Finite Group Databasebeta

← #29597561

Subgroups — #29597561

Order 15616.

676 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#101×D61C211yesmaximal, characteristic
2#21449462C211yesmaximal, characteristic
3C2×#16839560C211yesmaximal, characteristic, complemented
4C2×#16839560C211yesmaximal, characteristic, complemented
5#21445741C211yesmaximal, characteristic
6#21443946C211yesmaximal, characteristic, complemented
7C61×#1394C211yesmaximal, characteristic, complemented
8C22×Q8×D61C2211yescharacteristic
9C2×M16×D61—21no—
10C2×#14519777C411yescharacteristic
11C2×#14519775C2211yescharacteristic
12C2×#14519757C411yescharacteristic
13C2×#14519696C2211yescharacteristic
14C2×#14519696C2211yescharacteristic
15C2×#14519695—21no—
16C2×#14519695—21no—
17#101×D61—22no—
18#101×D61—22no—
19#16839725—21no—
20#16839683—21no—
21#16839683—21no—
22#16839667C411yescharacteristic
23#16839636—21no—
24#16839636—21no—
25C4×#11758198C411yescharacteristic
26#16839560—22no—
27#16839560—22no—
28C2×#101×C61C2211yescharacteristic
29C2×#101×C61C2211yescharacteristic
30C61×#391C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32C22×Dic122C2×C411yescharacteristic
33C22×Dic122D411yescharacteristic
34C22×Dic122D411yescharacteristic
35C2×Q8×D61—21no—
36C2×Q8×D61—21no—
37C2×Q8×D61—21no—
38C2×Q8×D61—21no—
39C2×Q8×D61—42no—
40C2×Q8×D61—41no—
41C2×Q8×D61—41no—
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C2×#11758194—21no—
46C2×#11758194—21no—
47C2×#11758189—41no—
48M16×D61—24no—
49M16×D61—42no—
50C2×C8×D61—41no—
51#14519777—42no—
52#14519775—21no—
53#14519775—21no—
54#14519775—21no—
55#14519775—21no—
56#14519757—41no—
57#14519757—41no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61—21no—
61C2×#11758196—21no—
62C2×#11758196—21no—
63C2×#11758198—21no—
64C2×#11758198—21no—
65C2×C4×Dic61C2×C411yescharacteristic
66#14519696—21no—
67#14519696—21no—
68#14519696—21no—
69#14519696D412yes—
70#14519695—24no—
71#14519695—42no—
72#14519689—41no—
73#14519689—41no—
74#14519684—21no—
75#14519684—21no—
76#14519684—21no—
77C22×Q8×C61C2311yescharacteristic
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×C4⋊C4×C61C2×C411yescharacteristic
81C2×C42×C61C2×C411yescharacteristic
82#101×C61—21no—
83#101×C61—21no—
84#101×C61—21no—
85#101×C61D412yes—
86#95×C61—21no—
87#95×C61—21no—
88C23×D61C22⋊C411yescharacteristic
89C2×Q8×C61—41no—
90C2×Q8×C61—41no—
91C2×Q8×C61C2×D411yescharacteristic
92C2×Q8×C61C2×D411yescharacteristic
93C2×Q8×C61#4111yescharacteristic
94C2×Q8×C61#4111yescharacteristic
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61C22×C411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×Dic61—21no—
101C22×Dic61—21no—
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C22⋊C411yescharacteristic
105Q8×D61—42no—
106Q8×D61—42no—
107Q8×D61—42no—
108Q8×D61—42no—
109Q8×D61—42no—
110Q8×D61—42no—
111Q8×D61—42no—
112Q8×D61—42no—
113C2×C4×D61—21no—
114C2×C4×D61—21no—
115C2×C4×D61—21no—
116C2×C4×D61—21no—
117C2×C4×D61—22no—
118C2×C4×D61—21no—
119C2×C4×D61—21no—
120C2×C4×D61—21no—
121C2×C4×D61—21no—
122C2×C4×D61—21no—
123C2×C4×D61—21no—
124C2×C4×D61—21no—
125C2×C4×D61—21no—
126C2×C4×D61—41no—
127C2×C4×D61—41no—
128C2×Dic122—21no—
129C2×Dic122—21no—
130C2×Dic122—21no—
131C2×Dic122—21no—
132C2×Dic122—21no—
133C2×Dic122—21no—
134C2×Dic122—22no—
135C2×Dic122—22no—
136C2×Dic122—21no—
137C2×Dic122—21no—
138C2×Dic122—41no—
139C2×Dic122—41no—
140C2×Dic122—41no—
141C2×Dic122—41no—
142C2×Dic122—41no—
143C2×Dic122—41no—
144M16×C61—22no—
145M16×C61—41no—
146M16×C61—41no—
147M16×C61—41no—
148C2×C8×C61—41no—
149C2×C8×C61—41no—
150C4⋊C4×C61—41no—
