Finite Group Databasebeta

← #29579033

Subgroups — #29579033

Order 15616.

596 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454174C211yesmaximal, characteristic
2#21445673C211yesmaximal, characteristic, complemented
3#21445567C211yesmaximal, characteristic, complemented
4C2×#16839502C211yesmaximal, characteristic, complemented
5C2×#16839501C211yesmaximal, characteristic, complemented
6C2×#16839501C211yesmaximal, characteristic, complemented
7C2×C61×#329C211yesmaximal, characteristic, complemented
8C2×#14519775C411yescharacteristic
9C2×#14519773C411yescharacteristic
10C2×#14519766C411yescharacteristic
11C2×#14519765C2211yescharacteristic
12C2×#14519764C411yescharacteristic
13C2×#14519706—21no—
14C2×#14519688C2211yescharacteristic
15C2×#14519688C2211yescharacteristic
16#16839662—21no—
17#16839662—21no—
18#16839662—21no—
19#16839662—21no—
20C42×Dic61C2211yescharacteristic
21#16839516—21no—
22#16839516—21no—
23#16839516—21no—
24#16839502—22no—
25#16839501—22no—
26#16839501—22no—
27C2×#124×C61C2211yescharacteristic
28C2×#97×C61C2211yescharacteristic
29C2×#97×C61C2211yescharacteristic
30C61×#329—22no—
31C22×Dic122C2×C411yescharacteristic
32C22×D244C2×C411yescharacteristic
33C22×C22⋊D61—21no—
34C22×C22⋊D61—21no—
35C22×#92418—21no—
36C22×#92418—21no—
37#14519775—42no—
38#14519773—42no—
39#14519766—42no—
40#14519765—21no—
41#14519765—21no—
42#14519765—21no—
43#14519765—21no—
44#14519764—42no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61C2×C411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C2×C4×Dic61D411yescharacteristic
59#14519706—24no—
60#14519688—21no—
61#14519688—21no—
62#14519688—21no—
63#14519688D412yescomplemented
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×D61—21no—
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—
96C2×C22⋊D61—42no—
97C2×C22⋊D61—42no—
98C2×C22⋊D61—42no—
99C22×Dic61—21no—
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104C2×D244—21no—
105C2×D244—21no—
106C2×D244—41no—
107C2×D244—41no—
108C2×Dic122—21no—
109C2×Dic122—21no—
110C2×Dic122—41no—
111C2×Dic122—41no—
112C2×C8×C61—22no—
113C2×C8×C61—22no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C42×C61C2×D411yescharacteristic
123C42×C61C2×D411yescharacteristic
124C42×C61#4111yescharacteristic
125C42×C61#4111yescharacteristic
126C22⋊Dic61—42no—
127C22⋊Dic61—42no—
128#11758198—42no—
129#11758198—41no—
130#11758198—41no—
131#11758198—41no—
132#11758198—41no—
133#11758198—42no—
134#11758196—42no—
135#11758196—42no—
136C4×Dic61—22no—
137C4×Dic61—22no—
138C4×Dic61—22no—
139C4×Dic61—41no—
140C4×Dic61—41no—
141C4×Dic61—41no—
142C2×#92418—22no—
143C2×#92418—22no—
144C2×#92418—41no—
145C2×#92418—41no—
146C2×#92418—41no—
147C2×#92418—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61C2×C22⋊C411yescharacteristic
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163Q8×C61—81no—
164Q8×C61—81no—
165D4×C61—81no—
166D4×C61—81no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61C4×D411yescharacteristic
177C2×C4×C61C4×D411yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12411yescharacteristic
181C2×C4×C61#12711yescharacteristic
182C22⋊D61—84no—
183C22⋊D61—84no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61#10012yes—
197C2×Dic61#10012yes—
198C2×Dic61#10412yes—
199D244—81no—
200D244—81no—
201Dic122—81no—
202Dic122—81no—
203C8×C61—42no—
204C8×C61—42no—
205#92418—42no—
206#92418—42no—
207#9689—611nomaximal, Sylow
208C22×C61—81no—
209C22×C61—81no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61#39011yescharacteristic
216C22×C61C2×#10011yescharacteristic
217C22×C61C2×#10011yescharacteristic
218C22×C61C2×#10411yescharacteristic
219C22×C61#42111yescharacteristic
220C22×C61#42111yescharacteristic
221C22×C61#42111yescharacteristic
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—81no—
236Dic61—22no—
237Dic61—22no—
238Dic61—22no—
239Dic61—41no—
240Dic61—81no—
241#2858—611no—
242#1767—611no—
243#1745—611no—
244C2×#329—611no—
245C2×#329—611no—
246C2×#329—611no—
247C2×#329D6111yescharacteristic, complemented
248C2×C61—161no—
249C2×C61#152711yescharacteristic
250C2×C61#153011yescharacteristic
251C2×C61#153311yescharacteristic
252C2×C61#153611yescharacteristic
253C2×C61#196311yescharacteristic
254C2×C61#196511yescharacteristic
255C2×C61#198011yescharacteristic
256D61—161no—
