Finite Group Databasebeta

← #29575630

Subgroups — #29575630

Order 15616.

600 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839817C211yesmaximal, characteristic, complemented
2#21454115C211yesmaximal, characteristic
3#21445582C211yesmaximal, characteristic, complemented
4C2×#16839502C211yesmaximal, characteristic, complemented
5#21443701C211yesmaximal, characteristic, complemented
6#21443701C211yesmaximal, characteristic, complemented
7C2×C61×#329C211yesmaximal, characteristic, complemented
8C2×#14519753C411yescharacteristic
9C2×#14519748C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11#16839817—22no—
12#16839817—22no—
13C2×#14519706—21no—
14C2×#14519689—21no—
15C2×#14519689—21no—
16C2×#14519688C2211yescharacteristic
17C2×#14519688C2211yescharacteristic
18#16839669C411yescharacteristic
19#16839665C411yescharacteristic
20#16839650—21no—
21#16839650—21no—
22#16839638—21no—
23#16839638—21no—
24#16839628C2211yescharacteristic
25#16839516—21no—
26#16839502—22no—
27C2×#124×C61C2211yescharacteristic
28C2×#97×C61C2211yescharacteristic
29C2×#97×C61C2211yescharacteristic
30C61×#329—22no—
31C22×C22⋊D61—21no—
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×#92418—21no—
36C22×#92418—21no—
37#14519753—42no—
38#14519748—42no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×#11758198—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C42×D61—21no—
50C42×D61—21no—
51C42×D61—21no—
52C42×D61—21no—
53#14519706—24no—
54#14519689—24no—
55#14519689—24no—
56#14519688—21no—
57#14519688—21no—
58#14519688—21no—
59#14519688D412yescomplemented
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64C22×Q8×C61C2×C411yescharacteristic
65C22×D4×C61C2×C411yescharacteristic
66C22×C8×C61—21no—
67C22×C8×C61—21no—
68#124×C61—21no—
69#124×C61—21no—
70#124×C61—21no—
71#124×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C42×C61C2311yescharacteristic
75#97×C61—21no—
76#97×C61—21no—
77#97×C61—21no—
78#97×C61D412yescomplemented
79C24×C61—21no—
80C23×D61C22⋊C411yescharacteristic
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—41no—
84C2×Q8×C61—41no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C22×C4×C61—21no—
90C22×C4×C61C22×C411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C2×C22⋊D61—42no—
94C2×C22⋊D61—42no—
95C2×C22⋊D61—42no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C2×C4×D61—22no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—22no—
109C2×C4×D61—41no—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C8×C61—22no—
114C2×C8×C61—22no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C42×C61C2×D411yescharacteristic
124C42×C61C2×D411yescharacteristic
125C42×C61#4111yescharacteristic
126C42×C61#4111yescharacteristic
127C22⋊Dic61—42no—
128C22⋊Dic61—42no—
129C22⋊Dic61—42no—
130#11758198—42no—
131C4⋊Dic61—41no—
132C4⋊Dic61—41no—
133#11758196—42no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C2×#92418—22no—
141C2×#92418—22no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145C2×#92418—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61C2×C22⋊C411yescharacteristic
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61#10012yes—
161Q8×C61—81no—
162Q8×C61—81no—
163D4×C61—81no—
164D4×C61—81no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61C4×D411yescharacteristic
175C2×C4×C61C4×D411yescharacteristic
176C2×C4×C61#12011yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12311yescharacteristic
180C22⋊D61—84no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61#10412yes—
196C4×D61—42no—
197C4×D61—42no—
198C4×D61—42no—
199C4×D61—42no—
200C4×D61—42no—
201C4×D61—42no—
202C8×C61—42no—
203C8×C61—42no—
204#92418—42no—
205#92418—42no—
206#9124—611nomaximal, Sylow
207C22×C61—81no—
208C22×C61—81no—
209C22×C61—81no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61#38611yescharacteristic
215C22×C61C2×#10011yescharacteristic
216C22×C61#41311yescharacteristic
217C22×C61C2×#10411yescharacteristic
218C22×C61#42111yescharacteristic
219C22×C61#42111yescharacteristic
220C22×C61#42111yescharacteristic
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—41no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—81no—
235Dic61—22no—
236Dic61—41no—
237Dic61—41no—
238Dic61—81no—
239Dic61—81no—
240C2×#432—611no—
241#2850—611no—
242#1749—611no—
243C2×#329—611no—
244C2×#329D6111yescharacteristic, complemented
245#1295—611no—
246#1295—611no—
247C2×C61—161no—
248C2×C61#152911yescharacteristic
249C2×C61#153011yescharacteristic
250C2×C61#153311yescharacteristic
251C2×C61#153511yescharacteristic
