Finite Group Databasebeta

← #29661868

Subgroups — #29661868

Order 15616.

908 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457033C211yesmaximal, characteristic, complemented
2#21456830C211yesmaximal, characteristic, complemented
3#21456164C211yesmaximal, characteristic, complemented
4#21445142C214yesmaximal, complemented
5#21445136C214yesmaximal, complemented
6#21444454C211yesmaximal, characteristic, complemented
7#21444434C211yesmaximal, characteristic, complemented
8#21444430C211yesmaximal, characteristic, complemented
9C61×#3548C211yesmaximal, characteristic
10#16840319C2211yescharacteristic
11#16840172C2212yes—
12#16840157C2212yes—
13#16840132C2212yes—
14#16840130—21no—
15#16840126—21no—
16#16840121C2212yes—
17#16840121C2212yes—
18#16840121C2212yes—
19#16840103—22no—
20#16840054—21no—
21#16840044—21no—
22#16839969—21no—
23#16839959—21no—
24#16839924—22no—
25#16839819C2211yescharacteristic
26#16839819C2211yescharacteristic
27#16839758—22no—
28C2×#14519688C2211yescharacteristic
29#16839504C2214yes—
30#16839502C2214yes—
31#16839502C2214yes—
32C61×#562C2214yes—
33C61×#554—21no—
34C61×#554—21no—
35C61×#550—21no—
36C61×#550—21no—
37C61×#547—21no—
38C61×#547—21no—
39C61×#540—22no—
40C61×#537—22no—
41C61×#537—22no—
42C61×#533C2211yescharacteristic
43C61×#532C2211yescharacteristic
44C61×#532C2211yescharacteristic
45C2×#11758202—22no—
46C2×#11758200—22no—
47C22×#92418—21no—
48#14519777C2311yescharacteristic
49#14519777C2311yescharacteristic
50#14519769—21no—
51#14519756—21no—
52#14519756—21no—
53C4×Dic122—21no—
54C4×Dic122—21no—
55#14519736—21no—
56#14519710—22no—
57#14519708—22no—
58C4⋊#92418—21no—
59C4⋊#92418—21no—
60#14519701—22no—
61#14519701—22no—
62#14519701—22no—
63#14519700—22no—
64#14519700—22no—
65#14519698—22no—
66#14519698—22no—
67#14519698—22no—
68C22⋊#92418—21no—
69C22⋊#92418—21no—
70#14519688—21no—
71#14519688C2312yes—
72#14519688C2312yes—
73#14519688C2312yes—
74C2×#41×C61—22no—
75C2×#41×C61—22no—
76C2×#41×C61D412yes—
77C2×#41×C61D412yes—
78C4⋊Q8×C61D411yescharacteristic
79C4⋊Q8×C61D411yescharacteristic
80C4⋊Q8×C61D411yescharacteristic
81C4⋊Q8×C61D411yescharacteristic
82#127×C61—22no—
83#127×C61D411yescharacteristic
84#127×C61D411yescharacteristic
85#125×C61—22no—
86#125×C61C2312yes—
87#124×C61C2312yes—
88#124×C61C2312yes—
89#123×C61—24no—
90#123×C61—24no—
91C22⋊Q8×C61—22no—
92C22⋊Q8×C61—22no—
93C22⋊Q8×C61—24no—
94C22⋊Q8×C61—24no—
95C22⋊Q8×C61—21no—
96C22⋊Q8×C61—21no—
97#121×C61—24no—
98#121×C61—24no—
99#121×C61—22no—
100#121×C61—22no—
101#121×C61—24no—
102#121×C61—24no—
103#121×C61—21no—
104#121×C61—21no—
105#121×C61—21no—
106#121×C61—21no—
107C4×Q8×C61—21no—
108C4×Q8×C61—21no—
109C4×D4×C61—22no—
110C4×D4×C61—22no—
111C4×D4×C61—21no—
112C4×D4×C61—21no—
113C4×D4×C61—21no—
114C4×D4×C61—21no—
115#117×C61D412yes—
116C2×C4⋊C4×C61—22no—
117C2×C4⋊C4×C61—22no—
118C2×C42×C61C2311yescharacteristic
119#41×C61—44no—
120#41×C61—82no—
121#41×C61—84no—
122#41×C61—84no—
123C2×Q8×C61—21no—
124C2×Q8×C61—21no—
125C2×Q8×C61C2×D412yes—
126C2×Q8×C61C2×D412yes—
127C2×D4×C61—24no—
128C2×D4×C61—24no—
129C2×D4×C61—22no—
130C2×D4×C61—22no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61C2×D412yes—
136C2×D4×C61C2×D412yes—
137C22×C4×C61—24no—
