Finite Group Databasebeta

← C2×#60342 #10574551

Subgroups — C2×#60342 #10574551

Order 512.

6212 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3482C211yesmaximal, characteristic
2#60342C2132yesmaximal, direct product factor
3C2×#2995C212yesmaximal, complemented
4C2×#2994C211yesmaximal, characteristic, complemented
5C2×#2993C211yesmaximal, characteristic, complemented
6C2×#2992C212yesmaximal, complemented
7C2×#2990C211yesmaximal, characteristic, complemented
8C2×#2989C212yesmaximal, complemented
9C2×#2989C211yesmaximal, characteristic, complemented
10C2×#2987C212yesmaximal, complemented
11C2×#2985C211yesmaximal, characteristic, complemented
12C2×#2984C211yesmaximal, characteristic, complemented
13C2×#2983C211yesmaximal, characteristic, complemented
14C2×#2970C212yesmaximal, complemented
15C2×#2970C211yesmaximal, characteristic, complemented
16C2×#2969C211yesmaximal, characteristic, complemented
17C2×#2968C212yesmaximal, complemented
18C2×#2967C212yesmaximal, complemented
19C2×#2966C211yesmaximal, characteristic, complemented
20C2×#2965C211yesmaximal, characteristic, complemented
21C2×Q8×M16C211yesmaximal, characteristic, complemented
22C2×#2962C211yesmaximal, characteristic, complemented
23C2×#2961C212yesmaximal, complemented
24C22×#446C211yesmaximal, characteristic, complemented
25#3482C4116yes—
26#3482C22116yes—
27C2×#557C411yescharacteristic
28C2×#556C412yes—
29C2×#556C411yescharacteristic
30C2×#552C411yescharacteristic
31C2×#552C412yes—
32C2×#552C411yescharacteristic
33C2×#552C412yes—
34C2×D4×Q8C411yescharacteristic
35C2×#548C411yescharacteristic
36C2×#548C411yescharacteristic
37C2×#547C411yescharacteristic
38C2×#547C412yes—
39C2×#533C2212yes—
40C2×#533C2211yescharacteristic
41C2×#529C2211yescharacteristic
42C2×#529C2212yes—
43C2×#529C2212yes—
44C2×#529C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47C2×C4×#41C2212yes—
48C22×C4×Q8C2211yescharacteristic
49C22×C4×Q8C2211yescharacteristic
50#2995C22132yescomplemented
51#2994C22116yescomplemented
52#2993C22116yescomplemented
53#2992C22132yescomplemented
54#2990C22116yescomplemented
55#2989C22132yescomplemented
56#2989C22116yescomplemented
57#2987C22132yescomplemented
58#2985C22116yescomplemented
59#2984C22116yescomplemented
60#2983C22116yescomplemented
61#2970C22132yescomplemented
62#2970C22116yescomplemented
63#2969C22116yescomplemented
64#2968C22132yescomplemented
65#2967C22132yescomplemented
66#2966C22116yescomplemented
67#2965C22116yescomplemented
68Q8×M16C22116yescomplemented
69#2962C22116yescomplemented
70#2961C22132yescomplemented
71C2×#446C2212yes—
72C2×#446C2211yescharacteristic
73C2×#446C2211yescharacteristic
74C2×#446C2211yescharacteristic
75C2×#446C2211yescharacteristic
76C2×#446C2212yes—
77C2×#446C2211yescharacteristic
78C2×#446C2212yes—
79C2×#446C2212yes—
80C2×#446C2212yes—
81C2×#446C2212yes—
82C2×#446C2212yes—
83C2×#446C2212yes—
84C2×#446C2211yescharacteristic
85C2×#446C2212yes—
86C2×#446C2211yescharacteristic
87C2×#446C2212yes—
88C2×#446C2211yescharacteristic
89C2×#446C2211yescharacteristic
90C2×#446C2212yes—
91C2×#446C2212yes—
92C2×#446C2211yescharacteristic
93C2×#446C2212yes—
94C2×#446C22116yescomplemented
95C2×C8×Q8C2211yescharacteristic
96C2×C8×Q8C2211yescharacteristic
97C2×C8×Q8C2211yescharacteristic
98C2×C8×Q8C2211yescharacteristic
99C2×#436C2211yescharacteristic
100C2×#436C2211yescharacteristic
