Finite Group Databasebeta

← #30601961

Subgroups — #30601961

Order 15616.

606 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 94 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#21461959C211yesmaximal, characteristic, complemented
2#21461958C211yesmaximal, characteristic, complemented
3#21461696C211yesmaximal, characteristic, complemented
4C8×C22⋊#6923C211yesmaximal, characteristic, complemented
5#21461256C211yesmaximal, characteristic, complemented
6#21461255C211yesmaximal, characteristic, complemented
7C2×#16839997C211yesmaximal, characteristic
8C2×#14519846—21no—
9C2×#14519836—22no—
10C2×#14519835—22no—
11D61⋊(C22⋊C8)C2211yescharacteristic
12C2×C8×#6923—21no—
13#16840704C2211yescharacteristic
14#16840704C2211yescharacteristic
15C4×C22⋊#6923C2211yescharacteristic
16#16840636—21no—
17(C2×#6923)⋊C8—21no—
18#16840614—22no—
19#16840613—22no—
20C22×#11758199C411yescharacteristic, complemented
21C22×C8×D61C2211yescharacteristic
22C2×#14519752C2211yescharacteristic
23C2×#14519748C2211yescharacteristic
24#16839997—21no—
25#16839997—21no—
26#16839997—21no—
27#16839997—21no—
28C2×#14519710C411yescharacteristic, complemented
29C2×#14519699C411yescharacteristic, complemented
30C2×#102×C61C411yescharacteristic, complemented
31C2×D61⋊C8—21no—
32C2×C4⋊#6923—21no—
33C2×C4⋊#6923—21no—
34C2×C22⋊#6923—21no—
35C2×C22⋊#6923—21no—
36C2×C22⋊#6923D412yes—
37C2×C4×#6923—21no—
38#14519846—42no—
39#14519836—44no—
40#14519835—44no—
41#14519834D412yes—
42C22⋊#92420—21no—
43C8×#6923—42no—
44(C2×#6923)⋊C4—21no—
45(C2×#6923)⋊C4—21no—
46(C2×#6923)⋊C4—21no—
47C22×D244—21no—
48C22×D244C2×C411yescharacteristic
49C22×C22⋊D61—21no—
50C22×C4×D61C2311yescharacteristic
51C2×#11758199—21no—
52C2×#11758199—21no—
53C2×#11758199—42no—
54C22×#92418C2×C411yescharacteristic
55C2×C8×D61—42no—
56C2×C8×D61D411yescharacteristic
57C2×C8×D61D411yescharacteristic
58C2×C8×D61D411yescharacteristic
59C2×C8×D61D411yescharacteristic
60#14519752—21no—
61#14519752—21no—
62#14519752—21no—
63#14519752—21no—
64#14519748—21no—
65#14519748—21no—
66#14519748—21no—
67#14519748—21no—
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×C22⋊Dic61—21no—
70C2×#11758198—21no—
71#14519710—21no—
72#14519710—21no—
73#14519699—21no—
74#14519699—21no—
75C22×D4×C61C2×C411yescharacteristic
76C22×C8×C61C2×C411yescharacteristic
77C2×C4⋊C4×C61C2×C411yescharacteristic
78#102×C61—21no—
79#102×C61—21no—
80C24×C61—21no—
81C23×D61—21no—
82C23×D61C2×D411yescharacteristic
83C22×#6923—22no—
84C22×#6923—41no—
85C22×#6923—41no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C22×C4×C61—21no—
91C22×C4×C61C22×C411yescharacteristic
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C2×C22⋊D61—42no—
95C2×C22⋊D61—42no—
96C22×Dic61—21no—
97C22×Dic61#4111yescharacteristic
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—41no—
101C2×D244—41no—
102C2×D244—41no—
103C2×D244—41no—
104C2×D244—42no—
105C2×D244—42no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×C4×D61C2×D411yescharacteristic
109C2×C4×D61C2×D411yescharacteristic
110C2×C4×D61C2×D411yescharacteristic
111C2×C4×D61#4111yescharacteristic
112C22⋊#6923—22no—
113C22⋊#6923—42no—
114C22⋊#6923—42no—
115C22⋊#6923D814yescomplemented
116C2×#92420—22no—
117C4⋊#6923—41no—
118C4⋊#6923—41no—
119C4⋊#6923—41no—
120C4⋊#6923—41no—
121C4×#6923—41no—
122C4×#6923—41no—
123D61⋊C8—41no—
124D61⋊C8—41no—
125C2×C8×C61—41no—
126C2×C8×C61C22⋊C411yescharacteristic
127C2×C8×C61C22⋊C411yescharacteristic
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C22⋊Dic61—41no—