138C22×C4×C61—24no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C2×Dic122—21no—
145C2×Dic122—21no—
146C4⋊C4×C61—24no—
147C4⋊C4×C61—24no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61C2×D412yes—
157C4⋊C4×C61C2×D412yes—
158C22⋊C4×C61—24no—
159C22⋊C4×C61—24no—
160C22⋊C4×C61—22no—
161C22⋊C4×C61—22no—
162C22⋊C4×C61—22no—
163C22⋊C4×C61—22no—
164C22⋊C4×C61—22no—
165C42×C61—22no—
166C42×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61C2411yescharacteristic
170C22⋊Dic61—41no—
171#11758202—82no—
172#11758200—82no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177#11758196—41no—
178#11758196—41no—
179C4×Dic61—41no—
180C2×#92418—22no—
181C2×#92418—22no—
182C2×#92418—22no—
183C2×#92418—42no—
184C23×C61—22no—
185C23×C61—22no—
186C23×C61#12011yescharacteristic
187Q8×C61—42no—
188Q8×C61—42no—
189Q8×C61—42no—
190Q8×C61—42no—
191D4×C61—42no—
192D4×C61—42no—
193D4×C61—42no—
194D4×C61—42no—
195D4×C61—42no—
196D4×C61—42no—
197D4×C61—82no—
198D4×C61—82no—
199D4×C61—84no—
200D4×C61—84no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—44no—
209C2×C4×C61—44no—
210C2×C4×C61—84no—
211C2×C4×C61—84no—
212C2×C4×C61#12011yescharacteristic
213C2×C4×C61#12011yescharacteristic
214C2×C4×C61#12011yescharacteristic
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×Dic61—41no—
219C2×Dic61—41no—
220Dic122—41no—
221Dic122—41no—
222Dic122—42no—
223#92418—42no—
224#92418—42no—
225#92418—42no—
226#19057—611nomaximal, Sylow
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—42no—
231C22×C61—42no—
232C22×C61—42no—
233C22×C61—42no—
234C22×C61—42no—
235C22×C61—42no—
236C22×C61C2×#12011yescharacteristic
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—21no—
242C4×C61—42no—
243C4×C61—42no—
244C4×C61—42no—
245C4×C61—42no—
246C4×C61#45512yes—
247Dic61—81no—
248Dic61—81no—
249#3548D6111yescharacteristic
250#3237—611no—
251#3216—611no—
252#3135—611no—
253#1662—614no—
254#1661—614no—
255#1536—611no—
256#1531—611no—
257#1530—611no—
258C2×C61—41no—
259C2×C61—82no—
260C2×C61—82no—
261C2×C61C2×#45511yescharacteristic
262C2×C61#301911yescharacteristic
263C2×C61#302011yescharacteristic
264#562C2×D6114yes—
265#554—21no—
266#554—21no—
267#550—21no—
268#550—21no—
269#547—21no—
270#547—21no—
271#540—22no—
272#537—22no—
273#537—22no—
274#533—611no—
275#533C2×D6111yescharacteristic
276#532C2×D6111yescharacteristic
277#532C2×D6111yescharacteristic
278#501—612no—
279#497—612no—
280#491—612no—
281#491—1221no—
282#490—1221no—
283#489—612no—
284#489—612no—
285#489—612no—
286#485—1222no—
287#477—1221no—
288#475—1221no—
289#462—1221no—
290#460—1221no—
291#452—1222no—
292#432—611no—
293#432—611no—
294#416—1222no—
295C2×#97—611no—
296#330—614no—
297#329—614no—
298#329—614no—
299C61#1905711yescharacteristic, complemented, Sylow
300C2×#41—22no—
301C2×#41—22no—
302C2×#41C22⋊D6112yes—
303C2×#41C22⋊D6112yes—
304C2×Q16—1222no—
305C2×SD16—1222no—
306C22×C8—1221no—
307C4⋊Q8—611no—
308C4⋊Q8—611no—
309C4⋊Q8C22⋊D6111yescharacteristic
310C4⋊Q8C22⋊D6111yescharacteristic
311C4⋊Q8C22⋊D6111yescharacteristic
312C4⋊Q8C22⋊D6111yescharacteristic
313#127—22no—
314#127C22⋊D6111yescharacteristic
315#127C22⋊D6111yescharacteristic
316#125—22no—
317#125—1221no—
318#125C22×D6112yes—
319#124C22×D6112yes—
