Finite Group Databasebeta

← #29696457

Subgroups — #29696457

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic
2C2×#16839838C211yesmaximal, characteristic
3#21448763C211yesmaximal, characteristic
4#21446778C211yesmaximal, characteristic, complemented
5#21446765C211yesmaximal, characteristic, complemented
6#21446249C211yesmaximal, characteristic, complemented
7#21446132C211yesmaximal, characteristic, complemented
8#21446128C211yesmaximal, characteristic, complemented
9#21445904C211yesmaximal, characteristic, complemented
10#21445903C211yesmaximal, characteristic, complemented
11#21445822C211yesmaximal, characteristic, complemented
12#103×Dic61C211yesmaximal, characteristic, complemented
13#21445539C211yesmaximal, characteristic, complemented
14#21445537C211yesmaximal, characteristic, complemented
15C61×#1894C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17#16840470—24no—
18#16840470C418yescomplemented
19C2×#14519776C2211yescharacteristic
20C2×#14519767—21no—
21C2×#14519757—21no—
22C2×#14519754—21no—
23C2×#14519753C2211yescharacteristic
24C2×Q8×Dic61C2211yescharacteristic
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×#14519737—21no—
27C2×#14519736C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16839838—24no—
32C2×#14519706C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839662—21no—
39#16839656—21no—
40#16839651—21no—
41#16839631C2211yescharacteristic
42#16839619C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44#16839613—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122—21no—
63C22×C22⋊D61D411yescharacteristic
64C23×Dic61—21no—
65C22×C4×D61—21no—
66C22×C4×D61C2311yescharacteristic
67C2×#11758189—22no—
68C2×#11758189—22no—
69C2×#11758189—41no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519776—22no—
73#14519776C2×C414yes—
74#14519767—28no—
75#14519757—28no—
76#14519754—28no—
77#14519753—22no—
78#14519753C2×C414yes—
79Q8×Dic61—22no—
80Q8×Dic61C2×C414yes—
81C4×C22⋊D61C2×C414yes—
82C4×C22⋊D61D414yes—
83#14519737—28no—
84#14519736—22no—
85#14519736—41no—
86#14519735—22no—
87#14519735—41no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2×C414yes—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196D411yescharacteristic
102C4⋊C4×D61—22no—
103C4⋊C4×D61C2×C414yes—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61D411yescharacteristic
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198D411yescharacteristic
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61C2311yescharacteristic
115#14519706—22no—
116#14519701—22no—
117#14519701—41no—
118C22⋊#92418—22no—
119#14519689—22no—
120C8×Dic61—22no—
121#14519684—21no—
122#14519684—21no—
123C22×Q8×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C2×M16×C61—22no—
126C2×M16×C61—22no—
127C2×M16×C61—41no—
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22⋊Q8×C61—22no—
131C22⋊Q8×C61C2×C414yes—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138#103×C61—22no—
139#103×C61—41no—
140#95×C61—21no—
141C24×C61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61C22×C412yes—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61C22⋊C414yes—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—24no—
168C22×Dic61—21no—
169C22×Dic61—81no—
170C22×Dic61—81no—
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—24no—
179C2×C4×D61—81no—
180C2×C4×D61—81no—
181C2×C4×D61C22×C412yes—
182C2×C4×D61C2×D412yes—
183C2×Dic122—24no—
184C2×Dic122—81no—
185C2×Dic122—81no—
186M16×C61—44no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61#4112yes—
193C4⋊C4×C61—24no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61C22×C412yes—
200C22⋊C4×C61—24no—
201C22⋊C4×C61—81no—
202C22⋊Dic61—42no—
203C22⋊Dic61C22⋊C414yes—
204#11758198—24no—
205#11758198—42no—
206#11758198—81no—
207#11758198C22⋊C414yes—
208C4⋊Dic61—24no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—24no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61C22×C412yes—
216C4⋊Dic61C22×C412yes—
217C4⋊Dic61#4112yes—
218#11758196—24no—
219#11758196—24no—
220#11758196—24no—
221#11758196—42no—
222#11758196—81no—
223#11758196C22⋊C414yes—
224C4×Dic61—24no—
225C4×Dic61—42no—
226C4×Dic61—42no—
