Finite Group Databasebeta

← #29697384

Subgroups — #29697384

Order 15616.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454477C211yesmaximal, characteristic, complemented
2#21454268C211yesmaximal, characteristic
3#21446532C211yesmaximal, characteristic, complemented
4#21446525C211yesmaximal, characteristic, complemented
5#21446469C211yesmaximal, characteristic, complemented
6#21446469C211yesmaximal, characteristic, complemented
7#21446096C211yesmaximal, characteristic, complemented
8#21446096C211yesmaximal, characteristic, complemented
9#21445918C211yesmaximal, characteristic, complemented
10#21445861C211yesmaximal, characteristic, complemented
11#21445763C211yesmaximal, characteristic
12#21445666C211yesmaximal, characteristic, complemented
13#21445659C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C61×#2896C211yesmaximal, characteristic
16C2×#14519784C2211yescharacteristic
17C2×#14519784C2211yescharacteristic
18#16839823—21no—
19#16839823—21no—
20#16839819—21no—
21#16839815—21no—
22C2×#14519713C2211yescharacteristic, complemented
23C2×#14519713C2211yescharacteristic, complemented
24#16839789C2211yescharacteristic, complemented
25#16839789C2211yescharacteristic, complemented
26C2×#14519704C2211yescharacteristic
27C2×#14519704C2211yescharacteristic
28C2×#14519704C2211yescharacteristic
29C2×#14519704C2211yescharacteristic
30#16839729—21no—
31#16839729—21no—
32#16839729C2211yescharacteristic
33#16839729C2211yescharacteristic
34#16839726—21no—
35#16839726C2211yescharacteristic
36#16839726C2211yescharacteristic
37C2×C22⋊#92418—21no—
38C2×C22⋊#92418C2211yescharacteristic
39#16839718C2211yescharacteristic, complemented
40#16839718C2211yescharacteristic, complemented
41C2×#14519687C2211yescharacteristic, complemented
42C2×C8×Dic61C2211yescharacteristic, complemented
43C4×C22⋊Dic61C2211yescharacteristic
44#16839527C2211yescharacteristic, complemented
45#16839527C2211yescharacteristic, complemented
46#16839521C2211yescharacteristic, complemented
47#16839521C2211yescharacteristic, complemented
48#16839521C2211yescharacteristic, complemented
49#16839521C2211yescharacteristic, complemented
50#16839516C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52C22×#41×C61C2211yescharacteristic
53C22×M16×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C61×#419C411yescharacteristic, complemented
56C61×#419C411yescharacteristic, complemented
57C61×#418C411yescharacteristic, complemented
58C61×#418C411yescharacteristic, complemented
59C61×#417C411yescharacteristic, complemented
60C61×#417C411yescharacteristic, complemented
61C61×#417C411yescharacteristic, complemented
62C61×#417C411yescharacteristic, complemented
63C61×#416C2211yescharacteristic
64C61×#416C2211yescharacteristic
65C61×#416C2211yescharacteristic
66C61×#416C2211yescharacteristic
67#14519784—22no—
68#14519784—22no—
69#14519784—41no—
70#14519784—41no—
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758194C2311yescharacteristic
74C2×#11758194C2311yescharacteristic
75C2×#11758194C2311yescharacteristic
76C2×#11758194C2311yescharacteristic
77C22×#92418—21no—
78C22×#92418—21no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C2×C22⋊Dic61—21no—
82C2×C4×Dic61C2311yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84#14519713—41no—
85#14519713—41no—
86C4⋊#92418—21no—
87C4⋊#92418—21no—
88C4⋊#92418—21no—
89C4⋊#92418—21no—
90#14519704—22no—
91#14519704—22no—
92#14519704—41no—