320#124C22×D6112yes—
321#123—24no—
322#123—24no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—1221no—
330C22⋊Q8—1221no—
331#121—24no—
332#121—24no—
333#121—22no—
334#121—22no—
335#121—24no—
336#121—24no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—1221no—
344C4×Q8—1221no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351#117—1221no—
352#117C22⋊D6112yes—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C42C22×D6111yescharacteristic
356#107—1222no—
357#106—1222no—
358C4⋊C8—1221no—
359C4⋊C8—1221no—
360#103—1222no—
361#103—1222no—
362#103—1222no—
363#103—1222no—
364#103—1222no—
365#102—1222no—
366#102—1222no—
367#102—1222no—
368C22⋊C8—1221no—
369C22⋊C8—1221no—
370#97—612no—
371#97—612no—
372#97—612no—
373#97—1221no—
374#41—44no—
375#41—82no—
376#41—84no—
377#41—84no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—1221no—
381C2×Q8—1221no—
382C2×Q8C2×C22⋊D6112yes—
383C2×Q8C2×C22⋊D6112yes—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4C2×C22⋊D6112yes—
393C2×D4C2×C22⋊D6112yes—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4C2×C22⋊D6111yescharacteristic
399C22×C4C2×C22⋊D6111yescharacteristic
400C22×C4C2×C22⋊D6111yescharacteristic
401Q16—4882no—
402SD16—4882no—
403C2×C8—1222no—
404C2×C8—1222no—
405C2×C8—1222no—
406C2×C8—2442no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—1221no—
418C4⋊C4—1221no—
419C4⋊C4—1221no—
420C4⋊C4—1221no—
421C4⋊C4—2441no—
422C4⋊C4—2441no—
423C4⋊C4C2×C22⋊D6112yes—
424C4⋊C4C2×C22⋊D6112yes—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—2441no—
433C42—22no—
434C42—2441no—
435C42C2×C22⋊D6111yescharacteristic
436C42C2×C22⋊D6111yescharacteristic
437C42C2×C22⋊D6111yescharacteristic
438C42C23×D6111yescharacteristic
439C23—22no—
440C23—22no—
441C23#1451974611yescharacteristic
442Q8—42no—
443Q8—42no—
444Q8—42no—
445Q8—42no—
446Q8—2441no—
447Q8—2441no—
448Q8—2442no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—82no—
456D4—82no—
457D4—84no—
458D4—84no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—84no—
469C2×C4—84no—
470C2×C4—2441no—
471C2×C4—2441no—
472C2×C4#1451974611yescharacteristic
473C2×C4#1451974611yescharacteristic
474C2×C4#1451974611yescharacteristic
475C2×C4C22×C22⋊D6111yescharacteristic
476C2×C4C22×C22⋊D6111yescharacteristic
477C2×C4C22×C22⋊D6111yescharacteristic
478C8—2442no—
479C8—2442no—
480C8—2442no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22C2×#1451974611yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—4881no—
501C4—4881no—
502C4#1683994012yes—
503C2—41no—
504C2—82no—
505C2—82no—
506C2C2×#1683994011yescharacteristic
507C2#2145517611yescharacteristic
508C2#2145518311yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3548C2
socleC22×C61C2×#120
hypercenter#3548D61
hypocenterC61#19057
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #21457033C2semidirect
2. #21456830C2semidirect
3. #21456164C2semidirect
4. #21445142C2semidirect
5. #21445136C2semidirect
6. #21444454C2semidirect
7. #21444434C2semidirect
8. #21444430C2semidirect
299. C61#19057semidirect

Maximal subgroups

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

subgroupindex
#214570332
#214568302
#214561642
#214451422
#214451362
#214444542
#214444342
#214444302
C61×#35482
#1905761