101C2×#436C2211yescharacteristic
102C2×#436C2212yes—
103C2×#436C2211yescharacteristic
104C2×#436C2212yes—
105C2×#435C2211yescharacteristic
106C2×#435C2211yescharacteristic
107C2×#435C2211yescharacteristic
108C2×#435C2211yescharacteristic
109C2×#435C2212yes—
110C2×#435C2212yes—
111C2×#435C2212yes—
112C2×#435C2212yes—
113C2×#435C2212yes—
114C2×#435C2212yes—
115C2×#435C2212yes—
116C2×#435C2212yes—
117C2×#435C2212yes—
118C2×#435C2212yes—
119C2×C8×D4C2212yes—
120C2×C8×D4C2211yescharacteristic
121C2×C8×D4C2212yes—
122C2×C8×D4C2212yes—
123C2×C8×D4C2211yescharacteristic
124C2×#433C2212yes—
125C2×#433C2212yes—
126C2×#433C2212yes—
127C2×#433C2212yes—
128C2×#433C2212yes—
129C2×#433C2212yes—
130C2×#432C2211yescharacteristic
131C2×#432C2212yes—
132C2×#432C2212yes—
133C2×#432C2212yes—
134C2×#432C2211yescharacteristic
135C2×#432C2212yes—
136C2×#432C2212yes—
137C2×#431C2211yescharacteristic
138C2×#431C2211yescharacteristic
139C2×#431C2211yescharacteristic
140C2×#431C2212yes—
141C2×#431C2211yescharacteristic
142C2×#424C2212yes—
143C2×#424C2212yes—
144C2×#424C2212yes—
145C2×#423C2212yes—
146C2×#423C2212yes—
147C2×#423C2211yescharacteristic
148C22×C4⋊C8C2212yes—
149C22×C4⋊C8C2211yescharacteristic
150C22×C4⋊C8C2211yescharacteristic
151C2×#405C2212yes—
152C2×#405C2212yes—
153C2×#405C2212yes—
154C2×C4×M16C2211yescharacteristic
155C2×C4×M16C2211yescharacteristic
156C2×C4×M16C2212yes—
157C22×#97C2212yes—
158C22×#97C2212yes—
159C22×C4×C8C2211yescharacteristic
160C22×#41C2×C411yescharacteristic
161C22×#41C2×C412yes—
162C22×#41C2×C411yescharacteristic
163C23×Q8C2×C411yescharacteristic
164C23×Q8C2×C411yescharacteristic
165C22×M16C2311yescharacteristic
166C22×M16C2311yescharacteristic
167C22×M16C2312yes—
168C22×M16C2311yescharacteristic
169C22×M16C2311yescharacteristic
170C22×M16C2312yes—
171C22×M16C2312yes—
172C23×C8C2311yescharacteristic
173C23×C8C2312yes—
174C23×C8C2311yescharacteristic
175C23×C8C2312yes—
176C23×C8C2312yes—
177C23×C8C2312yes—
178#557C2×C4116yes—
179#556C2×C4132yes—
180#556C2×C4116yes—
181#552C2×C4116yes—
182#552C2×C4132yes—
183#552C2×C4116yes—
184#552C2×C4132yes—
185D4×Q8C2×C4116yes—
186#548C2×C4116yes—
187#548C2×C4116yes—
188#547C2×C4116yes—
189#547C2×C4132yes—
190#533C2×C4116yes—
191#533C2×C418yes—
192#533C23116yes—
193#533C2318yes—
194C2×C4⋊Q8C2×C412yes—
195C2×C4⋊Q8C2×C411yescharacteristic
196C2×C4⋊Q8C2×C411yescharacteristic
197C2×C4⋊Q8C2×C412yes—
198#529C2×C418yes—
199#529C2×C4116yes—
200#529C2×C4116yes—
201#529C2×C418yes—
202#529C2318yes—
203#529C23116yes—
204#529C23116yes—
205#529C2318yes—
206C2×#126C2×C412yes—
207C2×#126C2×C412yes—
208C2×#126C2×C412yes—
209C2×#126C2×C412yes—
210C2×#126C2×C412yes—
211C2×#126C2×C412yes—
212C2×#125C2×C411yescharacteristic
213C2×#125C2×C412yes—
214C2×#125C2×C412yes—
215C2×#125C2×C411yescharacteristic
216C2×#125C2×C412yes—
217C2×#125C2×C412yes—
218C2×#125C2×C412yes—
219C2×#124C2×C411yescharacteristic
220C2×#124C2×C411yescharacteristic
221C2×#124C2×C412yes—
222C2×#124C2×C412yes—
223C2×#123C2×C412yes—
224C2×#123C2×C412yes—
225C2×#123C2×C412yes—
226C2×#123C2×C412yes—
227C2×#123C2×C412yes—
228C2×#123C2×C412yes—
229C2×C22⋊Q8C2×C411yescharacteristic
230C2×C22⋊Q8C2×C411yescharacteristic
231C2×C22⋊Q8C2×C412yes—
232C2×C22⋊Q8C2×C412yes—
233C2×C22⋊Q8C2×C412yes—
234C2×C22⋊Q8C2×C412yes—
235C2×C22⋊Q8C2×C412yes—
236C2×C22⋊Q8C2×C411yescharacteristic
