Finite Group Databasebeta

← C2×#21458206 #30558469

Subgroups — C2×#21458206 #30558469

Order 15616.

1942 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic
2C2×#16840467C211yesmaximal, characteristic
3#21458206C2116yesmaximal, direct product factor
4C2×#16840166C211yesmaximal, characteristic, complemented
5C2×#16840099C211yesmaximal, characteristic, complemented
6C2×#16840098C211yesmaximal, characteristic, complemented
7C2×#16840096C211yesmaximal, characteristic, complemented
8C2×#16840056C211yesmaximal, characteristic, complemented
9C2×#16840055C211yesmaximal, characteristic, complemented
10C2×#16840002C211yesmaximal, characteristic, complemented
11C2×#16840001C211yesmaximal, characteristic, complemented
12C2×#16839854C211yesmaximal, characteristic, complemented
13C2×#16839825C211yesmaximal, characteristic
14C22×#14519710C211yesmaximal, characteristic, complemented
15C2×#107×D61C211yesmaximal, characteristic, complemented
16C2×C61×#484C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840470—24no—
21#16840470C2218yes—
22#16840467—24no—
23#16840467C2218yes—
24C2×#14519776C2211yescharacteristic
25C2×#14519776C2211yescharacteristic
26C2×#14519767—21no—
27C2×#14519767—21no—
28C2×#14519757—21no—
29C2×#14519757C2211yescharacteristic
30C2×#14519756—21no—
31C2×#14519756C2211yescharacteristic
32C2×#14519755—21no—
33C2×#14519754—21no—
34C2×#14519753C2211yescharacteristic
35C2×Q8×Dic61C2211yescharacteristic
36C2×#14519742C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×C4×C22⋊D61C2211yescharacteristic
39C2×#14519737—21no—
40C22×C4⋊Dic61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840166C2218yescomplemented
44#16840099C2218yescomplemented
45#16840098C2218yescomplemented
46#16840096C2218yescomplemented
47#16840056C2218yescomplemented
48#16840055C2218yescomplemented
49#16840002C2218yescomplemented
50#16840001C2218yescomplemented
51#16839854C2218yescomplemented
52#16839825C2218yes—
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519710C2211yescharacteristic
59C2×#14519710C2211yescharacteristic
60C2×#14519710C2218yescomplemented
61#107×D61C2218yescomplemented
62C2×#14519706C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519701C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×C22⋊Q8×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C61×#484C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C22×C22⋊D61D411yescharacteristic
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C2×#11758202—24no—
86C2×#11758202C2314yes—
87C22×#92418—24no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2314yes—
90C22×#92418C2311yescharacteristic
91C2×C8×D61—24no—
92C2×C8×D61C2314yes—
93#14519776—22no—
94#14519776—22no—
95#14519776C2314yes—
96#14519776C2314yes—
97#14519767—28no—
98#14519767—28no—
99#14519757—22no—
100#14519757—28no—
101#14519757C2314yes—
102#14519756—22no—
103#14519756—28no—
104#14519756C2314yes—
105#14519755—28no—
106#14519754—28no—
107#14519753—22no—
108#14519753C2314yes—
109Q8×Dic61—22no—
110Q8×Dic61C2314yes—
111#14519742—22no—
112#14519742C2314yes—
113C4×C22⋊D61—28no—
114C4×C22⋊D61D414yes—
115C4×C22⋊D61C2314yes—
116#14519737—28no—
117C2×C4⋊Dic61—22no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2314yes—
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196D411yescharacteristic
133C4⋊C4×D61—22no—
134C4⋊C4×D61—22no—
135C4⋊C4×D61C2314yes—
136C4⋊C4×D61C2314yes—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61D411yescharacteristic
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198D411yescharacteristic
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61C2311yescharacteristic
145#14519711C2314yes—
146#14519711C2314yes—