93#14519704—41no—
94C22⋊#92418—21no—
95C22⋊#92418—21no—
96C22⋊#92418—21no—
97C22⋊#92418—21no—
98C22⋊#92418—21no—
99C22⋊#92418—21no—
100C22⋊#92418—21no—
101C22⋊#92418—21no—
102C22⋊#92418D411yescharacteristic
103C22⋊#92418D411yescharacteristic
104C22⋊#92418D411yescharacteristic
105C22⋊#92418D411yescharacteristic
106#14519688—21no—
107#14519688—21no—
108#14519687—41no—
109C4×#92418—21no—
110C4×#92418—21no—
111C8×Dic61—41no—
112#14519684—21no—
113C2×#41×C61—21no—
114C2×#41×C61—21no—
115C2×#41×C61—22no—
116C2×#41×C61—22no—
117C2×#41×C61—41no—
118C2×#41×C61—41no—
119C2×#41×C61C2×C411yescharacteristic
120C2×#41×C61C2×C411yescharacteristic
121C2×#41×C61C2311yescharacteristic
122C2×#41×C61C2311yescharacteristic
123C22×Q8×C61C2×C411yescharacteristic
124C22×D4×C61—21no—
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128C2×M16×C61—41no—
129C2×M16×C61—41no—
130C2×M16×C61C2×C411yescharacteristic
131C2×M16×C61C2×C411yescharacteristic
132C2×M16×C61C2×C411yescharacteristic
133C2×M16×C61C2×C411yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136#117×C61—21no—
137#117×C61—21no—
138#117×C61C2×C411yescharacteristic
139#117×C61C2×C411yescharacteristic
140#117×C61C2311yescharacteristic
141#117×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2×C411yescharacteristic
143C2×C4⋊C4×C61C2×C411yescharacteristic
144C2×C22⋊C4×C61—21no—
145C2×C42×C61—21no—
146#103×C61C2×C411yescharacteristic
147#103×C61C2×C411yescharacteristic
148#103×C61C2×C411yescharacteristic
149#103×C61C2×C411yescharacteristic
150#103×C61C2×C411yescharacteristic
151#103×C61C2×C411yescharacteristic
152#103×C61C2×C411yescharacteristic
153#103×C61C2×C411yescharacteristic
154#102×C61C2×C411yescharacteristic
155#102×C61C2×C411yescharacteristic
156#102×C61C2×C411yescharacteristic
157#102×C61C2×C411yescharacteristic
158#102×C61C2×C411yescharacteristic
159#102×C61C2×C411yescharacteristic
160#102×C61C2×C411yescharacteristic
161#102×C61C2×C411yescharacteristic
162C24×C61—21no—
163C24×C61#4111yescharacteristic
164#41×C61—21no—
165#41×C61—21no—
166#41×C61—22no—
167#41×C61—22no—
168#41×C61—21no—
169#41×C61—21no—
170#41×C61—21no—
171#41×C61—21no—
172#41×C61—42no—
173#41×C61—42no—
174#41×C61—41no—
175#41×C61—41no—
176#41×C61—42no—
177#41×C61—42no—
178#41×C61#4112yes—
179#41×C61#4112yes—
180C2×Q8×C61—21no—
181C2×Q8×C61—22no—
182C2×Q8×C61—41no—
183C2×Q8×C61C22×C411yescharacteristic
184C2×Q8×C61C22×C411yescharacteristic
185C2×D4×C61—21no—
186C2×D4×C61—22no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—41no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61C22×C411yescharacteristic
195C2×D4×C61C22×C411yescharacteristic
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—42no—
208C22×C4×C61—42no—
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61#4111yescharacteristic
214C22×C4×C61C2411yescharacteristic
215C22×Dic61—21no—
216C22×Dic61—21no—
217M16×C61—41no—
218M16×C61—41no—
219M16×C61—41no—
220M16×C61—41no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61C22×C411yescharacteristic
226C2×C8×C61C22×C411yescharacteristic
227C2×C8×C61C22×C411yescharacteristic
228C2×C8×C61C22×C411yescharacteristic
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C22×C411yescharacteristic
232C4⋊C4×C61C22×C411yescharacteristic
233C4⋊C4×C61C22×C411yescharacteristic
234C4⋊C4×C61C22×C411yescharacteristic
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C42×C61—21no—
240C42×C61—21no—
241C42×C61—21no—
