Finite Group Databasebeta

← C2×#60294 #10574401

Subgroups — C2×#60294 #10574401

Order 512.

6576 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3444C211yesmaximal, characteristic
2#60294C2132yesmaximal, direct product factor
3C2×#2990C214yesmaximal, complemented
4C2×#2989C212yesmaximal, complemented
5C2×#2988C212yesmaximal, complemented
6C2×#2985C212yesmaximal, complemented
7C2×#2981C212yesmaximal, complemented
8C2×#2977C214yesmaximal, complemented
9C2×#2968C214yesmaximal, complemented
10C2×#2966C214yesmaximal, complemented
11C2×#2925C214yesmaximal, complemented
12C22×#432C211yesmaximal, characteristic, complemented
13C22×#431C211yesmaximal, characteristic, complemented
14#3444C4116yes—
15#3444C22116yes—
16C2×#533C411yescharacteristic
17C2×#533C411yescharacteristic
18C2×#533C2211yescharacteristic
19C2×#532C411yescharacteristic
20C2×#532C411yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#529C412yes—
23C2×#529C412yes—
24C2×#529C412yes—
25C2×#529C412yes—
26C2×#529C2212yes—
27C2×#529C2212yes—
28C2×#525C412yes—
29C2×#525C412yes—
30C2×#525C2212yes—
31C2×C4×#41C2212yes—
32C2×C4×#41C2212yes—
33C2×C4×#41C2212yes—
34C23×C42C2211yescharacteristic
35#2990C22164yescomplemented
36#2989C22132yescomplemented
37#2988C22132yescomplemented
38#2985C22132yescomplemented
39#2981C22132yescomplemented
40#2977C22164yescomplemented
41#2968C22164yescomplemented
42#2966C22164yescomplemented
43C2×#446C2214yescomplemented
44C2×#446C2218yescomplemented
45C2×C8×Q8C2214yescomplemented
46C2×#436C2214yescomplemented
47C2×#435C2218yes—
48C2×#435C2218yes—
49C2×#435C2218yescomplemented
50C2×C8×D4C2218yes—
51C2×C8×D4C2218yes—
52C2×C8×D4C2214yescomplemented
53#2925C22164yescomplemented
54C2×#433C2218yes—
55C2×#433C2218yescomplemented
56C2×#432C2212yes—
57C2×#432C2212yes—
58C2×#432C2212yes—
59C2×#432C2212yes—
60C2×#432C22116yescomplemented
61C2×#432C2214yescomplemented
62C2×#431C2212yes—
63C2×#431C2212yes—
64C2×#431C2211yescharacteristic
65C2×#431C2211yescharacteristic
66C2×#431C2212yes—
67C2×#431C22116yescomplemented
68C2×#431C2214yescomplemented
69C2×#423C2214yescomplemented
70C22×C4⋊C8C2212yes—
71C22×C4⋊C8C2212yes—
72C22×C4⋊C8C2214yescomplemented
73C2×#408C2218yes—
74C22×C22⋊C8C2212yes—
75C22×C22⋊C8C2212yes—
76C2×#405C2218yescomplemented
77C22×#97C2212yes—
78C22×C4×C8C2212yes—
79C22×#41C2×C412yes—
80C22×#41C2×C412yes—
81C22×#41C2312yes—
82C24×C4C2×C411yescharacteristic
83C24×C4C2×C411yescharacteristic
84C24×C4C2311yescharacteristic
85C22×M16C2318yes—
86C23×C8C2314yes—
87C23×C8C2314yes—
88C23×C8C2318yes—
89#533C2×C4116yes—
90#533C2×C4116yes—
91#533C2×C418yes—
92#533C2318yes—
93#532C2×C4116yes—
94#532C2×C4116yes—
95#532C2×C418yes—
96#532C2318yes—
97C2×C4⋊Q8C2×C411yescharacteristic
98C2×C4⋊Q8C2×C411yescharacteristic
99C2×C4⋊Q8C2×C411yescharacteristic
100C2×#127C2×C411yescharacteristic
