Finite Group Databasebeta

← C2×#21457925 #30556598

Subgroups — C2×#21457925 #30556598

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic, complemented
2C2×#16840422C211yesmaximal, characteristic
3#21457925C2116yesmaximal, direct product factor
4C2×#16840123C211yesmaximal, characteristic, complemented
5C2×#16840082C211yesmaximal, characteristic, complemented
6C2×#16840090C211yesmaximal, characteristic, complemented
7C2×#16840046C211yesmaximal, characteristic, complemented
8C2×#16839994C211yesmaximal, characteristic, complemented
9C2×#16839986C211yesmaximal, characteristic, complemented
10C2×#16839922C211yesmaximal, characteristic, complemented
11C2×#16839916C211yesmaximal, characteristic, complemented
12C2×#16839866C211yesmaximal, characteristic, complemented
13C2×#16839831C211yesmaximal, characteristic, complemented
14C2×#16839764C211yesmaximal, characteristic, complemented
15C2×#103×D61C211yesmaximal, characteristic, complemented
16C2×C61×#470C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840470—24no—
23#16840470C2218yescomplemented
24#16840422—24no—
25#16840422C2218yes—
26C2×#14519776C2211yescharacteristic
27C2×#14519767—21no—
28C2×#14519766C2211yescharacteristic
29C2×#14519763—21no—
30C2×#14519757—21no—
31C2×#14519755—21no—
32C2×#14519754—21no—
33C2×#14519753C2211yescharacteristic
34C2×#14519752C2211yescharacteristic
35C2×#14519750—21no—
36C2×Q8×Dic61C2211yescharacteristic
37C2×#14519742C2211yescharacteristic
38C2×#14519739—21no—
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519737—21no—
41C22×C4⋊Dic61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840123C2218yescomplemented
44#16840090C2218yescomplemented
45#16840082C2218yescomplemented
46#16840046C2218yescomplemented
47#16839994C2218yescomplemented
48#16839986C2218yescomplemented
49#16839922C2218yescomplemented
50#16839916C2218yescomplemented
51#16839866C2218yescomplemented
52#16839831C2218yescomplemented
53C2×#14519708C2211yescharacteristic
54C2×#14519708C2211yescharacteristic
55C2×#14519706C2211yescharacteristic
56#16839764C2218yescomplemented
57C2×#14519702C2211yescharacteristic
58C2×#14519702C2211yescharacteristic
59C2×#14519701C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62#103×D61C2218yescomplemented
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#470C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—42no—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C2×Q8×D61—22no—
85C2×Q8×D61—24no—
86C2×Q8×D61—42no—
87C2×Q8×D61C2314yes—
88C22×D244—21no—
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61D411yescharacteristic
92C23×Dic61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61C2311yescharacteristic
97C2×#11758202—24no—
98C2×#11758202C2314yes—
99C2×#11758201—42no—
100C2×#11758201C2314yes—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—42no—
104C2×C8×D61C2314yes—
105#14519776—22no—
106#14519776C2314yes—
107#14519767—28no—
108#14519766—22no—
109#14519766C2314yes—
110#14519763—28no—
111#14519757—28no—
112#14519755—28no—
113#14519754—28no—
114#14519753—22no—
115#14519753C2314yes—
116#14519752—22no—
117#14519752C2314yes—
118#14519750—28no—
119Q8×Dic61—22no—
120Q8×Dic61C2314yes—
121#14519742—22no—
122#14519742C2314yes—
123#14519739—28no—
124C4×C22⋊D61D414yes—
125C4×C22⋊D61C2314yes—
126#14519737—28no—
127C2×C4⋊Dic61—22no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2314yes—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196D411yescharacteristic
138C4⋊C4×D61—22no—
139C4⋊C4×D61C2314yes—
140C2×C22⋊Dic61D411yescharacteristic
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198D411yescharacteristic
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519708C2314yes—
150#14519708C2314yes—
151#14519706C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519701C2314yes—
155#14519701C2314yes—
156#14519700C2314yes—
157#14519699C2314yes—
158#14519699C2314yes—
159#14519697C2314yes—
160C22⋊#92418C2314yes—
161#14519689C2314yes—
162#14519687C2314yes—
