4—1221no—
289C4×D4—1221no—
290C4×D4—1221no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—1221no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—611no—
296C2×C22⋊C4—611no—
297C2×C22⋊C4—1221no—
298C2×C22⋊C4—1221no—
299C2×C22⋊C4—1221no—
300C2×C22⋊C4—1221no—
301C2×C42—611no—
302C2×C42—611no—
303C2×C42C22×D6111yescharacteristic
304C4⋊C8—21no—
305C4⋊C8—21no—
306C4⋊C8—1221no—
307C4⋊C8—1221no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8—1222no—
311C22⋊C8—1222no—
312C22⋊C8—1221no—
313C22⋊C8—1221no—
314#97—21no—
315#97—612no—
316#97—1221no—
317#97C22⋊D6112yescomplemented
318#95—1221no—
319#95—1221no—
320#95—1221no—
321C24—21no—
322C24—611no—
323C24—611no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—41no—
327C2×Q8—41no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—1222no—
333C2×D4—1221no—
334C2×D4—1221no—
335C2×D4—4881no—
336C2×D4—4881no—
337C2×D4—2441no—
338C2×D4—2442no—
339C2×D4—2442no—
340C2×D4—2442no—
341C2×D4—2442no—
342C22×C4—21no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—1221no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—4881no—
352C22×C4—4881no—
353C22×C4C2×C4×D6111yescharacteristic
354C22×C4D4×D6111yescharacteristic
355C22×C4D4×D6111yescharacteristic
356M16—4882no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—1222no—
360C2×C8—4882no—
361C2×C8—2441no—
362C4⋊C4—1221no—
363C4⋊C4—1221no—
364C4⋊C4—2442no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—1221no—
370C22⋊C4—1221no—
371C22⋊C4—1221no—
372C22⋊C4—1221no—
373C22⋊C4—4881no—
374C22⋊C4—4881no—
375C22⋊C4—2442no—
376C22⋊C4—2442no—
377C42—2441no—
378C42—2441no—
379C42#1175822211yescharacteristic
380C42D4×D6111yescharacteristic
381C42#1175822411yescharacteristic
382C42C2×C22⋊D6111yescharacteristic
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—612no—
391C23—1221no—
392C23—1221no—
393C23—1221no—
394C23—1221no—
395C23—1221no—
396C23—2441no—
397C23—2441no—
398C23—2441no—
399C23—2441no—
400C23C22⋊C4×D6111yescharacteristic
401Q8—81no—
402Q8—81no—
403D4—81no—
404D4—81no—
405D4—4884no—
406D4—4884no—
407D4—2442no—
408D4—2442no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—1222no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—4881no—
420C2×C4—4881no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4#1451973711yescharacteristic
431C2×C4C4×C22⋊D6111yescharacteristic
432C2×C4#1451974511yescharacteristic
433C2×C4#1451974811yescharacteristic
434C2×C4#1451975011yescharacteristic
435C2×C4#1451975911yescharacteristic
436C8—42no—
437C8—81no—
438C8—4881no—
439C8—2442no—
440C22—21no—
441C22—21no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—1222no—
450C22—4881no—
451C22—4881no—
452C22—2442no—
453C22—2442no—
454C22—2441no—
455C22—2441no—
456C22—2441no—
457C22—2441no—
458C22—2441no—
459C22#1683963811yescharacteristic
460C22#100×D6111yescharacteristic
461C22#1683974311yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—81no—
469C4—4881no—
470C4—2442no—
471C4—2441no—
472C4—2441no—
473C2—21no—
474C2—21no—
475C2—161no—
476C2—4881no—
477C2—2442no—
478C2#2144619911yescharacteristic
479C2#2144627911yescharacteristic
480C2#2144634811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1533C2
socleC22×C61#386
prime radicalC2×#14519773C4
cosocleC2×C42×C61C23
hypercenter#1533D61
hypocenterC61#9447
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1533

Complements

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

NH ≅ G/Ntype
1. #21454847C2semidirect
3. #21444443C2semidirect
4. #21444159C2semidirect
5. #21443676C2semidirect
6. #21443674C2semidirect
7. C61×#1533C2semidirect
61. #14519688D4semidirect
79. #97×C61D4semidirect
236. #1533D61semidirect
271. C61#9447semidirect
317. #97C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214548472
#214507912
#214444432
#214441592
#214436762
#214436742
C61×#15332
#944761