101#529C2×C4132yes—
102#529C2×C4132yes—
103#529C2×C4132yes—
104#529C2×C4132yes—
105#529C2×C4116yes—
106#529C2×C4116yes—
107#529C23116yes—
108#529C23116yes—
109C2×#126C2×C414yes—
110C2×#126C2×C414yes—
111C2×#125C2×C412yes—
112C2×#125C2×C412yes—
113C2×#125C2×C412yes—
114C2×#124C2×C412yes—
115C2×#124C2×C412yes—
116C2×#124C2×C412yes—
117#525C2×C4132yes—
118#525C2×C4132yes—
119#525C2×C4116yes—
120#525C23116yes—
121C2×#123C2×C414yes—
122C2×#123C2×C414yes—
123C2×#123C2×C414yes—
124C2×C22⋊Q8C2×C412yes—
125C2×C22⋊Q8C2×C412yes—
126C2×C22⋊Q8C2×C412yes—
127C2×C22⋊Q8C2×C412yes—
128C2×C22⋊Q8C2×C412yes—
129C2×C22⋊Q8C2×C412yes—
130C2×#121C2×C412yes—
131C2×#121C2×C412yes—
132C2×#121C2×C412yes—
133C2×#121C2×C412yes—
134C2×#121C2×C412yes—
135C2×#121C2×C412yes—
136C2×#120C2×C414yes—
137C4×#41C2×C4116yes—
138C4×#41C2×C4116yes—
139C4×#41C2×C4116yes—
140C4×#41C23116yes—
141C4×#41C23116yes—
142C4×#41C23116yes—
143C2×C4×Q8C2×C412yes—
144C2×C4×Q8C2×C412yes—
145C2×C4×Q8C2×C412yes—
146C2×C4×Q8C2×C412yes—
147C2×C4×Q8C2312yes—
148C2×C4×Q8C2312yes—
149C2×C4×D4C2×C414yes—
150C2×C4×D4C2×C414yes—
151C2×C4×D4C2×C414yes—
152C2×C4×D4C2×C414yes—
153C2×C4×D4C2×C412yes—
154C2×C4×D4C2×C412yes—
155C2×C4×D4C2×C412yes—
156C2×C4×D4C2×C412yes—
157C2×C4×D4C2314yes—
158C2×C4×D4C2314yes—
159C2×C4×D4C2312yes—
160C2×C4×D4C2312yes—
161C2×#117C2×C412yes—
162C2×#117C2×C412yes—
163C2×#117C2×C414yes—
164C2×#117C2×C414yes—
165C2×#117C2314yes—
166C2×#117C2312yes—
167C22×C42C2×C411yescharacteristic
168C22×C42C2×C411yescharacteristic
169C22×C42C2×C411yescharacteristic
170C22×C42C2×C411yescharacteristic
171C22×C42C2×C411yescharacteristic
172C22×C42C2×C411yescharacteristic
173C22×C42C2×C418yes—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2314yes—
179C22×C42C2311yescharacteristic
180C22×C42C2311yescharacteristic
181C22×C42C2318yes—
182#446C23132yescomplemented
183#446C23164yescomplemented
184C8×Q8C23132yescomplemented
185#436C23132yescomplemented
186#435C23164yes—
187#435C23164yes—
188#435C23164yescomplemented
189C8×D4C23164yes—
190C8×D4C23164yes—
191C8×D4C23132yescomplemented
192#433C23164yes—
193#433C23164yescomplemented
194#432C23116yes—
195#432C23116yes—
196#432C23116yes—
197#432C23116yes—
198#432C23132yescomplemented
199#431C23116yes—
200#431C23116yes—
201#431C23116yes—
202#431C2318yes—
203#431C2318yes—
204#431C23132yescomplemented
205#423C23132yescomplemented
206C2×C4⋊C8C2312yes—
207C2×C4⋊C8C2314yes—
208C2×C4⋊C8C2312yes—
209C2×C4⋊C8C2314yes—
210C2×C4⋊C8C23116yes—
211C2×C4⋊C8C2314yes—
212C2×C4⋊C8C23116yes—
213C2×C4⋊C8C2318yes—
214C2×C4⋊C8C2318yes—
215C2×C4⋊C8C23132yescomplemented
216#408C23164yes—
217C2×C22⋊C8C2314yes—
218C2×C22⋊C8C2314yes—
219C2×C22⋊C8C2312yes—
220C2×C22⋊C8C2312yes—
221C2×C22⋊C8C23116yes—
222C2×C22⋊C8C2314yes—
223C2×C22⋊C8C23116yes—
224C2×C22⋊C8C2318yes—
225C2×C22⋊C8C2318yes—
