Finite Group Databasebeta

← C2×#21456482 #30549876

Subgroups — C2×#21456482 #30549876

Order 15616.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840379C211yesmaximal, characteristic
2C2×#16840372C211yesmaximal, characteristic, complemented
3#21456482C2116yesmaximal, direct product factor
4C2×#16840169C211yesmaximal, characteristic, complemented
5C2×#16840153C211yesmaximal, characteristic, complemented
6C2×#16840115C211yesmaximal, characteristic, complemented
7C2×#16840111C211yesmaximal, characteristic, complemented
8C2×#16840018C211yesmaximal, characteristic, complemented
9C2×#16840006C211yesmaximal, characteristic
10C2×#16840003C211yesmaximal, characteristic, complemented
11C2×#16839868C211yesmaximal, characteristic, complemented
12C2×#16839863C211yesmaximal, characteristic, complemented
13C2×#16839854C211yesmaximal, characteristic, complemented
14C2×#16839853C211yesmaximal, characteristic, complemented
15C2×#16839717C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21#16840379—24no—
22#16840379C2218yes—
23#16840372—24no—
24#16840372C2218yescomplemented
25C2×#14519776C2211yescharacteristic
26C2×#14519775C2211yescharacteristic
27C2×#14519770—21no—
28C2×#14519770—21no—
29C2×#14519770—21no—
30C2×#14519768—21no—
31C2×#14519768C2211yescharacteristic
32C2×#14519767—21no—
33C2×#14519764—21no—
34C2×#14519764C2211yescharacteristic
35C2×#14519758—21no—
36C2×#14519756C2211yescharacteristic
37C2×#14519756C2211yescharacteristic
38C2×#14519754—21no—
39C2×Q8×Dic61C2211yescharacteristic
40C2×#14519742C2211yescharacteristic
41C2×#14519742C2211yescharacteristic
42C2×D4×Dic61C2211yescharacteristic
43C2×#14519736C2211yescharacteristic
44#16840169C2218yescomplemented
45#16840153C2218yescomplemented
46#16840115C2218yescomplemented
47#16840111C2218yescomplemented
48#16840018C2218yescomplemented
49#16840006C2218yes—
50#16840003C2218yescomplemented
51#16839868C2218yescomplemented
52#16839863C2218yescomplemented
53#16839854C2218yescomplemented
54#16839853C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64#16839717C2218yescomplemented
65C2×#14519687C2211yescharacteristic
66C2×#14519687C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#465C2218yes—
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C23×Dic61—21no—
81C2×Dic244—24no—
82C2×Dic244C2314yes—
83C2×#11758202—24no—
84C2×#11758202C2314yes—
85C2×#11758200—24no—
86C2×#11758200C2314yes—
87C2×#11758194—24no—
88C2×#11758194C2314yes—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91#14519776—22no—
92#14519776C2314yes—
93#14519775—22no—
94#14519775C2314yes—
95#14519770—28no—
96#14519770—28no—
97#14519770—28no—
98#14519768—28no—
99#14519768—22no—
100#14519768C2314yes—
101#14519767—28no—
102#14519764—28no—
103#14519764—22no—
104#14519764C2314yes—
105#14519758—28no—
106#14519756—22no—
107#14519756—22no—
108#14519756C2314yes—
109#14519756C2314yes—
110#14519754—28no—
111Q8×Dic61—22no—
112Q8×Dic61C2314yes—
113#14519742—22no—
114#14519742—22no—
115#14519742C2314yes—
116#14519742C2314yes—
117D4×Dic61—22no—
118D4×Dic61C2314yes—
119#14519736D414yes—
120#14519736C2314yes—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61D411yescharacteristic
124C2×C4⋊Dic61D411yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61D411yescharacteristic
141C2×C22⋊Dic61D411yescharacteristic
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61C2311yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147#14519711C2314yes—
148#14519710C2314yes—
149#14519708C2314yes—