151C42×C61—41no—
152#11758198—24no—
153#11758198—41no—
154#11758198—41no—
155C4⋊Dic61—42no—
156C4⋊Dic61—42no—
157C4⋊Dic61—42no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161#11758196—41no—
162C4×Dic61—21no—
163C4×Dic61—21no—
164#11758194—22no—
165#11758194—41no—
166#11758194—41no—
167#11758194—41no—
168C2×#92418—41no—
169C2×#92418—41no—
170#11758189—44no—
171C8×D61—44no—
172C23×C61C2×C22⋊C411yescharacteristic
173C22×D61—21no—
174C22×D61—21no—
175C22×D61—22no—
176C22×D61—41no—
177C22×D61#9911yescharacteristic
178C22×D61#9911yescharacteristic
179Q8×C61—41no—
180Q8×C61—41no—
181Q8×C61—41no—
182Q8×C61—41no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—22no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—42no—
193C2×C4×C61—41no—
194C2×C4×C61C4×D411yescharacteristic
195C2×C4×C61C4×D411yescharacteristic
196C2×C4×C61#12011yescharacteristic
197C2×C4×C61#12111yescharacteristic
198C2×C4×C61#12111yescharacteristic
199C2×C4×C61#12311yescharacteristic
200C2×Dic61—21no—
201C2×Dic61—21no—
202C2×Dic61—22no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61#9912yes—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—22no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61—41no—
225C4×D61—41no—
226C4×D61—41no—
227Dic122—42no—
228Dic122—42no—
229Dic122—42no—
230Dic122—42no—
231Dic122—42no—
232Dic122—42no—
233Dic122—81no—
234Dic122—81no—
235C8×C61—42no—
236C8×C61—81no—
237#92418—42no—
238#92418—81no—
239#13094—611nomaximal, Sylow
240C22×C61—21no—
241C22×C61—21no—
242C22×C61#38611yescharacteristic
243C22×C61C2×#9911yescharacteristic
244C22×C61C2×#9911yescharacteristic
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—42no—
251C2×D61—42no—
252C2×D61#35612yescomplemented
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—42no—
260C4×C61—81no—
261Dic61—22no—
262Dic61—42no—
263Dic61—41no—
264Dic61—41no—
265Dic61—81no—
266C22×#101—611no—
267#2434—611no—
268C2×#356—611no—
269C2×#356—611no—
270#1784—611no—
271#1394—611no—
272#1394D6111yescharacteristic, complemented
273C2×C61—21no—
274C2×C61—21no—
275C2×C61#189811yescharacteristic
276C2×C61C2×#35611yescharacteristic
277C2×C61#213311yescharacteristic
278D61—22no—
279D61—41no—
280C23×Q8—611no—
281C22×M16—1221no—
282C2×C4⋊Q8—611no—
283C2×C4⋊Q8—611no—
284C2×C22⋊Q8—611no—
285C2×#101—611no—
286C2×#101—611no—
287C2×#101—1222no—
288C2×#101—1221no—
289C2×#101—1222no—
290C2×#101—1221no—
291C2×#101C2×D6111yescharacteristic
292C2×#101C2×D6111yescharacteristic
293#407—1221no—
294#395—1221no—
295#395—1221no—
296#391—611no—
297#391C2×D6111yescharacteristic
298#385—1221no—
299#385—1221no—
300C4×C22⋊C4—611no—
301#356—1222no—
302#356—1222no—
303C61#1309411yescharacteristic, complemented, Sylow
304C22×Q8—611no—
305C22×Q8—611no—
306C22×Q8—611no—
307C22×Q8—611no—
308C22×Q8—1221no—
309C22×Q8—1221no—
310C22×Q8—1221no—
311C22×Q8—1221no—
312C22×Q8—2441no—
313C22×Q8—2441no—
314C22×Q8—2442no—
315C22×Q8C22×D6111yescharacteristic
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C2×M16—21no—
320C2×M16—21no—
321C2×M16—1224no—
322C2×M16—1221no—
323C2×M16—1221no—
324C2×M16—2441no—
325C2×M16—2442no—
326C22×C8—2441no—
327C4⋊Q8—1221no—
328C4⋊Q8—1221no—
329C4⋊Q8—1221no—
330C4⋊Q8—1221no—
331C4⋊Q8—2442no—
332C22⋊Q8—2441no—
333C22⋊Q8—2441no—
334C2×C4⋊C4—1221no—
335C2×C4⋊C4—1221no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4—1221no—
338C2×C4⋊C4—1221no—
339C2×C4⋊C4C4×D6111yescharacteristic
340C2×C22⋊C4—1221no—
341C2×C22⋊C4—1221no—
342C2×C42—611no—
343C2×C42C4×D6111yescharacteristic
344#101—21no—
345#101—21no—
346#101—21no—
347#101—612no—
348#101—1224no—
349#101—1221no—