147#14519710C2314yes—
148#14519710C2314yes—
149#14519710C2314yes—
150#14519710C2314yes—
151#14519710C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519701C2314yes—
156#14519700C2314yes—
157#14519689C2314yes—
158C8×Dic61C2314yes—
159C22×Q8×C61C2311yescharacteristic
160C23×C4×C61—21no—
161C23×C4×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164C22⋊Q8×C61—22no—
165C22⋊Q8×C61C2314yes—
166C2×C4⋊C4×C61—22no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2314yes—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174#107×C61C2314yes—
175#107×C61C2314yes—
176#103×C61C2314yes—
177#103×C61C2314yes—
178C22⋊C8×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C23×D61C2×D411yescharacteristic
181C2×Q8×C61—21no—
182C2×Q8×C61—22no—
183C2×Q8×C61—22no—
184C2×Q8×C61C2412yes—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—24no—
192C22×C4×C61—82no—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61Q1618yescomplemented
198C2×C22⋊D61C2×D414yes—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—24no—
204C22×Dic61—82no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—82no—
213C2×C4×D61—82no—
214C2×C4×D61C2×D412yes—
215C2×C4×D61C2412yes—
216C2×Dic122—22no—
217C2×Dic122—22no—
218C2×Dic122—21no—
219C2×Dic122—24no—
220C2×Dic122—24no—
221C2×Dic122—82no—
222C2×Dic122—82no—
223C2×Dic122C2412yes—
224C2×C8×C61—22no—
225C2×C8×C61—22no—
226C2×C8×C61C2412yes—
227C2×C8×C61C2412yes—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—24no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61C2412yes—
234C4⋊C4×C61C2412yes—
235C4⋊C4×C61C2412yes—
236C22⋊C4×C61—24no—
237C22⋊Dic61—24no—
238C22⋊Dic61C2×D414yes—
239#11758202—28no—
240#11758198—24no—
241#11758198—24no—
242#11758198C2×D414yes—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—24no—
247C4⋊Dic61—24no—
248C4⋊Dic61—24no—
249C4⋊Dic61C2412yes—
250C4⋊Dic61C2412yes—
251C4⋊Dic61C2412yes—
252#11758196—24no—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196C2×D414yes—
260C4×Dic61—24no—
261C4×Dic61—24no—
262C4×Dic61C2×D412yes—
263C4×Dic61C2412yes—
264C2×#92418—22no—
265C2×#92418—28no—
266C2×#92418#4114yes—
267C2×#92418C2412yes—
268C2×#92418C2412yes—
269C8×D61—28no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61C2×Q1614yes—
273C23×C61C22×D412yes—
274C23×C61C22×D411yescharacteristic
275C22×D61—22no—
276C22×D61—22no—
277C22×D61C2×Q1614yes—
278C22×D61C22×D412yes—
279Q8×C61—22no—
280Q8×C61—22no—
281Q8×C61—42no—
282C2×C4×C61—22no—
283C2×C4×C61—24no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—84no—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4112yes—
298C2×C4×C612−1+412yes—
299C2×C4×C61C2511yescharacteristic
300C22⋊D61C2×Q16116yescomplemented
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—84no—
312C2×Dic61C2×Q1614yes—
313C2×Dic61C22×D412yes—
314C2×Dic61C22×D412yes—
315C2×Dic61C22×D412yes—
316C4×D61—24no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—84no—
320C4×D61—84no—
321Dic122—22no—
322Dic122—22no—
323Dic122—42no—
324Dic122—84no—
325Dic122—84no—
326C8×C61—22no—
327C8×C61—22no—
328#92418—22no—
329#92418C2×#4114yes—
330C2×#3338—611nomaximal, Sylow
331C22×C61—28no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61#54712yes—
335C22×C61C22×Q1614yes—
336C22×C61C22×Q1612yes—
337C22×C61#57612yes—
338C22×C61C23×D411yescharacteristic
339C2×D61—28no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61C22×Q1614yes—
343C4×C61—22no—
344C4×C61—42no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61—42no—
348C4×C61#54712yes—
349C4×C61C22×#4111yescharacteristic
350C4×C61C2×2−1+411yescharacteristic
351Dic61—22no—
352Dic61—22no—
353Dic61—42no—
354Dic61—42no—
355Dic61—42no—
356Dic61—42no—