227C4×Dic61—42no—
228C4×Dic61C22×C412yes—
229C4×Dic61C2×D412yes—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236#11758189—44no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61C2×C22⋊C412yes—
244C23×C61C22×D411yescharacteristic
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61C2×C22⋊C412yes—
252Q8×C61—22no—
253Q8×C61—22no—
254Q8×C61—41no—
255Q8×C61—41no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61C2×C22⋊C412yes—
275C2×C4×C61C23×C411yescharacteristic
276C2×C4×C61C22×D411yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C2×C4×C612−1+411yescharacteristic
281C22⋊D61—28no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—84no—
299C2×Dic61C2×C22⋊C412yes—
300C2×Dic61C2×C22⋊C412yes—
301C2×Dic61C2×C22⋊C412yes—
302C2×Dic61#13712yes—
303C2×Dic61#13712yes—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—84no—
309Dic122—84no—
310C8×C61—22no—
311C8×C61—41no—
312#92418—41no—
313#92418—41no—
314#22502—611nomaximal, Sylow
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61C22×C22⋊C411yescharacteristic
323C22×C61#54611yescharacteristic
324C22×C61#54711yescharacteristic
325C22×C61C2×#13711yescharacteristic
326C22×C61C2×#13711yescharacteristic
327C22×C61#57611yescharacteristic
328C22×C61#57711yescharacteristic
329C2×D61—22no—
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—41no—
333C2×D61—41no—
334C2×D61—41no—
335C2×D61—41no—
336C4×C61—22no—
337C4×C61—42no—
338C4×C61—42no—
339C4×C61—81no—
340C4×C61—81no—
341C4×C61C4×#4111yescharacteristic
342C4×C61#52011yescharacteristic
343C4×C61#54611yescharacteristic
344C4×C61#54711yescharacteristic
345Dic61—22no—
346Dic61—22no—
347Dic61—42no—
348Dic61—42no—
349Dic61—42no—
350Dic61—81no—
351Dic61#41914yes—
352C2×#554—611no—
353C2×#436—611no—
354#2354—611no—
355#1990—611no—
356#1987—611no—
357#1894—611no—
358#1894D6111yescharacteristic, complemented
359#1873—611no—
360#1873—611no—
361#1823—611no—
362#1823—611no—
363#1803—611no—
364C4×#103—611no—
365#1736—611no—
366#1736—611no—
367C2×C61—42no—
368C2×C61#233911yescharacteristic
369C2×C61C2×#41911yescharacteristic
370C2×C61#289711yescharacteristic
371C2×C61#333111yescharacteristic
372C2×C61#333311yescharacteristic
373C2×C61#335611yescharacteristic
374C2×C61#335711yescharacteristic
375D61—42no—
376C22×M16—611no—
377C22×M16C2×D6111yescharacteristic
378#554—618no—
379#554—1224no—
380C2×C4⋊Q8—611no—
381C2×#125—1221no—
382C2×C22⋊Q8—611no—
383C2×C22⋊Q8—1221no—
384C2×C22⋊Q8—1221no—
385C2×C22⋊Q8C2×D6111yescharacteristic
386C2×C4×Q8—611no—
387C2×C4×D4—611no—
388C2×C4×D4—1221no—
389C2×#117—611no—
390C2×#117—611no—
391C22×C4⋊C4—611no—
392C22×C4⋊C4—611no—
393#436—1224no—
394C2×C4⋊C8—611no—
395C2×#103—611no—
396C2×#103—611no—
397C2×#103C2×D6111yescharacteristic
398C2×#103C2×D6111yescharacteristic
399C2×C22⋊C8—611no—
400C2×C22⋊C8—611no—
401C2×C4×C8—611no—
402#390—1221no—
403#388—1221no—
404#388—1221no—
405#384—611no—
406#380—611no—
407#380C2×D6111yescharacteristic
408C4×C4⋊C4—611no—
409C4×C4⋊C4—1221no—
410#340—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417#340—611no—
418#340—611no—
419#340—611no—
420#340C2×D6111yescharacteristic
421#340C2×D6111yescharacteristic
422C61#2250211yescharacteristic, complemented, Sylow
423C22×Q8—1221no—
424C22×Q8C22×D6111yescharacteristic
425C22×D4—611no—
426C23×C4—611no—
427C23×C4—1221no—
428C23×C4—1221no—
429C23×C4C22×D6111yescharacteristic
430C2×M16—22no—
431C2×M16—22no—
432C2×M16—41no—
433C2×M16—1222no—
434C2×M16—1222no—
435C2×M16—2441no—
436C22×C8—611no—
437C22×C8—611no—
438C22×C8C22×D6111yescharacteristic
439C22×C8C22×D6111yescharacteristic
440C4⋊Q8—614no—
441C4⋊Q8—1222no—
442#125—1228no—
443C22⋊Q8—22no—
444C22⋊Q8—614no—
445C22⋊Q8—1228no—
446C22⋊Q8—1228no—
447C22⋊Q8—1222no—
448C22⋊Q8C4×D6114yes—
449C4×Q8—614no—
450C4×Q8—1222no—
451C4×D4—614no—
452C4×D4—614no—
453C4×D4—1228no—
454#117—1222no—
455#117—1222no—
456#117—2441no—
457#117—2441no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—614no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—614no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—1222no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1222no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C42—611no—