242C42×C61—21no—
243C22⋊Dic61—42no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248#11758194—21no—
249#11758194—21no—
250#11758194—21no—
251#11758194—21no—
252#11758194—21no—
253#11758194—21no—
254#11758194—21no—
255#11758194—21no—
256#11758194—42no—
257#11758194—42no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—42no—
267C2×#92418—42no—
268C2×#92418C2×D411yescharacteristic
269C2×#92418C2×D411yescharacteristic
270C2×#92418C2×D411yescharacteristic
271C2×#92418C2×D411yescharacteristic
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—81no—
281C23×C61C4×D411yescharacteristic
282C23×C61C4×D411yescharacteristic
283C23×C61C2×#4111yescharacteristic
284Q8×C61—21no—
285Q8×C61—21no—
286Q8×C61—21no—
287Q8×C61—42no—
288Q8×C61#11712yes—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—21no—
292D4×C61—21no—
293D4×C61—21no—
294D4×C61—42no—
295D4×C61—42no—
296D4×C61—42no—
297D4×C61—41no—
298D4×C61—41no—
299D4×C61#11712yes—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—81no—
325C2×C4×C61C4×D411yescharacteristic
326C2×C4×C61C4×D411yescharacteristic
327C2×C4×C61C23×C411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C2×Dic61—22no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C8×C61—21no—
340C8×C61—21no—
341C8×C61—21no—
342C8×C61—21no—
343#92418—21no—
344#92418—21no—
345#92418—21no—
346#92418—21no—
347#92418—41no—
348#92418—41no—
349#92418—41no—
350#92418—41no—
351#22588—611nomaximal, Sylow
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—22no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—84no—
369C22×C61C2×C4×D411yescharacteristic
370C22×C61#55111yescharacteristic
371C22×C61#55111yescharacteristic
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—22no—
375C4×C61—41no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61C2×#11711yescharacteristic
381C4×C61#51811yescharacteristic
382C4×C61#54611yescharacteristic
383C4×C61#54611yescharacteristic
384Dic61—42no—
385Dic61—81no—
386#2924—611no—
387#2896D6111yescharacteristic
388#2880—611no—
389#1938—611no—
390#1937—611no—
391#1929—611no—
392#1929—611no—
393#1866—611no—
394#1866—611no—
395#1826—611no—
396#1811—611no—
397#1789—611no—
398#1765—611no—
399#1764—611no—
400#1753—611no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—41no—
404C2×C61—41no—
405C2×C61—42no—
406C2×C61—81no—
407C2×C61#234211yescharacteristic
408C2×C61#295511yescharacteristic
409C2×C61#295611yescharacteristic
410C22×#41C2×D6111yescharacteristic
411C2×#131—611no—
412C2×#131—611no—
413C22×M16C2×D6111yescharacteristic
414C2×#117C2×D6111yescharacteristic
415#433—1221no—
416#433—1221no—
417#432—1221no—
418#431—1221no—
419C2×#108—611no—
420C2×#108—611no—
421#424—611no—
422#424—611no—
423C2×#104—611no—
424C2×#104—611no—
425C2×#104—611no—
426C2×#104—611no—
427#419Dic6111yescharacteristic, complemented
428#419Dic6111yescharacteristic, complemented
429#418Dic6111yescharacteristic, complemented
430#418Dic6111yescharacteristic, complemented
431#417Dic6111yescharacteristic, complemented
432#417Dic6111yescharacteristic, complemented
433#417Dic6111yescharacteristic, complemented
434#417Dic6111yescharacteristic, complemented
435#416C2×D6111yescharacteristic
436#416C2×D6111yescharacteristic
437#416C2×D6111yescharacteristic
438#416C2×D6111yescharacteristic
439#408—611no—
440#408—611no—
441#408—1221no—
442#408—1221no—
443#407—611no—
444#407—611no—
445#407—1221no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—1221no—