237C2×C22⋊Q8C2×C411yescharacteristic
238C2×C22⋊Q8C2×C412yes—
239C2×C22⋊Q8C2×C412yes—
240C2×#121C2×C411yescharacteristic
241C2×#121C2×C411yescharacteristic
242C2×#121C2×C412yes—
243C2×#121C2×C412yes—
244C4×#41C2×C418yes—
245C4×#41C2×C4116yes—
246C4×#41C2×C418yes—
247C4×#41C2318yes—
248C4×#41C23116yes—
249C4×#41C2318yes—
250C2×C4×Q8C2×C411yescharacteristic
251C2×C4×Q8C2×C411yescharacteristic
252C2×C4×Q8C2×C411yescharacteristic
253C2×C4×Q8C2×C411yescharacteristic
254C2×C4×Q8C2×C412yes—
255C2×C4×Q8C2×C412yes—
256C2×C4×Q8C2×C418yes—
257C2×C4×Q8C2×C418yes—
258C2×C4×Q8C2×C411yescharacteristic
259C2×C4×Q8C2×C411yescharacteristic
260C2×C4×Q8C2×C412yes—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2318yes—
267C2×C4×Q8C2318yes—
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2312yes—
270C2×C4×D4C2×C411yescharacteristic
271C2×C4×D4C2×C412yes—
272C2×C4×D4C2×C411yescharacteristic
273C2×C4×D4C2×C412yes—
274C2×C4×D4C2×C411yescharacteristic
275C2×C4×D4C2×C411yescharacteristic
276C2×C4×D4C2×C412yes—
277C2×C4×D4C2×C412yes—
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2312yes—
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2312yes—
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2312yes—
285C2×#117C2×C411yescharacteristic
286C2×#117C2×C412yes—
287C2×#117C2×C411yescharacteristic
288C2×#117C2×C412yes—
289C2×#117C2×C411yescharacteristic
290C2×#117C2×C412yes—
291C2×#117C2×C411yescharacteristic
292C2×#117C2×C412yes—
293C2×#117C2312yes—
294C2×#117C2312yes—
295C2×#117C2312yes—
296C22×C4⋊C4C2×C411yescharacteristic
297C22×C4⋊C4C2×C412yes—
298C22×C4⋊C4C2×C411yescharacteristic
299C22×C4⋊C4C2×C412yes—
300C22×C42C2311yescharacteristic
301C22×C42C2312yes—
302C22×C42C2312yes—
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2312yes—
306#446C23116yes—
307#446C2318yes—
308#446C2318yes—
309#446C2318yes—
310#446C2318yes—
311#446C23116yes—
312#446C2318yes—
313#446C23116yes—
314#446C23116yes—
315#446C23116yes—
316#446C23116yes—
317#446C23116yes—
318#446C23116yes—
319#446C2318yes—
320#446C23116yes—
321#446C2318yes—
322#446C23116yes—
323#446C2318yes—
324#446C2318yes—
325#446C23116yes—
326#446C23116yes—
327#446C2318yes—
328#446C23116yes—
329C8×Q8C2318yes—
330C8×Q8C2318yes—
331C8×Q8C2318yes—
332C8×Q8C2318yes—
333#436C2318yes—
334#436C2318yes—
335#436C2318yes—
336#436C23116yes—
337#436C2318yes—
338#436C23116yes—
339#435C2318yes—
340#435C2318yes—
341#435C2318yes—
342#435C2318yes—
343#435C23116yes—
344#435C23116yes—
345#435C23116yes—
346#435C23116yes—
347#435C23116yes—
348#435C23116yes—
349#435C23116yes—
350#435C23116yes—
351#435C23116yes—
352#435C23116yes—
353C8×D4C23116yes—
354C8×D4C2318yes—
355C8×D4C23116yes—
356C8×D4C23116yes—
357C8×D4C2318yes—
358#433C23116yes—
359#433C23116yes—
360#433C23116yes—
361#433C23116yes—
362#433C23116yes—
363#433C23116yes—
364#432C2318yes—
365#432C23116yes—
366#432C23116yes—
367#432C23116yes—
368#432C2318yes—
369#432C23116yes—
370#432C23116yes—
371#431C2318yes—
372#431C2318yes—
373#431C2318yes—
374#431C23116yes—
375#431C2318yes—
376#424C23116yes—
377#424C23116yes—
378#424C23116yes—
379#423C23116yes—
380#423C23116yes—
381#423C2318yes—
382C2×C4⋊C8C2311yescharacteristic
383C2×C4⋊C8C2311yescharacteristic
384C2×C4⋊C8C2312yes—
385C2×C4⋊C8C2312yes—
386C2×C4⋊C8C2312yes—
387C2×C4⋊C8C2311yescharacteristic
388C2×C4⋊C8C2312yes—
389C2×C4⋊C8C2312yes—