350#101—1221no—
351#101—1221no—
352#101—2442no—
353#101D24412yes—
354C22⋊C8—2441no—
355C22⋊C8—2441no—
356#95—21no—
357#95—21no—
358#95—1221no—
359#95—1221no—
360#95—1221no—
361C24—611no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—1222no—
365C2×Q8—1222no—
366C2×Q8—1221no—
367C2×Q8—1221no—
368C2×Q8—1221no—
369C2×Q8—1221no—
370C2×Q8—1221no—
371C2×Q8—1221no—
372C2×Q8—1221no—
373C2×Q8—1221no—
374C2×Q8—2441no—
375C2×Q8—2441no—
376C2×Q8—2441no—
377C2×Q8—2441no—
378C2×Q8—2441no—
379C2×Q8—2441no—
380C2×Q8—2442no—
381C2×Q8—2442no—
382C2×Q8—2442no—
383C2×Q8—2442no—
384C2×Q8—2442no—
385C2×Q8—2442no—
386C2×Q8—2442no—
387C2×Q8—2442no—
388C2×Q8C2×D24411yescharacteristic
389C2×Q8#1175822211yescharacteristic
390C2×Q8D4×D6111yescharacteristic
391C2×Q8#1175822611yescharacteristic
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—1222no—
398C22×C4—1221no—
399C22×C4—1221no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—1221no—
405C22×C4—1221no—
406C22×C4—1221no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4—1221no—
410C22×C4—1221no—
411C22×C4—1221no—
412C22×C4—2441no—
413C22×C4—2441no—
414C22×C4C2×C4×D6111yescharacteristic
415C22×C4D4×D6111yescharacteristic
416C22×C4D4×D6111yescharacteristic
417M16—22no—
418M16—41no—
419M16—41no—
420M16—41no—
421M16—1222no—
422M16—2444no—
423M16—2441no—
424M16—2441no—
425M16—2441no—
426C2×C8—41no—
427C2×C8—41no—
428C2×C8—2444no—
429C2×C8—2441no—
430C2×C8—2441no—
431C4⋊C4—41no—
432C4⋊C4—2442no—
433C4⋊C4—2442no—
434C4⋊C4—2442no—
435C4⋊C4—2441no—
436C4⋊C4—2441no—
437C4⋊C4—2441no—
438C4⋊C4—2441no—
439C22⋊C4—1224no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C42—41no—
443C42—1221no—
444C42—1221no—
445C23—611no—
446C23—611no—
447C23—1222no—
448C23—1221no—
449C23—1221no—
450C23—2441no—
451C23C22⋊C4×D6111yescharacteristic
452Q8—41no—
453Q8—41no—
454Q8—41no—
455Q8—41no—
456Q8—4881no—
457Q8—4881no—
458Q8—2442no—
459Q8—2442no—
460Q8—2442no—
461Q8—2442no—
462Q8—2442no—
463Q8—2442no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—612no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1222no—
483C2×C4—1221no—
484C2×C4—1221no—
485C2×C4—1221no—
486C2×C4—1221no—
487C2×C4—1221no—
488C2×C4—1221no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4#1451973911yescharacteristic
503C2×C4C4×D24411yescharacteristic
504C2×C4#1451974711yescharacteristic
505C2×C4#1451975011yescharacteristic
506C2×C4#1451975211yescharacteristic
507C2×C4#1451976211yescharacteristic
508C8—42no—
509C8—81no—
510C8—4881no—
511C8—2442no—
512C22—21no—
513C22—21no—
514C22—612no—
515C22—1221no—
516C22—1221no—
517C22—1221no—
518C22—1221no—
519C22—1221no—
520C22—2442no—
521C22—2442no—
522C22#1683964011yescharacteristic
523C22#99×D6111yescharacteristic
524C22#99×D6111yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—42no—
532C4—81no—
533C4—1222no—
534C4—4881no—
535C4—2442no—
536C4—2441no—
537C4—2441no—
538C2—21no—
539C2—21no—
540C2—1222no—
541C2—2441no—
542C2#2144627111yescharacteristic
543C2#356×D6111yescharacteristic
544C2#2144750511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1394C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC22×Q8×C61C23
hypercenter#1394D61
hypocenterC61#13094
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
3. C2×#16839560C2semidirect
4. C2×#16839560C2semidirect
6. #21443946C2semidirect
7. C61×#1394C2semidirect
252. C2×D61#356semidirect
272. #1394D61semidirect
303. C61#13094semidirect

Maximal subgroups

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

subgroupindex
C2×#101×D612
#214494622
C2×#168395602
#214457412
#214439462
C61×#13942
#1309461