131C22⋊Dic61—41no—
132#11758199—42no—
133#11758199—42no—
134#11758198—41no—
135#11758198—41no—
136C4⋊Dic61—21no—
137C4⋊Dic61—21no—
138C2×#92418—22no—
139C2×#92418C22⋊C411yescharacteristic
140C2×#92418C22⋊C411yescharacteristic
141C8×D61—22no—
142C8×D61—22no—
143C8×D61—41no—
144C8×D61—41no—
145C23×C61—41no—
146C23×C61—42no—
147C23×C61—81no—
148C23×C61—81no—
149C23×C61C4×D411yescharacteristic
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—42no—
154C22×D61—81no—
155C22×D61—81no—
156C22×D61#12111yescharacteristic
157C22×D61#12711yescharacteristic
158C22×D61C2×D812yes—
159C22×D61#13512yes—
160C2×#6923—24no—
161C2×#6923—42no—
162C2×#6923—42no—
163C2×#6923—81no—
164C2×#6923—81no—
165C2×#6923—81no—
166C2×#6923—81no—
167C2×#6923—81no—
168C2×#6923—81no—
169D4×C61—41no—
170D4×C61—41no—
171D4×C61—81no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—41no—
175C2×C4×C61—42no—
176C2×C4×C61C2×C22⋊C411yescharacteristic
177C2×C4×C61C4×D411yescharacteristic
178C22⋊D61—82no—
179C22⋊D61—81no—
180C22⋊D61—81no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—42no—
184C2×Dic61#12111yescharacteristic
185C2×Dic61#12411yescharacteristic
186D244—41no—
187D244—41no—
188D244—81no—
189D244—82no—
190D244—81no—
191D244—81no—
192C4×D61—21no—
193C4×D61—21no—
194C4×D61—21no—
195C4×D61—21no—
196C4×D61—41no—
197C4×D61—41no—
198#92420—42no—
199C8×C61—21no—
200C8×C61—21no—
201#92418—21no—
202#92418#9912yescomplemented
203#9783—611nomaximal, Sylow
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61—162no—
210C22×C61#39011yescharacteristic
211C22×C61C4×D812yes—
212C2×D61—21no—
213C2×D61—21no—
214C2×D61—21no—
215C2×D61—21no—
216C2×D61—42no—
217C2×D61—42no—
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C2×D61—162no—
222C2×D61#46612yes—
223C2×D61#49311yescharacteristic
224C2×D61#49511yescharacteristic
225#6923—44no—
226#6923—161no—
227#6923—161no—
228C4×C61—21no—
229C4×C61—81no—
230C4×C61C2×#9911yescharacteristic
231C4×C61#41011yescharacteristic
232Dic61—21no—
233Dic61—21no—
234Dic61—81no—
235C2×#466—611no—
236#1964—611no—
237#1964—611no—
238#1808—611no—
239C8×C22⋊C4—611no—
240#1519—611no—
241#1519—611no—
242C2×C61—22no—
243C2×C61—161no—
244C2×C61#196411yescharacteristic
245C2×C61#197011yescharacteristic
246C2×C61#197611yescharacteristic
247D61—22no—
248D61—21no—
249D61—21no—
250D61—161no—
251C22×D8—611no—
252C23×C8—611no—
253C2×#121—611no—
254C2×#121—611no—
255#466—1221no—
256#466—1221no—
257#466—1221no—
258#466—1221no—
259C2×#107—611no—
260C2×#107—1221no—
261C2×#102—611no—
262C2×#102#692311yescharacteristic, complemented
263C2×#99—1222no—
264C2×#99—1222no—
265C2×C22⋊C8—611no—
266C2×C4×C8—1221no—
267#380—611no—
268#380—611no—
269C4×C22⋊C4—611no—
270#340—1221no—
271#336—1221no—
272#327—1222no—
273#327—1222no—
274C61#978311yescharacteristic, complemented, Sylow
275C22×D4—611no—
276C22×D4—1221no—
277C22×D4—1221no—
278C22×D4C2×#692311yescharacteristic
279C23×C4—611no—
280C2×D8—1221no—
281C2×D8—1221no—
282C2×D8—2442no—
283C22×C8—611no—
284C22×C8—611no—
285C22×C8—611no—
286C22×C8—611no—
287C22×C8—611no—
288C22×C8—1221no—
289C22×C8—2442no—
290C22×C8C2×#692311yescharacteristic
291#121—1221no—
292#121—1221no—
293#121—1221no—
294#121—1221no—
295#121—1221no—
296#121—1221no—
297#121—1221no—
298#121—1221no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4C2×#692311yescharacteristic
303C2×C22⋊C4—612no—
304C2×C22⋊C4—1221no—
305C2×C22⋊C4—1221no—
306C2×C22⋊C4—1221no—
307C2×C22⋊C4—1221no—
308C2×C42—1221no—
309#107—1221no—
310#107—1221no—