257C2×C4⋊Q8—611no—
258C2×#127—611no—
259C2×#124—611no—
260C2×#124—611no—
261C2×#124—611no—
262C2×#124C2×D6111yescharacteristic
263C2×C4⋊C8—1221no—
264C2×#97—611no—
265C2×#97—611no—
266C2×#97C2×D6111yescharacteristic
267C2×#97C2×D6111yescharacteristic
268#390—1221no—
269#390—1221no—
270#390—1221no—
271#390—1221no—
272C43—611no—
273#336—1221no—
274#336—1221no—
275#336—1221no—
276#329—22no—
277#329—1222no—
278#329—1222no—
279#329—1222no—
280C61#968911yescharacteristic, complemented, Sylow
281C22×Q8—611no—
282C22×Q8C4×D6111yescharacteristic
283C22×D4—611no—
284C22×D4—1221no—
285C22×D4—1221no—
286C22×D4C4×D6111yescharacteristic
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—1221no—
290C22×C8—1221no—
291C4⋊Q8—2442no—
292#127—2442no—
293#124—21no—
294#124—21no—
295#124—21no—
296#124—21no—
297#124—1221no—
298#124—1221no—
299#124—1221no—
300#124—1221no—
301#124—2442no—
302#124—2442no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4—1221no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—1221no—
309C2×C22⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C42—611no—
314C2×C42—611no—
315C2×C42—611no—
316C2×C42—611no—
317C2×C42—611no—
318C2×C42—611no—
319C2×C42C22×D6111yescharacteristic
320C4⋊C8—1224no—
321#97—21no—
322#97—21no—
323#97—21no—
324#97—612no—
325#97—1221no—
326#97—1221no—
327#97—1221no—
328#97C22⋊D6112yescomplemented
329C24—21no—
330C24—1221no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8—1221no—
336C2×Q8—1221no—
337C2×Q8—2441no—
338C2×Q8—2441no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—1221no—
344C2×D4—1221no—
345C2×D4—2441no—
346C2×D4—2441no—
347C2×D4—2442no—
348C2×D4—2442no—
349C2×D4—2442no—
350C2×D4—2442no—
351C2×D4—2442no—
352C2×D4—2442no—
353C22×C4—21no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—1221no—
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—2442no—
375C4⋊C4—2442no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—2442no—
381C22⋊C4—2442no—
382C22⋊C4—2442no—
383C22⋊C4—2442no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C42—1222no—
389C42—1222no—
390C42—1222no—
391C42—2441no—
392C42—2441no—
393C42—2441no—
394C42#1175822211yescharacteristic
395C42D4×D6111yescharacteristic
396C42#1175822411yescharacteristic
397C42C2×C22⋊D6111yescharacteristic
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—2441no—
406C23—2441no—
407C23—2441no—
408C23—2441no—
409C23—2441no—
410C23—2441no—
411C23—2441no—
412C23C22⋊C4×D6111yescharacteristic
413Q8—81no—
414Q8—81no—
415Q8—4881no—
416Q8—4881no—
417D4—81no—
418D4—81no—
419D4—4881no—
420D4—4881no—
421D4—4884no—
422D4—4884no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4#1451973711yescharacteristic
448C2×C4C4×C22⋊D6111yescharacteristic
449C2×C4#1451974911yescharacteristic
450C2×C4#1451975011yescharacteristic
451C2×C4#1451976311yescharacteristic
452C2×C4#1451977311yescharacteristic
453C8—42no—
454C8—42no—
455C8—2442no—
456C8—2442no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—4881no—
465C22—4881no—
466C22—4881no—
467C22—4881no—
468C22—4881no—
469C22—4881no—
470C22—4881no—
471C22#1683966211yescharacteristic
472C22#100×D6111yescharacteristic
473C22#100×D6111yescharacteristic
474C22#104×D6111yescharacteristic
475C22#1683977711yescharacteristic
476C22#1683977711yescharacteristic
477C22#1683977711yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—81no—
485C4—1222no—
486C4—1222no—
487C4—1222no—
488C4—4881no—
489C4—2441no—
490C2—161no—
491C2—9761no—
492C2#2144441511yescharacteristic
493C2#2144442811yescharacteristic
494C2#2144444111yescharacteristic
495C2#2144445211yescharacteristic
496C2#2144664911yescharacteristic
497C2#2144665711yescharacteristic
498C2#2144673611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#329C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C4
cosocleC2×C42×C61C23
hypercenterC2×#329D61
hypocenterC61#9689
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
2. #21445673C2semidirect
3. #21445567C2semidirect
4. C2×#16839502C2semidirect
5. C2×#16839501C2semidirect
6. C2×#16839501C2semidirect
7. C2×C61×#329C2semidirect
63. #14519688D4semidirect
78. #97×C61D4semidirect
247. C2×#329D61semidirect
280. C61#9689semidirect
328. #97C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214541742
#214456732
#214455672
C2×#168395022
C2×#168395012
C2×C61×#3292
#968961