163C22×Q8×C61C2311yescharacteristic
164C22×Q8×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C2×Q16×C61—42no—
167C2×Q16×C61C2314yes—
168C2×M16×C61—42no—
169C2×M16×C61C2314yes—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22⋊Q8×C61—22no—
173C22⋊Q8×C61—22no—
174C22⋊Q8×C61C2314yes—
175C22⋊Q8×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182#106×C61C2314yes—
183#103×C61C2314yes—
184#103×C61C2314yes—
185C24×C61C2×D411yescharacteristic
186C23×D61—21no—
187C23×D61C2×D411yescharacteristic
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61C2412yes—
195C2×Q8×C61C2412yes—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2412yes—
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—44no—
209C2×C22⋊D61C2×D414yes—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—24no—
214C22×Dic61—82no—
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218Q8×D61—28no—
219Q8×D61—44no—
220Q8×D61—48no—
221#11758222—28no—
222#11758222—44no—
223#11758222—48no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—24no—
227C2×D244—21no—
228C2×D244—44no—
229C2×D244C2412yes—
230C2×C4×D61—22no—
231C2×C4×D61—22no—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—24no—
235C2×C4×D61—44no—
236C2×C4×D61—44no—
237C2×C4×D61—82no—
238C2×C4×D61C2×D412yes—
239C2×C4×D61C2412yes—
240C2×Dic122—21no—
241C2×Dic122—22no—
242C2×Dic122—24no—
243C2×Dic122—24no—
244C2×Dic122—44no—
245C2×Dic122—82no—
246C2×Dic122#4114yes—
247C2×Dic122C2412yes—
248Q16×C61—44no—
249M16×C61—44no—
250C2×C8×C61—22no—
251C2×C8×C61—22no—
252C2×C8×C61C2412yes—
253C2×C8×C61C2412yes—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C2412yes—
259C4⋊C4×C61C2412yes—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊Dic61C2×D414yes—
263#11758202—28no—
264#11758201—44no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198C2×D414yes—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—24no—
273C4⋊Dic61—24no—
274C4⋊Dic61C2412yes—
275C4⋊Dic61C2412yes—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196—24no—
280#11758196C2×D414yes—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61C2×D412yes—
284C4×Dic61C2412yes—
285C2×#92418—22no—
286C2×#92418—22no—
287C2×#92418C2412yes—
288C2×#92418C2412yes—
289C8×D61—44no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61C22×D412yes—
294C23×C61C22×D411yescharacteristic
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61#13714yes—
302C22×D61C22×D412yes—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—42no—
308Q8×C61—42no—
309C2×C4×C61—22no—
310C2×C4×C61—24no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C2×#4112yes—
324C2×C4×C61H(5,𝔽2)12yes—
325C2×C4×C61C2511yescharacteristic
326C22⋊D61—28no—
327C22⋊D61—48no—
328C2×Dic61—24no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—84no—
338C2×Dic61C22×D412yes—
339C2×Dic61C22×D412yes—
340C2×Dic61C22×D412yes—
341D244—22no—
342D244—22no—
343D244—48no—
344D244—42no—
345C4×D61—24no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—48no—
349C4×D61—48no—
350C4×D61—84no—
351Dic122—24no—
352Dic122—22no—
353Dic122—48no—
354Dic122—84no—
355Dic122C2×#4114yes—
356C8×C61—22no—
357C8×C61—22no—
358#92418—22no—
359#92418—22no—
360C2×#3316—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—44no—
365C22×C61#54612yes—
366C22×C61C2×#13712yes—
367C22×C61#57712yes—
368C22×C61C23×D411yescharacteristic
369C2×D61—22no—
370C2×D61—28no—
371C2×D61—22no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—84no—
376C2×D61C2×#13714yes—
377C4×C61—22no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61#54612yes—
383C4×C61C22×#4111yescharacteristic
384C4×C61C2×H(5,𝔽2)11yescharacteristic
385Dic61—24no—
386Dic61—22no—
387Dic61—22no—
388Dic61—22no—
389Dic61—42no—
390Dic61—42no—
391C2×#554—611no—
392C2×#548—611no—
393#3316—6116no—
394C2×#489—611no—
395C2×#481—611no—
396C2×#483—611no—
397C2×#475—611no—
398C2×#470D6111yescharacteristic, complemented
399C2×#465—611no—
400C2×#464—611no—
401C2×#452—611no—
402C2×#451—611no—
403C2×#441—611no—
404C2×#435—611no—