150#14519702C2314yes—
151#14519702C2314yes—
152#14519701C2314yes—
153#14519700C2314yes—
154#14519700C2314yes—
155#14519698C2314yes—
156#14519687C2314yes—
157#14519687C2314yes—
158C8×Dic61C2314yes—
159C8×Dic61C2314yes—
160C22×Q8×C61C2311yescharacteristic
161C22×D4×C61—21no—
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C2×SD16×C61—24no—
165C2×SD16×C61C2314yes—
166C22×C8×C61—24no—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2314yes—
169C22×C8×C61C2311yescharacteristic
170C22⋊Q8×C61—22no—
171C22⋊Q8×C61C2314yes—
172#121×C61—22no—
173#121×C61C2314yes—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179#106×C61C2314yes—
180#103×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C2×Q8×C61—21no—
185C2×Q8×C61—22no—
186C2×Q8×C61—22no—
187C2×Q8×C61C2412yes—
188C2×D4×C61—24no—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—82no—
193C2×D4×C61C2412yes—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2411yescharacteristic
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—24no—
208C22×Dic61—82no—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C2×Dic122—22no—
214C2×Dic122—22no—
215C2×Dic122—22no—
216C2×Dic122—22no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—24no—
220C2×Dic122—82no—
221C2×Dic122C2412yes—
222C2×Dic122C2412yes—
223SD16×C61—28no—
224C2×C8×C61—22no—
225C2×C8×C61—28no—
226C2×C8×C61#4114yes—
227C2×C8×C61C2412yes—
228C2×C8×C61C2412yes—
229C4⋊C4×C61—24no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C2412yes—
233C4⋊C4×C61C2412yes—
234C22⋊C4×C61—24no—
235C22⋊C4×C61—24no—
236C22⋊Dic61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61—24no—
239C22⋊Dic61—24no—
240C22⋊Dic61—24no—
241C22⋊Dic61C2×D414yes—
242C22⋊Dic61C2×D414yes—
243#11758202—28no—
244#11758200—28no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—24no—
248C4⋊Dic61—24no—
249C4⋊Dic61C2×D414yes—
250C4⋊Dic61C2×D414yes—
251C4⋊Dic61C2412yes—
252C4⋊Dic61C2412yes—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261C4×Dic61—24no—
262C4×Dic61—24no—
263C4×Dic61—24no—
264C4×Dic61C2×D412yes—
265C4×Dic61C2×D412yes—
266C4×Dic61C2412yes—
267C4×Dic61C2412yes—
268#11758194—28no—
269C2×#92418—22no—
270C2×#92418#4114yes—
271C2×#92418C2412yes—
272C2×#92418C2412yes—
273Dic244—28no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61C22×D412yes—
282C23×C61C22×D411yescharacteristic
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—42no—
286D4×C61—22no—
287D4×C61—22no—
288D4×C61—42no—
289D4×C61—84no—
290C2×C4×C61—22no—
291C2×C4×C61—24no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61C22×D412yes—
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4112yes—
303C2×C4×C61C2×#4112yes—
304C2×C4×C61C2511yescharacteristic
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—84no—
318C2×Dic61C22×D412yes—
319C2×Dic61C22×D412yes—
320C2×Dic61C22×D412yes—
321C2×Dic61C22×D412yes—
322Dic122—22no—
323Dic122—22no—
324Dic122—22no—
325Dic122—22no—
326Dic122—42no—
327Dic122—42no—
328Dic122—84no—
329C8×C61—22no—
330C8×C61C2×#4114yes—
331#92418—22no—
332#92418C2×#4114yes—
333C2×#3178—611nomaximal, Sylow
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—44no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—84no—
342C22×C61#53212yes—
343C22×C61#57712yes—
344C22×C61#57812yes—
345C22×C61C23×D411yescharacteristic
346C4×C61—22no—
347C4×C61—42no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61#53212yes—
351C4×C61C22×#4111yescharacteristic
352C4×C61C22×#4111yescharacteristic
353Dic61—22no—
354Dic61—22no—
355Dic61—22no—