226#405C23164yescomplemented
227C2×#97C2314yes—
228C2×#97C2314yes—
229C2×#97C23116yes—
230C2×#97C2318yes—
231C2×C4×C8C2314yes—
232C2×C4×C8C2312yes—
233C2×C4×C8C2312yes—
234C2×C4×C8C23116yes—
235C2×C4×C8C2318yes—
236C25C22×C411yescharacteristic
237C2×#41—216no—
238C2×#41—48no—
239C2×#41—48no—
240C2×#41C22×C4116yes—
241C2×#41C22×C418yes—
242C2×#41C22×C4116yes—
243C2×#41C2418yes—
244C22×Q8C22×C412yes—
245C22×Q8C22×C412yes—
246C22×Q8C22×C412yes—
247C22×D4C22×C414yes—
248C22×D4C22×C414yes—
249C22×D4C22×C412yes—
250C22×D4C22×C414yes—
251C22×D4C22×C412yes—
252C22×D4C22×C412yes—
253C23×C4—28no—
254C23×C4—44no—
255C23×C4—44no—
256C23×C4C22×C411yescharacteristic
257C23×C4C22×C414yes—
258C23×C4C22×C411yescharacteristic
259C23×C4C22×C411yescharacteristic
260C23×C4C22×C411yescharacteristic
261C23×C4C22×C411yescharacteristic
262C23×C4C22×C411yescharacteristic
263C23×C4C22×C411yescharacteristic
264C23×C4C22×C418yes—
265C23×C4C22×C414yes—
266C23×C4C22×C411yescharacteristic
267C23×C4C22×C411yescharacteristic
268C23×C4C22×C411yescharacteristic
269C23×C4C22×C411yescharacteristic
270C23×C4C22×C411yescharacteristic
271C23×C4C22×C411yescharacteristic
272C23×C4C22×C411yescharacteristic
273C23×C4C22×C418yes—
274C23×C4C22×C414yes—
275C23×C4C22×C411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2414yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2414yes—
281C2×M16—416no—
282C2×M16C24132yes—
283C22×C8—416no—
284C22×C8—48no—
285C22×C8—48no—
286C22×C8C2414yes—
287C22×C8C2418yes—
288C22×C8C2414yes—
289C22×C8C24116yes—
290C22×C8C24116yes—
291C22×C8C24132yes—
292C4⋊Q8C22×C418yes—
293C4⋊Q8C22×C418yes—
294C4⋊Q8C22×C418yes—
295#127C22×C418yes—
296#126C22×C4132yes—
297#126C22×C4132yes—
298#125C22×C4116yes—
299#125C22×C4116yes—
300#125C22×C4116yes—
301#124C22×C4116yes—
302#124C22×C4116yes—
303#124C22×C4116yes—
304#123C22×C4132yes—
305#123C22×C4132yes—
306#123C22×C4132yes—
307C22⋊Q8C22×C4116yes—
308C22⋊Q8C22×C4116yes—
309C22⋊Q8C22×C4116yes—
310C22⋊Q8C22×C4116yes—
311C22⋊Q8C22×C4116yes—
312C22⋊Q8C22×C4116yes—
313#121C22×C4116yes—
314#121C22×C4116yes—
315#121C22×C4116yes—
316#121C22×C4116yes—
317#121C22×C4116yes—
318#121C22×C4116yes—
319#120C22×C4132yes—
320C4×Q8C22×C4116yes—
321C4×Q8C22×C4116yes—
322C4×Q8C22×C4116yes—
323C4×Q8C22×C4116yes—
324C4×Q8C22×C418yes—
325C4×Q8C22×C418yes—
326C4×Q8C2418yes—
327C4×Q8C2418yes—
328C4×D4C22×C4132yes—
329C4×D4C22×C4132yes—
330C4×D4C22×C4132yes—
331C4×D4C22×C4132yes—
332C4×D4C22×C4116yes—
333C4×D4C22×C4116yes—
334C4×D4C22×C4116yes—
335C4×D4C22×C4116yes—
336C4×D4C22×C4116yes—
337C4×D4C22×C4116yes—
338C4×D4C22×C418yes—
339C4×D4C22×C418yes—
340C4×D4C24116yes—
341C4×D4C24116yes—
342C4×D4C2418yes—
343C4×D4C2418yes—
344#117C22×C4116yes—
345#117C22×C4116yes—
346#117C22×C4132yes—
347#117C22×C4132yes—
348#117C22×C418yes—
349#117C22×C4116yes—
350#117C2418yes—