487C2×C42—1221no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491C4⋊C8—1222no—
492#103—22no—
493#103—41no—
494#103—1222no—
495#103—2441no—
496C22⋊C8—1222no—
497C22⋊C8—1222no—
498C4×C8—1222no—
499#95—21no—
500#95—1221no—
501#95—1221no—
502C24—611no—
503C24D4×D6111yescharacteristic
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—1224no—
510C2×Q8—4881no—
511C2×Q8—4881no—
512C2×Q8C2×C4×D6112yes—
513C2×D4—614no—
514C2×D4—1222no—
515C2×D4—1222no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—1224no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1224no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—4881no—
540C22×C4—4881no—
541C22×C4—4881no—
542C22×C4—4881no—
543C22×C4C2×C4×D6112yes—
544C22×C4D4×D6112yes—
545C22×C4D4×D6111yescharacteristic
546C22×C4C23×D6111yescharacteristic
547M16—44no—
548M16—2444no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8#1175822412yes—
561C4⋊C4—21no—
562C4⋊C4—24no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—614no—
568C4⋊C4—612no—
569C4⋊C4—612no—
570C4⋊C4—612no—
571C4⋊C4—1224no—
572C4⋊C4—1224no—
573C4⋊C4—1224no—
574C4⋊C4—1224no—
575C4⋊C4—1221no—
576C4⋊C4—1221no—
577C4⋊C4—1221no—
578C4⋊C4—1224no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—4881no—
582C4⋊C4—2442no—
583C4⋊C4C2×C4×D6112yes—
584C22⋊C4—24no—
585C22⋊C4—81no—
586C22⋊C4—614no—
587C22⋊C4—614no—
588C22⋊C4—1224no—
589C22⋊C4—4881no—
590C22⋊C4—2442no—
591C22⋊C4—2442no—
592C42—612no—
593C42—612no—
594C42—1224no—
595C42—2442no—
596C42—2442no—
597C42—2442no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—612no—
605C23—1221no—
606C23—1221no—
607C23—1221no—
608C23—1221no—
609C23—1221no—
610C23—1221no—
611C23C22⋊C4×D6112yes—
612C23C2×D4×D6111yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—4884no—
618D4—1228no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—612no—
638C2×C4—612no—
639C2×C4—612no—
640C2×C4—612no—
641C2×C4—612no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—4884no—
654C2×C4—4884no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4C22⋊C4×D6112yes—
665C2×C4C22×C4×D6111yescharacteristic
666C2×C4C2×D4×D6111yescharacteristic
667C2×C4#41×D6111yescharacteristic
668C2×C4C2×#1175822411yescharacteristic
669C2×C4#1451982211yescharacteristic
670C2×C4#1451982411yescharacteristic
671C8—22no—
672C8—41no—
673C8—2441no—
674C8—2441no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—1222no—
683C22—1222no—
684C22—1222no—
685C22—2441no—
686C22—2441no—
687C22—2441no—
688C22—2441no—
689C22C2×C22⋊C4×D6111yescharacteristic
690C22#1684040111yescharacteristic
691C22#1684041211yescharacteristic
692C22#137×D6111yescharacteristic
693C22#137×D6111yescharacteristic
694C22#1684056611yescharacteristic
695C22#1684057111yescharacteristic
696C4—22no—
697C4—42no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4—614no—
702C4—1222no—
703C4—1222no—
704C4—4881no—
705C4—2442no—
706C4—2442no—
707C4—2442no—
708C4C4×#1175822411yescharacteristic
709C4#1684024111yescharacteristic
710C4#1684039911yescharacteristic
711C4#1684041011yescharacteristic
712C2—42no—
713C2—2442no—
714C2#2144864511yescharacteristic
715C2#419×D6111yescharacteristic
716C2#2145434311yescharacteristic
717C2#2145813011yescharacteristic
718C2#2145815211yescharacteristic
719C2#2145842911yescharacteristic
720C2#2145844011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1894C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1894D61
hypocenterC61#22502
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #21446778C2semidirect
5. #21446765C2semidirect
6. #21446249C2semidirect
7. #21446132C2semidirect
8. #21446128C2semidirect
9. #21445904C2semidirect
10. #21445903C2semidirect
11. #21445822C2semidirect
12. #103×Dic61C2semidirect
13. #21445539C2semidirect
14. #21445537C2semidirect
15. C61×#1894C2semidirect
18. #16840470C4semidirect
358. #1894D61semidirect
422. C61#22502semidirect

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168398382
#214487632
#214467782
#214467652
#214462492
#214461322
#214461282
#214459042
#214459032
#214458222
#103×Dic612
#214455392
#214455372
C61×#18942
#2250261