405C2×#417—611no—
406C22×#103—611no—
407C2×C61—42no—
408C2×C61#331614yescomplemented
409C2×C61C2×#54611yescharacteristic
410C2×C61C22×#13711yescharacteristic
411C2×C61C2×#57711yescharacteristic
412D61—24no—
413D61—82no—
414C22×#41—611no—
415C23×Q8—611no—
416C22×Q16—611no—
417C22×Q16C2×D6111yescharacteristic
418C22×SD16—611no—
419C22×M16C2×D6111yescharacteristic
420C23×C8—611no—
421#554—618no—
422#554—1224no—
423#548—618no—
424#548—1224no—
425C2×C4⋊Q8—611no—
426C2×#125—1221no—
427C2×#124—611no—
428C2×#124—1221no—
429C2×C22⋊Q8—611no—
430C2×C22⋊Q8—1221no—
431C2×C22⋊Q8—1221no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8C2×D6111yescharacteristic
434C2×C22⋊Q8C2×D6111yescharacteristic
435C2×#121—611no—
436C2×#121—1221no—
437C2×C4×Q8—611no—
438C2×C4×Q8—611no—
439C2×C4×D4—611no—
440C2×C4×D4—1221no—
441C2×C4×D4—1221no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444#489—618no—
445#483—618no—
446#481—618no—
447#475—618no—
448#470C2×D6118yescomplemented
449#465—618no—
450#464—618no—
451#452—618no—
452#451—618no—
453#441—618no—
454#435—618no—
455C2×#106—611no—
456C2×#106—611no—
457C2×#106C2×D6111yescharacteristic
458C2×C4⋊C8—611no—
459#417—618no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—618no—
466C2×#103C2×D6111yescharacteristic
467C2×#103C2×D6111yescharacteristic
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×#97—611no—
474C61C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—614no—
476C2×#41—1224no—
477C2×#41—1222no—
478C2×#41—2442no—
479C22×Q8—614no—
480C22×Q8—611no—
481C22×Q8—1221no—
482C22×Q8—1221no—
483C22×Q8—1222no—
484C22×Q8—1224no—
485C22×Q8—2442no—
486C22×Q8C22×D6111yescharacteristic
487C22×Q8C22×D6111yescharacteristic
488C22×D4—611no—
489C22×D4—611no—
490C22×D4—1221no—
491C22×D4—1221no—
492C23×C4—611no—
493C23×C4—1221no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4—1221no—
497C23×C4C22×D6111yescharacteristic
498C2×Q16—42no—
499C2×Q16—614no—
500C2×Q16—1224no—
501C2×Q16C22×D6114yes—
502C2×SD16—614no—
503C2×SD16—2442no—
504C2×M16—42no—
505C2×M16C22×D6114yes—
506C22×C8—611no—
507C22×C8—611no—
508C22×C8—614no—
509C22×C8—2442no—
510C22×C8C22×D6111yescharacteristic
511C22×C8C22×D6111yescharacteristic
512C4⋊Q8—614no—
513C4⋊Q8—1222no—
514#125—1228no—
515#124—614no—
516#124—1222no—
517#124—1228no—
518C22⋊Q8—22no—
519C22⋊Q8—22no—
520C22⋊Q8—614no—
521C22⋊Q8—1228no—
522C22⋊Q8—1228no—
523C22⋊Q8—1228no—
524C22⋊Q8—1222no—
525C22⋊Q8C22×D6114yes—
526C22⋊Q8C22×D6114yes—
527#121—614no—
528#121—1228no—
529#121—1222no—
530C4×Q8—614no—
531C4×Q8—614no—
532C4×Q8—1222no—
533C4×Q8—1222no—
534C4×D4—614no—
535C4×D4—614no—
536C4×D4—1228no—
537C4×D4—1228no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—614no—
544C2×C4⋊C4—614no—
545C2×C4⋊C4—1222no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1222no—
553C2×C4⋊C4C22×D6111yescharacteristic
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—611no—
558C2×C22⋊C4—611no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C42—611no—
564C2×C42—1221no—
565C2×C42—1221no—
566#106—614no—
567#106—614no—
568#106C22×D6114yes—
569C4⋊C8—614no—
570#103—614no—
571#103—614no—
572#103—614no—
573#103—614no—
574#103—614no—
575#103C22×D6114yes—
576#103C22×D6114yes—
577#102—614no—
578#102—614no—
579#102—614no—
580C22⋊C8—614no—
581C22⋊C8—614no—
582#97—614no—
583C24—611no—
584C24—1221no—
585C24D4×D6111yescharacteristic
586#41—1228no—
587#41—2444no—
588#41—2448no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—614no—
596C2×Q8—612no—
597C2×Q8—1224no—
598C2×Q8—1224no—
599C2×Q8—1221no—
600C2×Q8—1222no—
601C2×Q8—1228no—
602C2×Q8—4882no—
603C2×Q8—2444no—
604C2×Q8—2444no—
605C2×Q8—2448no—
606C2×Q8C23×D6112yes—
607C2×Q8C23×D6112yes—
608C2×D4—614no—
609C2×D4—612no—
610C2×D4—1224no—
611C2×D4—1224no—
612C2×D4—1224no—
613C2×D4—1221no—
614C2×D4—1222no—
615C2×D4—1222no—
616C2×D4—2444no—
617C2×D4—2444no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—1224no—
630C22×C4—1224no—
631C22×C4—1221no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1224no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1224no—