311#107—2442no—
312#102—21no—
313#102—21no—
314#102—1221no—
315#102—1221no—
316#99—2444no—
317#99—2444no—
318C22⋊C8—612no—
319C22⋊C8—1221no—
320C4×C8—2442no—
321#95—1221no—
322#95—1221no—
323#95—1221no—
324C24—21no—
325C24—611no—
326C24—1221no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—1221no—
332C2×D4—1221no—
333C2×D4—2441no—
334C2×D4—2441no—
335C2×D4—2442no—
336C2×D4—2441no—
337C2×D4—2441no—
338C2×D4—2442no—
339C2×D4—2442no—
340C2×D4—2441no—
341C2×D4—2441no—
342C2×D4—2442no—
343C22×C4—21no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—1222no—
350C22×C4—1221no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4C22×#692311yescharacteristic
356D8—2442no—
357D8—2442no—
358C2×C8—41no—
359C2×C8—611no—
360C2×C8—611no—
361C2×C8—1222no—
362C2×C8—1222no—
363C2×C8—1222no—
364C2×C8—1222no—
365C2×C8—2441no—
366C2×C8—2441no—
367C2×C8—2441no—
368C2×C8—2441no—
369C2×C8C22⋊#692311yescharacteristic
370C2×C8C22⋊#692311yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—1221no—
374C4⋊C4—1221no—
375C4⋊C4—2441no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C22⋊C4—614no—
380C22⋊C4—1222no—
381C22⋊C4—2441no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C22⋊C4—2442no—
386C22⋊C4—2442no—
387C42—2441no—
388C42—2441no—
389C23—41no—
390C23—42no—
391C23—81no—
392C23—81no—
393C23—611no—
394C23—611no—
395C23—612no—
396C23—612no—
397C23—4881no—
398C23—4881no—
399C23—2441no—
400C23—2441no—
401C23—2442no—
402C23—2441no—
403C23D4×#692311yescharacteristic
404D4—41no—
405D4—41no—
406D4—81no—
407D4—4881no—
408D4—4882no—
409D4—4881no—
410D4—4881no—
411D4—4882no—
412D4—4881no—
413D4—4881no—
414D4—2441no—
415D4—2441no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—611no—
421C2×C4—611no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1224no—
427C2×C4—4881no—
428C2×C4—4881no—
429C2×C4—4881no—
430C2×C4—4881no—
431C2×C4—4881no—
432C2×C4—4881no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4C2×C22⋊#692311yescharacteristic
441C2×C4D4×#692311yescharacteristic
442C8—21no—
443C8—21no—
444C8—612no—
445C8—1221no—
446C8—2442no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—162no—
453C22—612no—
454C22—611no—
455C22—611no—
456C22—1221no—
457C22—1221no—
458C22—1221no—
459C22—1221no—
460C22—9762no—
461C22—4881no—
462C22—4881no—
463C22—4881no—
464C22—2442no—
465C22—2442no—
466C22#1684071411yescharacteristic
467C22D8×#692312yes—
468C4—21no—
469C4—81no—
470C4—1221no—
471C4—1221no—
472C4—9761no—
473C4—9761no—
474C4—4881no—
475C4—2444no—
476C4D61⋊#9911yescharacteristic
477C4#1684074111yescharacteristic
478C2—22no—
479C2—161no—
480C2—1221no—
481C2—1222no—
482C2—1221no—
483C2—9761no—
484C2#2146196011yescharacteristic
485C2#2146196611yescharacteristic
486C2#2146197711yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#102×C61C4
socleC22×C61#390
prime radicalC2×#16839997C2
cosocleC22×C4×D61C23
hypercenterC2×#102#6923
hypocenterC61#9783
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #21461959C2semidirect
2. #21461958C2semidirect
3. #21461696C2semidirect
4. C8×C22⋊#6923C2semidirect
5. #21461256C2semidirect
6. #21461255C2semidirect
20. C22×#11758199C4semidirect
28. C2×#14519710C4semidirect
29. C2×#14519699C4semidirect
30. C2×#102×C61C4semidirect
115. C22⋊#6923D8semidirect
202. #92418#99semidirect
262. C2×#102#6923semidirect
274. C61#9783semidirect

Maximal subgroups

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

subgroupindex
#214619592
#214619582
#214616962
C8×C22⋊#69232
#214612562
#214612552
C2×#168399972
#978361