390C2×C4⋊C8C2312yes—
391C2×C4⋊C8C23116yes—
392C2×C4⋊C8C2318yes—
393C2×C4⋊C8C2318yes—
394C2×C4⋊C8C2311yescharacteristic
395C2×C4⋊C8C2312yes—
396C2×C4⋊C8C2312yes—
397C2×C4⋊C8C2312yes—
398C2×C4⋊C8C2312yes—
399C2×C4⋊C8C2311yescharacteristic
400C2×C4⋊C8C2311yescharacteristic
401C2×C4⋊C8C2312yes—
402C2×C4⋊C8C2312yes—
403C2×C4⋊C8C2311yescharacteristic
404C2×C4⋊C8C2311yescharacteristic
405C2×C4⋊C8C2312yes—
406C2×C4⋊C8C2311yescharacteristic
407C2×C4⋊C8C2311yescharacteristic
408C2×C4⋊C8C2312yes—
409C2×C4⋊C8C2312yes—
410C2×C22⋊C8C2311yescharacteristic
411C2×C22⋊C8C2311yescharacteristic
412C2×C22⋊C8C2312yes—
413C2×C22⋊C8C2311yescharacteristic
414C2×C22⋊C8C2312yes—
415C2×C22⋊C8C2311yescharacteristic
416C2×C22⋊C8C2311yescharacteristic
417C2×C22⋊C8C2311yescharacteristic
418C2×C22⋊C8C2312yes—
419C2×C22⋊C8C2312yes—
420C2×C22⋊C8C2312yes—
421C2×C22⋊C8C2312yes—
422C2×C22⋊C8C2312yes—
423#405C23116yes—
424#405C23116yes—
425#405C23116yes—
426C4×M16C2318yes—
427C4×M16C2318yes—
428C4×M16C23116yes—
429C2×#97C2312yes—
430C2×#97C2311yescharacteristic
431C2×#97C2312yes—
432C2×#97C2312yes—
433C2×#97C2312yes—
434C2×#97C2312yes—
435C2×#97C2312yes—
436C2×#97C23116yes—
437C2×#97C23116yes—
438C2×#97C2311yescharacteristic
439C2×#97C2311yescharacteristic
440C2×#97C2312yes—
441C2×#97C2311yescharacteristic
442C2×#97C2312yes—
443C2×#97C2312yes—
444C2×#97C2312yes—
445C2×C4×C8C2311yescharacteristic
446C2×C4×C8C2311yescharacteristic
447C2×C4×C8C2311yescharacteristic
448C2×C4×C8C2311yescharacteristic
449C2×C4×C8C2318yes—
450C2×C4×C8C2312yes—
451C2×C4×C8C2311yescharacteristic
452C2×C4×C8C2311yescharacteristic
453C2×C4×C8C2312yes—
454C2×C4×C8C2312yes—
455C2×C4×C8C2312yes—
456C2×C4×C8C2312yes—
457C2×#41—44no—
458C2×#41—48no—
459C2×#41—44no—
460C2×#41C22×C418yes—
461C2×#41C22×C4116yes—
462C2×#41C22×C418yes—
463C22×Q8—44no—
464C22×Q8—44no—
465C22×Q8C22×C411yescharacteristic
466C22×Q8C22×C411yescharacteristic
467C22×Q8C22×C411yescharacteristic
468C22×Q8C22×C412yes—
469C22×Q8C22×C412yes—
470C22×Q8C22×C411yescharacteristic
471C22×Q8C22×C412yes—
472C22×Q8C22×C418yes—
473C22×Q8C22×C418yes—
474C22×D4C22×C411yescharacteristic
475C22×D4C22×C411yescharacteristic
476C22×D4C22×C412yes—
477C22×D4C22×C411yescharacteristic
478C22×D4C22×C411yescharacteristic
479C22×D4C22×C412yes—
480C22×D4C22×C412yes—
481C23×C4C22×C411yescharacteristic
482C23×C4C22×C412yes—
483C23×C4C22×C411yescharacteristic
484C23×C4C22×C411yescharacteristic
485C23×C4C22×C411yescharacteristic
486C23×C4C22×C411yescharacteristic
487C23×C4C22×C412yes—
488C23×C4C22×C412yes—
489C23×C4C22×C412yes—
490C23×C4C22×C412yes—
491C23×C4C22×C412yes—
492C23×C4C22×C411yescharacteristic
493C23×C4C2412yes—
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C23×C4C2411yescharacteristic
497C2×M16—24no—
498C2×M16—24no—
499C2×M16—42no—
500C2×M16—44no—
501C2×M16—44no—
502C2×M16—44no—
503C2×M16—42no—
504C2×M16C2414yes—
505C2×M16C2414yes—
506C2×M16C2418yes—
507C2×M16C2414yes—
508C2×M16C2414yes—
509C2×M16C2418yes—
510C2×M16C2418yes—
511C22×C8—24no—
512C22×C8—28no—
513C22×C8—44no—
514C22×C8—44no—
515C22×C8—44no—
516C22×C8—42no—
517C22×C8C2414yes—
518C22×C8C2418yes—
519C22×C8C2412yes—
520C22×C8C2412yes—
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2412yes—
525C22×C8C2411yescharacteristic
526C22×C8C2412yes—
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2414yes—
531C22×C8C2418yes—