356Dic61—22no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#542—611no—
362C2×#541—611no—
363#3178—6116no—
364C2×#501—611no—
365C2×#497—611no—
366C2×#488—611no—
367C2×#487—611no—
368C2×#470—611no—
369C2×#468—611no—
370C2×#467—611no—
371C2×#465D6111yescharacteristic
372C2×#441—611no—
373C2×#440—611no—
374C2×C4×Q16—611no—
375C2×C4×SD16—611no—
376C2×#405—611no—
377C2×C61—42no—
378C2×C61—82no—
379C2×C61#317814yescomplemented
380C2×C61C2×#53211yescharacteristic
381C2×C61C2×#57711yescharacteristic
382C2×C61C2×#57811yescharacteristic
383C22×Q16—611no—
384C22×Q16—611no—
385C22×SD16—611no—
386C22×SD16C2×D6111yescharacteristic
387C22×M16—611no—
388C23×C8C2×D6111yescharacteristic
389#542—618no—
390#542—1224no—
391#541—618no—
392#541—1224no—
393C2×C4⋊Q8—611no—
394C2×C4⋊Q8—611no—
395C2×#126—1221no—
396C2×#126—1221no—
397C2×#126—1221no—
398C2×#125—611no—
399C2×#125—1221no—
400C2×#125—1221no—
401C2×#124—611no—
402C2×#124—1221no—
403C2×#123—1221no—
404C2×C22⋊Q8—611no—
405C2×C22⋊Q8—611no—
406C2×C22⋊Q8—1221no—
407C2×C22⋊Q8C2×D6111yescharacteristic
408C2×#121C2×D6111yescharacteristic
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×Q8—611no—
412C2×C4×D4—611no—
413C2×#117—611no—
414#501—618no—
415#497—618no—
416#488—618no—
417#487—618no—
418#470—618no—
419#468—618no—
420#467—618no—
421#465C2×D6118yes—
422#441—618no—
423#440—618no—
424C4×Q16—618no—
425C4×SD16—618no—
426C2×#107—611no—
427C2×#107—611no—
428C2×#106—611no—
429C2×#106C2×D6111yescharacteristic
430C2×#103—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103C2×D6111yescharacteristic
436C2×#102—611no—
437C2×#102C2×D6111yescharacteristic
438#405—618no—
439C2×#97—611no—
440C2×#97—611no—
441C2×C4×C8—611no—
442C2×C4×C8—611no—
443C61C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—611no—
445C22×Q8—611no—
446C22×Q8—1221no—
447C22×Q8C22×D6111yescharacteristic
448C22×D4—21no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—1221no—
451C23×C4C22×D6111yescharacteristic
452C2×Q16—614no—
453C2×Q16—614no—
454C2×Q16—1224no—
455C2×Q16—1224no—
456C2×SD16—24no—
457C2×SD16—614no—
458C2×SD16—1224no—
459C2×SD16C22×D6114yes—
460C2×M16—614no—
461C2×M16—1224no—
462C22×C8—24no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8C22×D6111yescharacteristic
466C22×C8C22×D6114yes—
467C22×C8C22×D6111yescharacteristic
468C4⋊Q8—614no—
469C4⋊Q8—614no—
470C4⋊Q8—1222no—
471C4⋊Q8—1222no—
472#126—1228no—
473#126—1228no—
474#126—1228no—
475#125—614no—
476#125—1222no—
477#125—1228no—
478#125—1228no—
479#124—614no—
480#124—1222no—
481#124—1228no—
482#123—1228no—
483C22⋊Q8—22no—
484C22⋊Q8—614no—
485C22⋊Q8—614no—
486C22⋊Q8—1228no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8C22×D6114yes—
490#121—22no—
491#121C22×D6114yes—
492C4×Q8—614no—
493C4×Q8—614no—
494C4×Q8—614no—
495C4×Q8—1222no—
496C4×Q8—1222no—
497C4×Q8—1222no—
498C4×D4—614no—
499C4×D4—1222no—
500#117—614no—
501#117—614no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4C22×D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—611no—
529C2×C42—611no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42—1221no—
533#107—614no—
534#107—614no—
535#106—614no—
536#106C22×D6114yes—
537#103—614no—
538#103—614no—
539#103—614no—
540#103—614no—
541#103—614no—
542#103C22×D6114yes—
543#102—614no—
544#102C22×D6114yes—
545#97—614no—
546#97—614no—
547C4×C8—614no—
548C4×C8—614no—
549C24—21no—
550C24D4×D6111yescharacteristic
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—612no—
555C2×Q8—612no—