638C22×C4—4882no—
639C22×C4—4882no—
640C22×C4—2444no—
641C22×C4—2444no—
642C22×C4D4×D6112yes—
643C22×C4D4×D6111yescharacteristic
644C22×C4C23×D6112yes—
645C22×C4C23×D6111yescharacteristic
646Q16—44no—
647Q16—1228no—
648SD16—2444no—
649M16—44no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—612no—
653C2×C8—612no—
654C2×C8—1222no—
655C2×C8—1222no—
656C2×C8—2444no—
657C2×C8C23×D6112yes—
658C2×C8C23×D6112yes—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—614no—
664C4⋊C4—612no—
665C4⋊C4—612no—
666C4⋊C4—1224no—
667C4⋊C4—1224no—
668C4⋊C4—1224no—
669C4⋊C4—1224no—
670C4⋊C4—1224no—
671C4⋊C4—1221no—
672C4⋊C4—1224no—
673C4⋊C4—1221no—
674C4⋊C4C23×D6112yes—
675C4⋊C4C23×D6112yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—614no—
679C22⋊C4—614no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—1224no—
684C42—612no—
685C42—612no—
686C42—1224no—
687C42—1224no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—614no—
692C23—612no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—2442no—
697C23—2442no—
698C23—2442no—
699C23C2×D4×D6112yes—
700C23C2×D4×D6111yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—42no—
706Q8—42no—
707Q8—614no—
708Q8—1222no—
709Q8—1224no—
710Q8—4884no—
711Q8—2448no—
712D4—1228no—
713D4—1222no—
714D4—1222no—
715D4—2448no—
716D4—2448no—
717D4—2442no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—612no—
731C2×C4—612no—
732C2×C4—612no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1224no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1224no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—4884no—
744C2×C4—4884no—
745C2×C4—2448no—
746C2×C4—2448no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4C2×D4×D6112yes—
750C2×C4C2×D4×D6111yescharacteristic
751C2×C4#41×D6112yes—
752C2×C4#1451982212yes—
753C2×C4C24×D6111yescharacteristic
754C8—22no—
755C8—22no—
756C8—1222no—
757C8—1222no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—614no—
763C22—1228no—
764C22—1222no—
765C22—1222no—
766C22—4884no—
767C22—2442no—
768C22—2442no—
769C22—2442no—
770C22#1684040112yes—
771C22#137×D6112yes—
772C22#1684057112yes—
773C22C22×D4×D6111yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—1222no—
780C4—1224no—
781C4—1222no—
782C4—1222no—
783C4—2442no—
784C4—2442no—
785C4#1684040112yes—
786C4C2×#41×D6111yescharacteristic
787C4C2×#1451982211yescharacteristic
788C2—42no—
789C2—1224no—
790C2—4882no—
791C2#2145792514yesdirect product factor
792C2C2×#1684040111yescharacteristic
793C2C2×#137×D6111yescharacteristic
794C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#470C2
socleC23×C61C22×D4
prime radicalC2×#16840422C2
hypercenterC2×#470D61
hypocenterC61C2×#3316
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C2×#16840470C2semidirect
3. #21457925C2direct (N × H)
4. C2×#16840123C2semidirect
5. C2×#16840082C2semidirect
6. C2×#16840090C2semidirect
7. C2×#16840046C2semidirect
8. C2×#16839994C2semidirect
9. C2×#16839986C2semidirect
10. C2×#16839922C2semidirect
11. C2×#16839916C2semidirect
12. C2×#16839866C2semidirect
13. C2×#16839831C2semidirect
14. C2×#16839764C2semidirect
15. C2×#103×D61C2semidirect
16. C2×C61×#470C2semidirect
23. #16840470C22semidirect
43. #16840123C22semidirect
44. #16840090C22semidirect
45. #16840082C22semidirect
46. #16840046C22semidirect
47. #16839994C22semidirect
48. #16839986C22semidirect
49. #16839922C22semidirect
50. #16839916C22semidirect
51. #16839866C22semidirect
52. #16839831C22semidirect
56. #16839764C22semidirect
62. #103×D61C22semidirect
73. C61×#470C22semidirect
398. C2×#470D61semidirect
408. C2×C61#3316semidirect
448. #470C2×D61semidirect
474. C61C2×#3316semidirect
791. C2#21457925direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168404222
#214579252
C2×#168401232
C2×#168400822
C2×#168400902
C2×#168400462
C2×#168399942
C2×#168399862
C2×#168399222
C2×#168399162
C2×#168398662
C2×#168398312
C2×#168397642
C2×#103×D612
C2×C61×#4702
C2×#331661