532C22×C8C2418yes—
533C22×C8C2418yes—
534C22×C8C2411yescharacteristic
535C4⋊Q8C22×C4116yes—
536C4⋊Q8C22×C418yes—
537C4⋊Q8C22×C418yes—
538C4⋊Q8C22×C4116yes—
539#126C22×C4116yes—
540#126C22×C4116yes—
541#126C22×C4116yes—
542#126C22×C4116yes—
543#126C22×C4116yes—
544#126C22×C4116yes—
545#125C22×C418yes—
546#125C22×C4116yes—
547#125C22×C4116yes—
548#125C22×C418yes—
549#125C22×C4116yes—
550#125C22×C4116yes—
551#125C22×C4116yes—
552#124C22×C418yes—
553#124C22×C418yes—
554#124C22×C4116yes—
555#124C22×C4116yes—
556#123C22×C4116yes—
557#123C22×C4116yes—
558#123C22×C4116yes—
559#123C22×C4116yes—
560#123C22×C4116yes—
561#123C22×C4116yes—
562C22⋊Q8C22×C418yes—
563C22⋊Q8C22×C418yes—
564C22⋊Q8C22×C4116yes—
565C22⋊Q8C22×C4116yes—
566C22⋊Q8C22×C4116yes—
567C22⋊Q8C22×C4116yes—
568C22⋊Q8C22×C4116yes—
569C22⋊Q8C22×C418yes—
570C22⋊Q8C22×C418yes—
571C22⋊Q8C22×C4116yes—
572C22⋊Q8C22×C4116yes—
573#121C22×C418yes—
574#121C22×C418yes—
575#121C22×C4116yes—
576#121C22×C4116yes—
577C4×Q8C22×C414yes—
578C4×Q8C22×C414yes—
579C4×Q8C22×C414yes—
580C4×Q8C22×C418yes—
581C4×Q8C22×C418yes—
582C4×Q8C22×C418yes—
583C4×Q8C22×C418yes—
584C4×Q8C22×C418yes—
585C4×Q8C22×C418yes—
586C4×Q8C22×C4116yes—
587C4×Q8C22×C4116yes—
588C4×Q8C22×C418yes—
589C4×Q8C22×C418yes—
590C4×Q8C22×C4116yes—
591C4×Q8C22×C414yes—
592C4×Q8C22×C418yes—
593C4×Q8C2414yes—
594C4×Q8C2414yes—
595C4×Q8C2414yes—
596C4×Q8C2418yes—
597C4×Q8C2418yes—
598C4×Q8C2414yes—
599C4×Q8C2418yes—
600C4×D4C22×C418yes—
601C4×D4C22×C4116yes—
602C4×D4C22×C418yes—
603C4×D4C22×C4116yes—
604C4×D4C22×C418yes—
605C4×D4C22×C418yes—
606C4×D4C22×C4116yes—
607C4×D4C22×C4116yes—
608C4×D4C22×C414yes—
609C4×D4C22×C414yes—
610C4×D4C22×C418yes—
611C4×D4C22×C414yes—
612C4×D4C22×C418yes—
613C4×D4C22×C414yes—
614C4×D4C22×C418yes—
615C4×D4C2414yes—
616C4×D4C2414yes—
617C4×D4C2418yes—
618C4×D4C2414yes—
619C4×D4C2418yes—
620C4×D4C2414yes—
621C4×D4C2418yes—
622#117C22×C418yes—
623#117C22×C4116yes—
624#117C22×C418yes—
625#117C22×C4116yes—
626#117C22×C418yes—
627#117C22×C4116yes—
628#117C22×C418yes—
629#117C22×C4116yes—
630#117C22×C418yes—
631#117C22×C418yes—
632#117C22×C418yes—
633#117C2418yes—
634#117C2418yes—
635#117C2418yes—
636C2×C4⋊C4C22×C412yes—
637C2×C4⋊C4C22×C411yescharacteristic
638C2×C4⋊C4C22×C412yes—
639C2×C4⋊C4C22×C412yes—
640C2×C4⋊C4C22×C411yescharacteristic
641C2×C4⋊C4C22×C411yescharacteristic
642C2×C4⋊C4C22×C412yes—
643C2×C4⋊C4C22×C412yes—
644C2×C4⋊C4C22×C412yes—
645C2×C4⋊C4C22×C412yes—
646C2×C4⋊C4C22×C412yes—
647C2×C4⋊C4C22×C412yes—
648C2×C4⋊C4C22×C418yes—
649C2×C4⋊C4C22×C4116yes—
650C2×C4⋊C4C22×C418yes—
651C2×C4⋊C4C22×C4116yes—
652C2×C4⋊C4C22×C411yescharacteristic
653C2×C4⋊C4C22×C411yescharacteristic
654C2×C4⋊C4C22×C411yescharacteristic
655C2×C4⋊C4C22×C412yes—
656C2×C4⋊C4C22×C412yes—
657C2×C4⋊C4C22×C411yescharacteristic
658C2×C4⋊C4C22×C412yes—
659C2×C4⋊C4C22×C412yes—
660C2×C4⋊C4C22×C411yescharacteristic
661C2×C4⋊C4C22×C411yescharacteristic
662C2×C4⋊C4C22×C412yes—
663C2×C4⋊C4C22×C411yescharacteristic
664C2×C4⋊C4C22×C412yes—
665C2×C4⋊C4C22×C412yes—
666C2×C4⋊C4C22×C412yes—
667C2×C4⋊C4C22×C412yes—
668C2×C4⋊C4C22×C412yes—
669C2×C4⋊C4C22×C412yes—
670C2×C4⋊C4C22×C412yes—
671C2×C22⋊C4C22×C411yescharacteristic
672C2×C22⋊C4C22×C411yescharacteristic
673C2×C22⋊C4C22×C411yescharacteristic
674C2×C22⋊C4C22×C412yes—
675C2×C22⋊C4C22×C411yescharacteristic
676C2×C22⋊C4C22×C412yes—