351#117C24116yes—
352C2×C4⋊C4C22×C412yes—
353C2×C4⋊C4C22×C412yes—
354C2×C4⋊C4C22×C414yes—
355C2×C4⋊C4C22×C414yes—
356C2×C4⋊C4C22×C412yes—
357C2×C4⋊C4C22×C412yes—
358C2×C4⋊C4C22×C414yes—
359C2×C4⋊C4C22×C414yes—
360C2×C4⋊C4C22×C412yes—
361C2×C4⋊C4C22×C412yes—
362C2×C4⋊C4C22×C414yes—
363C2×C4⋊C4C22×C414yes—
364C2×C22⋊C4C22×C414yes—
365C2×C22⋊C4C22×C414yes—
366C2×C22⋊C4C22×C414yes—
367C2×C22⋊C4C22×C414yes—
368C2×C22⋊C4C22×C414yes—
369C2×C22⋊C4C22×C414yes—
370C2×C22⋊C4C22×C414yes—
371C2×C22⋊C4C22×C414yes—
372C2×C22⋊C4C22×C414yes—
373C2×C42C22×C411yescharacteristic
374C2×C42C22×C411yescharacteristic
375C2×C42C22×C414yes—
376C2×C42C22×C414yes—
377C2×C42C22×C411yescharacteristic
378C2×C42C22×C411yescharacteristic
379C2×C42C22×C411yescharacteristic
380C2×C42C22×C411yescharacteristic
381C2×C42C22×C4116yes—
382C2×C42C22×C414yes—
383C2×C42C22×C414yes—
384C2×C42C22×C414yes—
385C2×C42C22×C411yescharacteristic
386C2×C42C22×C411yescharacteristic
387C2×C42C22×C411yescharacteristic
388C2×C42C22×C411yescharacteristic
389C2×C42C22×C411yescharacteristic
390C2×C42C22×C414yes—
391C2×C42C22×C414yes—
392C2×C42C22×C418yes—
393C2×C42C22×C418yes—
394C2×C42C22×C418yes—
395C2×C42C22×C418yes—
396C2×C42C22×C411yescharacteristic
397C2×C42C22×C414yes—
398C2×C42C22×C418yes—
399C2×C42C22×C418yes—
400C2×C42C24116yes—
401C2×C42C2414yes—
402C2×C42C2414yes—
403C2×C42C2414yes—
404C2×C42C2414yes—
405C2×C42C2414yes—
406C2×C42C2414yes—
407C2×C42C2411yescharacteristic
408C2×C42C2414yes—
409C2×C42C2411yescharacteristic
410C2×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412C4⋊C8C2418yes—
413C4⋊C8C24116yes—
414C4⋊C8C2418yes—
415C4⋊C8C24116yes—
416C4⋊C8C24116yes—
417C4⋊C8C24132yes—
418C4⋊C8C24132yes—
419C22⋊C8C24116yes—
420C22⋊C8C24116yes—
421C22⋊C8C2418yes—
422C22⋊C8C2418yes—
423C22⋊C8C24116yes—
424C22⋊C8C24132yes—
425C22⋊C8C24132yes—
426#97C24116yes—
427#97C24116yes—
428#97C24132yes—
429C4×C8C24116yes—
430C4×C8C2418yes—
431C4×C8C2418yes—
432C4×C8C24132yes—
433C24—24no—
434C24—24no—
435C24—42no—
436C24C23×C414yes—
437C24C23×C411yescharacteristic
438C24C23×C414yes—
439C24C23×C411yescharacteristic
440C24C23×C411yescharacteristic
441#41—264no—
442#41—416no—
443#41—416no—
444#41—432no—
445C2×Q8—28no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8C23×C418yes—
449C2×Q8C23×C418yes—
450C2×Q8C23×C418yes—
451C2×D4—216no—
452C2×D4—216no—
453C2×D4—28no—
454C2×D4—44no—
455C2×D4—48no—
456C2×D4—44no—
457C2×D4C23×C4116yes—
458C2×D4C23×C4116yes—
459C2×D4C23×C418yes—
460C2×D4C23×C4116yes—
461C2×D4C23×C418yes—
462C2×D4C23×C418yes—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—232no—
471C22×C4—216no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—24no—
477C22×C4—48no—
478C22×C4—48no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—416no—
487C22×C4—48no—
488C22×C4#13118yes—
489C22×C4C23×C411yescharacteristic