448#405—611no—
449#405—611no—
450C2×#97—611no—
451C2×C4×C8—611no—
452C4×C22⋊C4—611no—
453#341—611no—
454#341—611no—
455#339—611no—
456#339—611no—
457#339—611no—
458#339—611no—
459#336—611no—
460#336—611no—
461C61#2258811yescharacteristic, complemented, Sylow
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×Dic6111yescharacteristic
469C2×#41C2×Dic6111yescharacteristic
470C2×#41C22×D6111yescharacteristic
471C2×#41C22×D6111yescharacteristic
472C22×Q8C2×Dic6111yescharacteristic
473C22×D4—21no—
474C22×D4C2×Dic6111yescharacteristic
475C23×C4—21no—
476C23×C4C22×D6111yescharacteristic
477#131—1222no—
478#131—1222no—
479#131—2441no—
480#131—2441no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—611no—
484C2×M16—611no—
485C2×M16—611no—
486C2×M16—611no—
487C2×M16—1221no—
488C2×M16—1221no—
489C2×M16C2×Dic6111yescharacteristic
490C2×M16C2×Dic6111yescharacteristic
491C2×M16C2×Dic6111yescharacteristic
492C2×M16C2×Dic6111yescharacteristic
493C22×C8—611no—
494C22×C8—611no—
495C22×C8—1221no—
496C22×C8—1221no—
497C22×C8C22×D6111yescharacteristic
498C22×C8C22×D6111yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×Dic6111yescharacteristic
502#117C2×Dic6111yescharacteristic
503#117C22×D6111yescharacteristic
504#117C22×D6111yescharacteristic
505C2×C4⋊C4C2×Dic6111yescharacteristic
506C2×C4⋊C4C2×Dic6111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1221no—
509C2×C42—21no—
510C2×C42—611no—
511C2×C42—611no—
512#108—2441no—
513#108—2441no—
514C4⋊C8—1221no—
515C4⋊C8—1221no—
516C4⋊C8—1221no—
517C4⋊C8—1221no—
518#104—1222no—
519#104—1222no—
520#104—2441no—
521#104—2441no—
522#103C2×Dic6111yescharacteristic
523#103C2×Dic6111yescharacteristic
524#103C2×Dic6111yescharacteristic
525#103C2×Dic6111yescharacteristic
526#103C2×Dic6111yescharacteristic
527#103C2×Dic6111yescharacteristic
528#103C2×Dic6111yescharacteristic
529#103C2×Dic6111yescharacteristic
530#102C2×Dic6111yescharacteristic
531#102C2×Dic6111yescharacteristic
532#102C2×Dic6111yescharacteristic
533#102C2×Dic6111yescharacteristic
534#102C2×Dic6111yescharacteristic
535#102C2×Dic6111yescharacteristic
536#102C2×Dic6111yescharacteristic
537#102C2×Dic6111yescharacteristic
538C22⋊C8—611no—
539C22⋊C8—611no—
540C22⋊C8—611no—
541C22⋊C8—611no—
542C22⋊C8—1221no—
543C22⋊C8—1221no—
544C22⋊C8—1221no—
545C22⋊C8—1221no—
546C22⋊C8—1221no—
547C22⋊C8—1221no—
548C22⋊C8—1221no—
549C22⋊C8—1221no—
550#97—1221no—
551#97—1221no—
552#97—2441no—
553C4×C8—1221no—
554C4×C8—1221no—
555C4×C8—2441no—
556#95—1221no—
557C24—21no—
558C24#1175822411yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1175822212yes—
574#41#1175822212yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×Dic6111yescharacteristic
579C2×Q8C22×Dic6111yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×Dic6111yescharacteristic
590C2×D4C22×Dic6111yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4D4×D6111yescharacteristic
607C22×C4D4×D6111yescharacteristic
608C22×C4#1175822411yescharacteristic
609C22×C4C22×Dic6111yescharacteristic
610C22×C4C22×Dic6111yescharacteristic
611C22×C4C23×D6111yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—1221no—
617M16—1221no—
618M16—1221no—
619M16—1221no—
620M16—1221no—
621M16—1221no—
622M16—1221no—
623M16—1221no—
624M16—2442no—
625M16—2442no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—611no—
631C2×C8—611no—
632C2×C8—611no—
633C2×C8—611no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—2442no—