357Dic61C22×Q1614yes—
358C2×#554—611no—
359C2×#554—611no—
360#3338—6116no—
361C2×#500—611no—
362C2×#484—611no—
363C2×#484—611no—
364C2×#484—611no—
365C2×#484D6111yescharacteristic, complemented
366C2×#477—611no—
367C2×#477—611no—
368C2×#467—611no—
369C2×#467—611no—
370C2×C4×Q16—611no—
371C2×C8×D4—611no—
372C22×#107—611no—
373C22×#107—611no—
374C2×C61—24no—
375C2×C61#333814yescomplemented
376C2×C61C2×#54711yescharacteristic
377C2×C61C23×Q1611yescharacteristic
378C2×C61C2×#57611yescharacteristic
379D61—24no—
380C22×Q16—611no—
381C23×C8—611no—
382C23×C8—611no—
383#554—618no—
384#554—618no—
385#554—1224no—
386#554—1224no—
387C2×C4⋊Q8—611no—
388C2×C4⋊Q8—611no—
389C2×#125—1221no—
390C2×#125—1221no—
391C2×C22⋊Q8—611no—
392C2×C22⋊Q8—611no—
393C2×C22⋊Q8—611no—
394C2×C22⋊Q8—1221no—
395C2×C22⋊Q8—1221no—
396C2×C22⋊Q8—1221no—
397C2×C22⋊Q8—1221no—
398C2×C22⋊Q8C2×D6111yescharacteristic
399C2×C4×Q8—611no—
400C2×C4×Q8—611no—
401C2×C4×D4—611no—
402C2×C4×D4—1221no—
403C2×C4×D4—1221no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4C2×D6111yescharacteristic
408#500—618no—
409#484—618no—
410#484—618no—
411#484—618no—
412#484C2×D6118yescomplemented
413#477—618no—
414#477—618no—
415#467—618no—
416#467—618no—
417C4×Q16—618no—
418C8×D4—618no—
419C2×#107—611no—
420C2×#107—611no—
421C2×#107—611no—
422C2×#107—611no—
423C2×#107—618no—
424C2×#107—611no—
425C2×#107—611no—
426C2×#107—611no—
427C2×#107—618no—
428C2×#107C2×D6111yescharacteristic
429C2×#107C2×D6111yescharacteristic
430C2×C4⋊C8—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103C2×D6111yescharacteristic
436C2×#103C2×D6111yescharacteristic
437C2×C22⋊C8—611no—
438C2×C22⋊C8C2×D6111yescharacteristic
439C2×C4×C8—611no—
440C61C2×#333811yescharacteristic, complemented, Sylow
441C22×Q8—611no—
442C22×Q8—1221no—
443C22×Q8—1221no—
444C22×Q8C22×D6111yescharacteristic
445C22×D4—611no—
446C23×C4—21no—
447C23×C4—611no—
448C23×C4—1221no—
449C23×C4—1221no—
450C23×C4—1221no—
451C23×C4C22×D6111yescharacteristic
452C2×Q16—614no—
453C2×Q16—1224no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—614no—
457C22×C8—614no—
458C22×C8—1224no—
459C22×C8—1224no—
460C22×C8C22×D6111yescharacteristic
461C22×C8C22×D6111yescharacteristic
462C4⋊Q8—614no—
463C4⋊Q8—614no—
464C4⋊Q8—1222no—
465C4⋊Q8—1222no—
466#125—1228no—
467#125—1228no—
468C22⋊Q8—22no—
469C22⋊Q8—614no—
470C22⋊Q8—614no—
471C22⋊Q8—614no—
472C22⋊Q8—1228no—
473C22⋊Q8—1228no—
474C22⋊Q8—1228no—
475C22⋊Q8—1228no—
476C22⋊Q8—1222no—
477C22⋊Q8—1222no—
478C22⋊Q8—1222no—
479C22⋊Q8C22×D6114yes—
480C4×Q8—614no—
481C4×Q8—614no—
482C4×Q8—1222no—
483C4×Q8—1222no—
484C4×D4—614no—
485C4×D4—614no—
486C4×D4—1228no—
487C4×D4—1228no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—614no—
496C2×C4⋊C4—614no—
497C2×C4⋊C4—614no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6114yes—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C42—611no—
522C2×C42—1221no—
523C2×C42—1221no—
524#107—614no—
525#107—614no—
526#107—614no—
527#107—614no—
528#107—614no—
529#107—614no—
530#107—614no—
531#107C22×D6114yes—
532#107C22×D6114yes—
533C4⋊C8—614no—
534#103—614no—
535#103—614no—
536#103—614no—
537#103—614no—
538#103C22×D6114yes—
539#103C22×D6114yes—
540C22⋊C8—614no—
541C22⋊C8C22×D6114yes—
542C4×C8—614no—
543C24—611no—
544C24D4×D6111yescharacteristic
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—612no—
549C2×Q8—1224no—
550C2×Q8—1224no—
551C2×Q8—1221no—
552C2×Q8—1222no—
553C2×Q8—1222no—
554C2×Q8—4882no—
555C2×Q8—4882no—
556C2×Q8C23×D6112yes—
557C2×D4—614no—
558C2×D4—618no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—1224no—
573C22×C4—1224no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1224no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—4882no—