252C2×C61#187111yescharacteristic
253C2×C61#189711yescharacteristic
254C2×C61#190011yescharacteristic
255D61—42no—
256C2×#124C2×D6111yescharacteristic
257C2×C22⋊Q8—611no—
258C2×#121—611no—
259C22×C42—611no—
260#432—1222no—
261#432—1222no—
262C2×C4⋊C8—1221no—
263C2×C22⋊C8—1221no—
264C2×C22⋊C8—1221no—
265C2×#97—611no—
266C2×#97—611no—
267C2×#97C2×D6111yescharacteristic
268C2×#97C2×D6111yescharacteristic
269#391—611no—
270#390—611no—
271#388—1221no—
272#388—1221no—
273#386—1221no—
274#386—1221no—
275#382—611no—
276#336—1221no—
277#329—22no—
278#329—1222no—
279C61#912411yescharacteristic, complemented, Sylow
280C22×Q8C4×D6111yescharacteristic
281C22×D4—1221no—
282C22×D4C4×D6111yescharacteristic
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—1221no—
289C22×C8—1221no—
290#124—21no—
291#124—21no—
292#124—21no—
293#124—21no—
294C22⋊Q8—2442no—
295#121—2442no—
296C2×C4⋊C4—611no—
297C2×C4⋊C4—611no—
298C2×C4⋊C4—1221no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—1221no—
302C2×C22⋊C4—1221no—
303C2×C22⋊C4—1221no—
304C2×C22⋊C4—1221no—
305C2×C42—611no—
306C2×C42—611no—
307C2×C42—611no—
308C2×C42—1221no—
309C2×C42—1221no—
310C2×C42—1221no—
311C2×C42—1221no—
312C2×C42C22×D6111yescharacteristic
313C4⋊C8—1224no—
314C22⋊C8—1224no—
315C22⋊C8—1224no—
316#97—21no—
317#97—21no—
318#97—21no—
319#97—612no—
320#97—1221no—
321#97—1221no—
322#97—1221no—
323#97C22⋊D6112yescomplemented
324#95—1221no—
325#95—1221no—
326#95—1221no—
327#95—1221no—
328C24—21no—
329C24—611no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—2442no—
339C2×D4—2442no—
340C2×D4—2442no—
341C22×C4—21no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—1222no—
346C22×C4—1222no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—2441no—
356C22×C4—2441no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4C2×C4×D6111yescharacteristic
360C22×C4D4×D6111yescharacteristic
361C22×C4D4×D6111yescharacteristic
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—1222no—
369C2×C8—1222no—
370C2×C8—2441no—
371C2×C8—2441no—
372C2×C8—2441no—
373C2×C8—2441no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C4⋊C4—2442no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—2442no—
382C22⋊C4—2442no—
383C22⋊C4—2442no—
384C22⋊C4—2442no—
385C42—1221no—
386C42—1221no—
387C42—1221no—
388C42—1221no—
389C42—1221no—
390C42—1221no—
391C42#1175822211yescharacteristic
392C42D4×D6111yescharacteristic
393C42#1175822411yescharacteristic
394C42C2×C22⋊D6111yescharacteristic
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—612no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1221no—
408C23—1221no—
409C23C22⋊C4×D6111yescharacteristic
410Q8—81no—
411Q8—81no—
412D4—81no—
413D4—81no—
414D4—4884no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—612no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—2442no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4#1451973711yescharacteristic
446C2×C4C4×C22⋊D6111yescharacteristic
447C2×C4#1451974511yescharacteristic
448C2×C4#1451974811yescharacteristic
449C2×C4#1451975011yescharacteristic
450C2×C4#1451975911yescharacteristic
451C8—42no—
452C8—42no—
453C8—2442no—
454C8—2442no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—1222no—
463C22—1222no—
464C22—1222no—
465C22—2441no—
466C22—2441no—
467C22—2441no—
468C22—2441no—
469C22#1683963811yescharacteristic
470C22#100×D6111yescharacteristic
471C22#1683974311yescharacteristic
472C22#104×D6111yescharacteristic
473C22#1683977711yescharacteristic
474C22#1683977711yescharacteristic
475C22#1683977711yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—81no—
483C4—1222no—
484C4—4881no—
485C4—4881no—
486C4—2441no—
487C4—2441no—
488C2—161no—
489C2—2442no—
490C2#2144442311yescharacteristic
491C2#2144442811yescharacteristic
492C2#2144444111yescharacteristic
493C2#2144444711yescharacteristic
494C2#2144611811yescharacteristic
495C2#2144626411yescharacteristic
496C2#2144627911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#329C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C42×C61C23
hypercenterC2×#329D61
hypocenterC61#9124
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
1. C2×#16839817C2semidirect
3. #21445582C2semidirect
4. C2×#16839502C2semidirect
5. #21443701C2semidirect
6. #21443701C2semidirect
7. C2×C61×#329C2semidirect
59. #14519688D4semidirect
78. #97×C61D4semidirect
244. C2×#329D61semidirect
279. C61#9124semidirect
323. #97C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398172
#214541152
#214455822
C2×#168395022
#214437012
C2×C61×#3292
#912461