643C2×C8—2442no—
644C2×C8C22×Dic6111yescharacteristic
645C2×C8C22×Dic6111yescharacteristic
646C2×C8C22×Dic6111yescharacteristic
647C2×C8C22×Dic6111yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×Dic6111yescharacteristic
651C4⋊C4C22×Dic6111yescharacteristic
652C4⋊C4C22×Dic6111yescharacteristic
653C4⋊C4C22×Dic6111yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—2442no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1221no—
664C42—1221no—
665C42—1221no—
666C42—1221no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23D4×Dic6111yescharacteristic
677C23D4×Dic6111yescharacteristic
678C23C2×#1175822411yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1451973612yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1451973612yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—1222no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4D4×Dic6111yescharacteristic
727C2×C4D4×Dic6111yescharacteristic
728C2×C4C23×Dic6111yescharacteristic
729C2×C4C2×D4×D6111yescharacteristic
730C2×C4C2×#1175822211yescharacteristic
731C2×C4C2×#1175822211yescharacteristic
732C2×C4#1451982211yescharacteristic
733C2×C4#1451982211yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—1221no—
739C8—1221no—
740C8—1221no—
741C8—1221no—
742C8—2441no—
743C8—2441no—
744C8—2441no—
745C8—2441no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×D4×Dic6111yescharacteristic
764C22#1684043811yescharacteristic
765C22#1684043811yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—4881no—
775C4—2442no—
776C4C2×#1451973611yescharacteristic
777C4#1684023711yescharacteristic
778C4#1684040211yescharacteristic
779C4#1684040211yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2144866811yescharacteristic
787C2#2145472211yescharacteristic
788C2#2145472911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2896C2
socleC22×C61C2×C4×D4
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenter#2896D61
hypocenterC61#22588
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #21454477C2semidirect
3. #21446532C2semidirect
4. #21446525C2semidirect
5. #21446469C2semidirect
6. #21446469C2semidirect
7. #21446096C2semidirect
8. #21446096C2semidirect
9. #21445918C2semidirect
10. #21445861C2semidirect
12. #21445666C2semidirect
13. #21445659C2semidirect
14. #21445600C2semidirect
22. C2×#14519713C22semidirect
23. C2×#14519713C22semidirect
24. #16839789C22semidirect
25. #16839789C22semidirect
39. #16839718C22semidirect
40. #16839718C22semidirect
41. C2×#14519687C22semidirect
42. C2×C8×Dic61C22semidirect
44. #16839527C22semidirect
45. #16839527C22semidirect
46. #16839521C22semidirect
47. #16839521C22semidirect
48. #16839521C22semidirect
49. #16839521C22semidirect
50. #16839516C22semidirect
51. #16839516C22semidirect
55. C61×#419C4semidirect
56. C61×#419C4semidirect
57. C61×#418C4semidirect
58. C61×#418C4semidirect
59. C61×#417C4semidirect
60. C61×#417C4semidirect
61. C61×#417C4semidirect
62. C61×#417C4semidirect
427. #419Dic61semidirect
428. #419Dic61semidirect
429. #418Dic61semidirect
430. #418Dic61semidirect
431. #417Dic61semidirect
432. #417Dic61semidirect
433. #417Dic61semidirect
434. #417Dic61semidirect
461. C61#22588semidirect

Maximal subgroups

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

subgroupindex
#214544772
#214542682
#214465322
#214465252
#214464692
#214460962
#214459182
#214458612
#214457632
#214456662
#214456592
#214456002
C61×#28962
#2258861