582C22×C4—4882no—
583C22×C4—4882no—
584C22×C4D4×D6112yes—
585C22×C4D4×D6111yescharacteristic
586C22×C4C23×D6112yes—
587C22×C4C23×D6111yescharacteristic
588Q16—1228no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—614no—
592C2×C8—612no—
593C2×C8—612no—
594C2×C8—1228no—
595C2×C8—1228no—
596C2×C8—1222no—
597C2×C8C23×D6112yes—
598C2×C8C23×D6112yes—
599C4⋊C4—21no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—614no—
605C4⋊C4—612no—
606C4⋊C4—612no—
607C4⋊C4—612no—
608C4⋊C4—1224no—
609C4⋊C4—1224no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1221no—
617C4⋊C4—1224no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1224no—
621C4⋊C4C23×D6112yes—
622C4⋊C4C23×D6112yes—
623C4⋊C4C23×D6112yes—
624C22⋊C4—24no—
625C22⋊C4—614no—
626C22⋊C4—614no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C42—612no—
631C42—612no—
632C42—1224no—
633C42—1224no—
634C23—22no—
635C23—22no—
636C23—614no—
637C23—612no—
638C23—1222no—
639C23—1222no—
640C23Q16×D6114yes—
641C23C2×D4×D6112yes—
642C23C2×D4×D6111yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—1222no—
647Q8—1222no—
648Q8—4884no—
649Q8—4884no—
650Q8—2442no—
651D4—6116no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—614no—
666C2×C4—612no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1224no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—4884no—
679C2×C4—4884no—
680C2×C4—4884no—
681C2×C4—2442no—
682C2×C4—2442no—
683C2×C4—2442no—
684C2×C4—2442no—
685C2×C4C2×D4×D6112yes—
686C2×C4C2×D4×D6111yescharacteristic
687C2×C4#41×D6112yes—
688C2×C4#1451982412yes—
689C2×C4C24×D6111yescharacteristic
690C8—22no—
691C8—22no—
692C8—614no—
693C8—1222no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—614no—
698C22—1228no—
699C22—1222no—
700C22—1222no—
701C22#1684041012yes—
702C22C2×Q16×D6114yes—
703C22C2×Q16×D6112yes—
704C22#1684056612yes—
705C22C22×D4×D6111yescharacteristic
706C4—22no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—614no—
712C4—1222no—
713C4—1222no—
714C4—2442no—
715C4—2442no—
716C4—2442no—
717C4—2442no—
718C4#1684041012yes—
719C4C2×#41×D6111yescharacteristic
720C4C2×#1451982411yescharacteristic
721C2—24no—
722C2—1224no—
723C2#2145820614yesdirect product factor
724C2C2×#1684041011yescharacteristic
725C2C22×Q16×D6111yescharacteristic
726C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#484C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenterC2×#484D61
hypocenterC61C2×#3338
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #21458206C2direct (N × H)
4. C2×#16840166C2semidirect
5. C2×#16840099C2semidirect
6. C2×#16840098C2semidirect
7. C2×#16840096C2semidirect
8. C2×#16840056C2semidirect
9. C2×#16840055C2semidirect
10. C2×#16840002C2semidirect
11. C2×#16840001C2semidirect
12. C2×#16839854C2semidirect
14. C22×#14519710C2semidirect
15. C2×#107×D61C2semidirect
16. C2×C61×#484C2semidirect
43. #16840166C22semidirect
44. #16840099C22semidirect
45. #16840098C22semidirect
46. #16840096C22semidirect
47. #16840056C22semidirect
48. #16840055C22semidirect
49. #16840002C22semidirect
50. #16840001C22semidirect
51. #16839854C22semidirect
60. C2×#14519710C22semidirect
61. #107×D61C22semidirect
71. C61×#484C22semidirect
197. C2×C22⋊D61Q16semidirect
300. C22⋊D61C2×Q16semidirect
365. C2×#484D61semidirect
375. C2×C61#3338semidirect
412. #484C2×D61semidirect
440. C61C2×#3338semidirect
723. C2#21458206direct (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×#168404672
#214582062
C2×#168401662
C2×#168400992
C2×#168400982
C2×#168400962
C2×#168400562
C2×#168400552
C2×#168400022
C2×#168400012
C2×#168398542
C2×#168398252
C22×#145197102
C2×#107×D612
C2×C61×#4842
C2×#333861