677C2×C22⋊C4C22×C412yes—
678C2×C22⋊C4C22×C412yes—
679C2×C22⋊C4C22×C412yes—
680C2×C22⋊C4C22×C411yescharacteristic
681C2×C22⋊C4C22×C412yes—
682C2×C22⋊C4C22×C411yescharacteristic
683C2×C22⋊C4C22×C412yes—
684C2×C22⋊C4C22×C412yes—
685C2×C22⋊C4C22×C412yes—
686C2×C22⋊C4C22×C412yes—
687C2×C22⋊C4C22×C412yes—
688C2×C22⋊C4C22×C412yes—
689C2×C22⋊C4C22×C412yes—
690C2×C42C22×C412yes—
691C2×C42C22×C411yescharacteristic
692C2×C42C22×C411yescharacteristic
693C2×C42C22×C412yes—
694C2×C42C22×C411yescharacteristic
695C2×C42C22×C412yes—
696C2×C42C22×C412yes—
697C2×C42C22×C411yescharacteristic
698C2×C42C22×C412yes—
699C2×C42C22×C412yes—
700C2×C42C22×C411yescharacteristic
701C2×C42C22×C411yescharacteristic
702C2×C42C22×C414yes—
703C2×C42C22×C418yes—
704C2×C42C22×C414yes—
705C2×C42C22×C418yes—
706C2×C42C22×C414yes—
707C2×C42C22×C418yes—
708C2×C42C2414yes—
709C2×C42C2418yes—
710C2×C42C2414yes—
711C2×C42C2418yes—
712C2×C42C2418yes—
713C2×C42C2414yes—
714C2×C42C2412yes—
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C4⋊C8C2414yes—
722C4⋊C8C2414yes—
723C4⋊C8C2418yes—
724C4⋊C8C2418yes—
725C4⋊C8C2418yes—
726C4⋊C8C2414yes—
727C4⋊C8C2418yes—
728C4⋊C8C2418yes—
729C4⋊C8C2418yes—
730C4⋊C8C2414yes—
731C4⋊C8C2418yes—
732C4⋊C8C2418yes—
733C4⋊C8C2418yes—
734C4⋊C8C2418yes—
735C4⋊C8C2414yes—
736C4⋊C8C2414yes—
737C4⋊C8C2418yes—
738C4⋊C8C2418yes—
739C4⋊C8C2414yes—
740C4⋊C8C2414yes—
741C4⋊C8C2418yes—
742C4⋊C8C2414yes—
743C4⋊C8C2414yes—
744C4⋊C8C2418yes—
745C4⋊C8C2418yes—
746C22⋊C8C2414yes—
747C22⋊C8C2414yes—
748C22⋊C8C2418yes—
749C22⋊C8C2414yes—
750C22⋊C8C2418yes—
751C22⋊C8C2414yes—
752C22⋊C8C2414yes—
753C22⋊C8C2414yes—
754C22⋊C8C2418yes—
755C22⋊C8C2418yes—
756C22⋊C8C2418yes—
757C22⋊C8C2418yes—
758C22⋊C8C2418yes—
759#97C2418yes—
760#97C2414yes—
761#97C2418yes—
762#97C2418yes—
763#97C2418yes—
764#97C2418yes—
765#97C2418yes—
766#97C2414yes—
767#97C2414yes—
768#97C2418yes—
769#97C2414yes—
770#97C2418yes—
771#97C2418yes—
772#97C2418yes—
773C4×C8C2414yes—
774C4×C8C2414yes—
775C4×C8C2414yes—
776C4×C8C2414yes—
777C4×C8C2418yes—
778C4×C8C2414yes—
779C4×C8C2414yes—
780C4×C8C2418yes—
781C4×C8C2418yes—
782C4×C8C2418yes—
783C4×C8C2418yes—
784C24C23×C411yescharacteristic
785C24C23×C412yes—
786C24C23×C411yescharacteristic
787C24C23×C411yescharacteristic
788#41—416no—
789#41—432no—
790#41—416no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—44no—
795C2×Q8—44no—
796C2×Q8—42no—
797C2×Q8—44no—
798C2×Q8—416no—
799C2×Q8—416no—
800C2×Q8C23×C414yes—
801C2×Q8C23×C414yes—
802C2×Q8C23×C414yes—
803C2×Q8C23×C418yes—
804C2×Q8C23×C418yes—
805C2×Q8C23×C414yes—
806C2×Q8C23×C418yes—
807C2×D4—24no—
808C2×D4—28no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—42no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4C23×C414yes—
815C2×D4C23×C414yes—
816C2×D4C23×C418yes—
817C2×D4C23×C414yes—
818C2×D4C23×C414yes—
819C2×D4C23×C418yes—
820C2×D4C23×C418yes—
821C22×C4—24no—
822C22×C4—28no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—22no—
827C22×C4—24no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—24no—
833C22×C4—22no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—42no—
838C22×C4—44no—
839C22×C4—42no—
840C22×C4—44no—
841C22×C4C23×C411yescharacteristic
842C22×C4C23×C411yescharacteristic
843C22×C4C23×C412yes—
844C22×C4C23×C412yes—
845C22×C4C23×C411yescharacteristic
846C22×C4C23×C411yescharacteristic
847C22×C4C23×C412yes—