490C22×C4C23×C411yescharacteristic
491C22×C4C23×C411yescharacteristic
492C22×C4C23×C411yescharacteristic
493C22×C4C23×C412yes—
494C22×C4C23×C412yes—
495C22×C4C23×C412yes—
496C22×C4C23×C411yescharacteristic
497C22×C4C23×C411yescharacteristic
498C22×C4C23×C411yescharacteristic
499C22×C4C23×C411yescharacteristic
500C22×C4C23×C411yescharacteristic
501C22×C4C23×C414yes—
502C22×C4C23×C414yes—
503C22×C4C23×C414yes—
504C22×C4C23×C414yes—
505C22×C4C23×C414yes—
506C22×C4C23×C414yes—
507C22×C4C23×C414yes—
508C22×C4C23×C414yes—
509C22×C4C23×C418yes—
510C22×C4C23×C414yes—
511C22×C4C23×C414yes—
512C22×C4C23×C4116yes—
513C22×C4C23×C414yes—
514C22×C4C23×C414yes—
515C22×C4C23×C414yes—
516C22×C4C23×C414yes—
517C22×C4C23×C414yes—
518C22×C4C23×C414yes—
519C22×C4C23×C414yes—
520C22×C4C23×C4116yes—
521C22×C4C23×C411yescharacteristic
522C22×C4C23×C411yescharacteristic
523C22×C4C23×C414yes—
524C22×C4C2512yes—
525C22×C4C2512yes—
526C22×C4C2512yes—
527C22×C4C2518yes—
528C22×C4C2511yescharacteristic
529M16—432no—
530C2×C8—28no—
531C2×C8—216no—
532C2×C8—28no—
533C2×C8—432no—
534C2×C8—416no—
535C2×C8—416no—
536C2×C8C2518yes—
537C2×C8C2518yes—
538C2×C8C25116yes—
539C4⋊C4C23×C418yes—
540C4⋊C4C23×C418yes—
541C4⋊C4C23×C4116yes—
542C4⋊C4C23×C4116yes—
543C4⋊C4C23×C418yes—
544C4⋊C4C23×C418yes—
545C4⋊C4C23×C4116yes—
546C4⋊C4C23×C4116yes—
547C4⋊C4C23×C418yes—
548C4⋊C4C23×C418yes—
549C4⋊C4C23×C4116yes—
550C4⋊C4C23×C4116yes—
551C22⋊C4C23×C4116yes—
552C22⋊C4C23×C4116yes—
553C22⋊C4C23×C4116yes—
554C22⋊C4C23×C4116yes—
555C22⋊C4C23×C4116yes—
556C22⋊C4C23×C4116yes—
557C22⋊C4C23×C4116yes—
558C22⋊C4C23×C4116yes—
559C22⋊C4C23×C4116yes—
560C42C23×C412yes—
561C42C23×C414yes—
562C42C23×C414yes—
563C42C23×C412yes—
564C42C23×C414yes—
565C42C23×C414yes—
566C42C23×C414yes—
567C42C23×C414yes—
568C42C23×C412yes—
569C42C23×C412yes—
570C42C23×C414yes—
571C42C23×C414yes—
572C42C23×C414yes—
573C42C23×C414yes—
574C42C23×C414yes—
575C42C23×C414yes—
576C42C23×C4116yes—
577C42C23×C4116yes—
578C42C23×C418yes—
579C42C2512yes—
580C42C2512yes—
581C42C2518yes—
582C42C2512yes—
583C42C2512yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—28no—
590C23—28no—
591C23—22no—
592C23—28no—
593C23—28no—
594C23—22no—
595C23—28no—
596C23—44no—
597C23—416no—
598C23C2×#13114yes—
599C23#56814yes—
600C23C24×C418yes—
601C23C24×C412yes—
602C23C24×C412yes—
603C23C24×C412yes—
604C23C24×C411yescharacteristic
605Q8—216no—
606Q8—48no—
607Q8—48no—
608D4—232no—
609D4—232no—
610D4—216no—
611D4—48no—
612D4—48no—
613D4—416no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—28no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—28no—
628C2×C4—28no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—28no—
632C2×C4—28no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—216no—
638C2×C4—28no—
639C2×C4—28no—
640C2×C4—28no—