556C2×Q8—1224no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8—1222no—
560C2×Q8—1222no—
561C2×Q8—1222no—
562C2×Q8—1222no—
563C2×Q8—4882no—
564C2×Q8C23×D6112yes—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—82no—
570C2×D4C23×D6112yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—1224no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—4882no—
586C22×C4D4×D6112yes—
587C22×C4D4×D6111yescharacteristic
588C22×C4C23×D6112yes—
589C22×C4C23×D6111yescharacteristic
590Q16—1228no—
591Q16—1228no—
592SD16—28no—
593SD16—1228no—
594M16—1228no—
595C2×C8—22no—
596C2×C8—28no—
597C2×C8—614no—
598C2×C8—612no—
599C2×C8—612no—
600C2×C8—1222no—
601C2×C8#1175822414yes—
602C2×C8C23×D6112yes—
603C2×C8C23×D6112yes—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—614no—
608C4⋊C4—614no—
609C4⋊C4—612no—
610C4⋊C4—612no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1224no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4C23×D6112yes—
624C4⋊C4C23×D6112yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—614no—
628C22⋊C4—614no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C42—612no—
635C42—612no—
636C42—612no—
637C42—612no—
638C42—1224no—
639C42—1224no—
640C42—1224no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C2×D4×D6112yes—
649C23C2×D4×D6111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—1222no—
654Q8—1222no—
655Q8—1222no—
656Q8—1222no—
657Q8—4884no—
658Q8—2442no—
659Q8—2442no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—4884no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2442no—
691C2×C4C2×D4×D6112yes—
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4#41×D6112yes—
694C2×C4C2×#1175822412yes—
695C2×C4C24×D6111yescharacteristic
696C8—22no—
697C8—614no—
698C8—1222no—
699C8C2×#1175822414yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1684030712yes—
709C22#1684056812yes—
710C22#1684057612yes—
711C22C22×D4×D6111yescharacteristic
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—1222no—
717C4—1222no—
718C4—1222no—
719C4—1222no—
720C4—2442no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4#1684030712yes—
725C4C2×#41×D6111yescharacteristic
726C4C22×#1175822411yescharacteristic
727C2—42no—
728C2—82no—
729C2#2145648214yesdirect product factor
730C2C2×#1684030711yescharacteristic
731C2C2×#1684056811yescharacteristic
732C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC2×#465D61
hypocenterC61C2×#3178
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. C2×#16840372C2semidirect
3. #21456482C2direct (N × H)
4. C2×#16840169C2semidirect
5. C2×#16840153C2semidirect
6. C2×#16840115C2semidirect
7. C2×#16840111C2semidirect
8. C2×#16840018C2semidirect
10. C2×#16840003C2semidirect
11. C2×#16839868C2semidirect
12. C2×#16839863C2semidirect
13. C2×#16839854C2semidirect
14. C2×#16839853C2semidirect
15. C2×#16839717C2semidirect
24. #16840372C22semidirect
44. #16840169C22semidirect
45. #16840153C22semidirect
46. #16840115C22semidirect
47. #16840111C22semidirect
48. #16840018C22semidirect
50. #16840003C22semidirect
51. #16839868C22semidirect
52. #16839863C22semidirect
53. #16839854C22semidirect
54. #16839853C22semidirect
64. #16839717C22semidirect
379. C2×C61#3178semidirect
443. C61C2×#3178semidirect
729. C2#21456482direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403792
C2×#168403722
#214564822
C2×#168401692
C2×#168401532
C2×#168401152
C2×#168401112
C2×#168400182
C2×#168400062
C2×#168400032
C2×#168398682
C2×#168398632
C2×#168398542
C2×#168398532
C2×#168397172
C2×C61×#4652
C2×#317861