848C22×C4C23×C411yescharacteristic
849C22×C4C23×C412yes—
850C22×C4C23×C412yes—
851C22×C4C23×C411yescharacteristic
852C22×C4C23×C414yes—
853C22×C4C23×C412yes—
854C22×C4C23×C411yescharacteristic
855C22×C4C23×C411yescharacteristic
856C22×C4C23×C412yes—
857C22×C4C23×C412yes—
858C22×C4C23×C412yes—
859C22×C4C23×C411yescharacteristic
860C22×C4C23×C412yes—
861C22×C4C23×C411yescharacteristic
862C22×C4C23×C414yes—
863C22×C4C23×C418yes—
864C22×C4C23×C414yes—
865C22×C4C23×C414yes—
866C22×C4C23×C414yes—
867C22×C4C23×C414yes—
868C22×C4C23×C418yes—
869C22×C4C23×C418yes—
870C22×C4C23×C418yes—
871C22×C4C23×C418yes—
872C22×C4C23×C418yes—
873C22×C4C23×C414yes—
874C22×C4C23×C411yescharacteristic
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2514yes—
878C22×C4C2512yes—
879C22×C4C2511yescharacteristic
880M16—28no—
881M16—28no—
882M16—44no—
883M16—48no—
884M16—48no—
885M16—48no—
886M16—44no—
887C2×C8—22no—
888C2×C8—24no—
889C2×C8—22no—
890C2×C8—22no—
891C2×C8—24no—
892C2×C8—24no—
893C2×C8—22no—
894C2×C8—24no—
895C2×C8—22no—
896C2×C8—22no—
897C2×C8—22no—
898C2×C8—28no—
899C2×C8—216no—
900C2×C8—48no—
901C2×C8—48no—
902C2×C8—48no—
903C2×C8—44no—
904C2×C82−1+414yes—
905C2×C8C2512yes—
906C2×C8C2512yes—
907C2×C8C2512yes—
908C2×C8C2512yes—
909C2×C8C2514yes—
910C2×C8C2512yes—
911C2×C8C2512yes—
912C2×C8C2514yes—
913C2×C8C2512yes—
914C2×C8C2514yes—
915C2×C8C2514yes—
916C2×C8C2512yes—
917C4⋊C4C23×C418yes—
918C4⋊C4C23×C414yes—
919C4⋊C4C23×C418yes—
920C4⋊C4C23×C418yes—
921C4⋊C4C23×C414yes—
922C4⋊C4C23×C414yes—
923C4⋊C4C23×C418yes—
924C4⋊C4C23×C418yes—
925C4⋊C4C23×C418yes—
926C4⋊C4C23×C418yes—
927C4⋊C4C23×C418yes—
928C4⋊C4C23×C418yes—
929C4⋊C4C23×C414yes—
930C4⋊C4C23×C414yes—
931C4⋊C4C23×C414yes—
932C4⋊C4C23×C418yes—
933C4⋊C4C23×C418yes—
934C4⋊C4C23×C414yes—
935C4⋊C4C23×C418yes—
936C4⋊C4C23×C418yes—
937C4⋊C4C23×C414yes—
938C4⋊C4C23×C414yes—
939C4⋊C4C23×C418yes—
940C4⋊C4C23×C414yes—
941C4⋊C4C23×C418yes—
942C4⋊C4C23×C418yes—
943C4⋊C4C23×C418yes—
944C4⋊C4C23×C418yes—
945C4⋊C4C23×C418yes—
946C4⋊C4C23×C418yes—
947C4⋊C4C23×C418yes—
948C22⋊C4C23×C414yes—
949C22⋊C4C23×C414yes—
950C22⋊C4C23×C414yes—
951C22⋊C4C23×C418yes—
952C22⋊C4C23×C414yes—
953C22⋊C4C23×C418yes—
954C22⋊C4C23×C418yes—
955C22⋊C4C23×C418yes—
956C22⋊C4C23×C418yes—
957C22⋊C4C23×C414yes—
958C22⋊C4C23×C418yes—
959C22⋊C4C23×C414yes—
960C22⋊C4C23×C418yes—
961C22⋊C4C23×C418yes—
962C22⋊C4C23×C418yes—
963C22⋊C4C23×C418yes—
964C22⋊C4C23×C418yes—
965C22⋊C4C23×C418yes—
966C22⋊C4C23×C418yes—
967C42C23×C414yes—
968C42C23×C412yes—
969C42C23×C412yes—
970C42C23×C418yes—
971C42C23×C414yes—
972C42C23×C412yes—
973C42C23×C412yes—
974C42C23×C414yes—
975C42C23×C414yes—
976C42C23×C414yes—
977C42C23×C418yes—
978C42C23×C414yes—
979C42C23×C418yes—
980C42C23×C418yes—
981C42C23×C414yes—
982C42C23×C418yes—
983C42C23×C418yes—
984C42C23×C414yes—
985C42C23×C414yes—
986C42C2512yes—
987C42C2512yes—
988C42C2514yes—
989C42C2512yes—
990C42C2514yes—
991C42C2514yes—
992C42C2512yes—
993C23—22no—
994C23—22no—
995C23—24no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23#56814yes—
1005C23C24×C412yes—
1006C23C24×C414yes—
1007C23C24×C412yes—
1008C23C24×C412yes—
1009C23C24×C411yescharacteristic
1010Q8—28no—
1011Q8—28no—
1012Q8—28no—
1013Q8—48no—
1014Q8—48no—
1015Q8—44no—
1016Q8—48no—
1017D4—28no—
1018D4—216no—
1019D4—28no—
1020D4—28no—
1021D4—44no—
1022D4—48no—