641C2×C4—28no—
642C2×C4—232no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—416no—
651C2×C4C2×#13114yes—
652C2×C4C2×#13114yes—
653C2×C4C2×#131116yes—
654C2×C4C24×C412yes—
655C2×C4C24×C412yes—
656C2×C4C24×C412yes—
657C2×C4C24×C412yes—
658C2×C4C24×C412yes—
659C2×C4C24×C412yes—
660C2×C4C24×C412yes—
661C2×C4C24×C412yes—
662C2×C4C24×C412yes—
663C2×C4C24×C418yes—
664C2×C4C24×C418yes—
665C2×C4C24×C418yes—
666C2×C4C24×C411yescharacteristic
667C2×C4C24×C412yes—
668C2×C4C24×C412yes—
669C2×C4#58514yes—
670C2×C4C2611yescharacteristic
671C8—28no—
672C8—216no—
673C8—28no—
674C22—22no—
675C22—22no—
676C22—28no—
677C22—28no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—28no—
682C22—22no—
683C22—28no—
684C22—22no—
685C22—28no—
686C22—416no—
687C22—416no—
688C22—44no—
689C22#342812yes—
690C22C22×#13114yes—
691C22C22×#13112yes—
692C22C2×#56814yes—
693C22C2×#56812yes—
694C22C25×C411yescharacteristic
695C4—22no—
696C4—22no—
697C4—28no—
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—28no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—28no—
707C4#342812yes—
708C4C22×#13114yes—
709C4C22×#13114yes—
710C4C2×#58512yes—
711C2—24no—
712C2—24no—
713C2—48no—
714C2—42no—
715C2#6029414yesdirect product factor
716C2C2×#342811yescharacteristic
717C2C23×#13111yescharacteristic
718C2C22×#56811yescharacteristic
subgroupG/H
centerC22×C4C25
commutatorC22C25×C4
Frattini, cosocleC2×C4C26
socleC23C24×C4
prime radicalC2×#3444C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60294C2direct (N × H)
3. C2×#2990C2semidirect
4. C2×#2989C2semidirect
5. C2×#2988C2semidirect
6. C2×#2985C2semidirect
7. C2×#2981C2semidirect
8. C2×#2977C2semidirect
9. C2×#2968C2semidirect
10. C2×#2966C2semidirect
11. C2×#2925C2semidirect
12. C22×#432C2semidirect
13. C22×#431C2semidirect
35. #2990C22semidirect
36. #2989C22semidirect
37. #2988C22semidirect
38. #2985C22semidirect
39. #2981C22semidirect
40. #2977C22semidirect
41. #2968C22semidirect
42. #2966C22semidirect
43. C2×#446C22semidirect
44. C2×#446C22semidirect
45. C2×C8×Q8C22semidirect
46. C2×#436C22semidirect
49. C2×#435C22semidirect
52. C2×C8×D4C22semidirect
53. #2925C22semidirect
55. C2×#433C22semidirect
60. C2×#432C22semidirect
61. C2×#432C22semidirect
67. C2×#431C22semidirect
68. C2×#431C22semidirect
69. C2×#423C22semidirect
72. C22×C4⋊C8C22semidirect
76. C2×#405C22semidirect
182. #446C23semidirect
183. #446C23semidirect
184. C8×Q8C23semidirect
185. #436C23semidirect
188. #435C23semidirect
191. C8×D4C23semidirect
193. #433C23semidirect
198. #432C23semidirect
204. #431C23semidirect
205. #423C23semidirect
215. C2×C4⋊C8C23semidirect
226. #405C23semidirect
715. C2#60294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#34442
#602942
C2×#29902
C2×#29892
C2×#29882
C2×#29852
C2×#29812
C2×#29772
C2×#29682
C2×#29662
C2×#29252
C22×#4322
C22×#4312