1023D4—48no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—28no—
1036C2×C4—216no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—28no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—28no—
1056C2×C4—28no—
1057C2×C4—28no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—44no—
1062C2×C4—48no—
1063C2×C4—44no—
1064C2×C4—48no—
1065C2×C4#56814yes—
1066C2×C4C24×C412yes—
1067C2×C4C24×C412yes—
1068C2×C4C24×C412yes—
1069C2×C4C24×C412yes—
1070C2×C4C24×C414yes—
1071C2×C4C24×C412yes—
1072C2×C4C24×C414yes—
1073C2×C4C24×C414yes—
1074C2×C4C24×C412yes—
1075C2×C4C24×C412yes—
1076C2×C4C24×C412yes—
1077C2×C4C24×C414yes—
1078C2×C4C24×C414yes—
1079C2×C4C24×C414yes—
1080C2×C4C24×C412yes—
1081C2×C4C24×C414yes—
1082C2×C4C24×C412yes—
1083C2×C4C24×C411yescharacteristic
1084C2×C4C24×C412yes—
1085C2×C4C2×2−1+412yes—
1086C2×C4#58512yes—
1087C2×C4C2611yescharacteristic
1088C8—22no—
1089C8—24no—
1090C8—22no—
1091C8—22no—
1092C8—24no—
1093C8—24no—
1094C8—22no—
1095C8—24no—
1096C8—22no—
1097C8—22no—
1098C8—22no—
1099C8C2×2−1+414yes—
1100C22—22no—
1101C22—28no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—22no—
1111C22—22no—
1112C22—44no—
1113C22—44no—
1114C22—48no—
1115C22C4×2−1+412yes—
1116C22C2×#56814yes—
1117C22C2×#56812yes—
1118C22C2×#56812yes—
1119C22C25×C411yescharacteristic
1120C4—22no—
1121C4—24no—
1122C4—22no—
1123C4—22no—
1124C4—24no—
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—24no—
1129C4—22no—
1130C4—24no—
1131C4—24no—
1132C4—24no—
1133C4—22no—
1134C4—24no—
1135C4—22no—
1136C4—22no—
1137C4C4×2−1+412yes—
1138C4C2×#56814yes—
1139C4C22×2−1+411yescharacteristic
1140C4C2×#58511yescharacteristic
1141C2—24no—
1142C2—42no—
1143C2—42no—
1144C2—44no—
1145C2#6034214yesdirect product factor
1146C2C2×C4×2−1+411yescharacteristic
1147C2C22×#56811yescharacteristic
1148C2C22×#56811yescharacteristic
subgroupG/H
centerC22×C4C25
commutatorC22C25×C4
Frattini, cosocleC2×C4C26
socleC23C24×C4
prime radicalC2×#3482C2
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. #60342C2direct (N × H)
3. C2×#2995C2semidirect
4. C2×#2994C2semidirect
5. C2×#2993C2semidirect
6. C2×#2992C2semidirect
7. C2×#2990C2semidirect
8. C2×#2989C2semidirect
9. C2×#2989C2semidirect
10. C2×#2987C2semidirect
11. C2×#2985C2semidirect
12. C2×#2984C2semidirect
13. C2×#2983C2semidirect
14. C2×#2970C2semidirect
15. C2×#2970C2semidirect
16. C2×#2969C2semidirect
17. C2×#2968C2semidirect
18. C2×#2967C2semidirect
19. C2×#2966C2semidirect
20. C2×#2965C2semidirect
21. C2×Q8×M16C2semidirect
22. C2×#2962C2semidirect
23. C2×#2961C2semidirect
24. C22×#446C2semidirect
50. #2995C22semidirect
51. #2994C22semidirect
52. #2993C22semidirect
53. #2992C22semidirect
54. #2990C22semidirect
55. #2989C22semidirect
56. #2989C22semidirect
57. #2987C22semidirect
58. #2985C22semidirect
59. #2984C22semidirect
60. #2983C22semidirect
61. #2970C22semidirect
62. #2970C22semidirect
63. #2969C22semidirect
64. #2968C22semidirect
65. #2967C22semidirect
66. #2966C22semidirect
67. #2965C22semidirect
68. Q8×M16C22semidirect
69. #2962C22semidirect
70. #2961C22semidirect
94. C2×#446C22semidirect
1145. C2#60342direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#34822
#603422
C2×#29952
C2×#29942
C2×#29932
C2×#29922
C2×#29902
C2×#29892
C2×#29872
C2×#29852
C2×#29842
C2×#29832
C2×#29702
C2×#29692
C2×#29682
C2×#29672
C2×#29662
C2×#29652
C2×Q8×M162
C2×#29622
C2×#29612
C22×#4462