Finite Group Databasebeta

← C2×#11349 #358606

Subgroups — C2×#11349 #358606

Order 512.

1622 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2905C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C2×#1742C211yesmaximal, characteristic
4C2×#1733C211yesmaximal, characteristic
5C22×#338C211yesmaximal, characteristic
6C22×H(3,ℤ/4)C211yesmaximal, characteristic
7C22×H(3,ℤ/4)C211yesmaximal, characteristic
8#11349C218yesmaximal, direct product factor
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16#2905—22no—
17#2905—22no—
18#2905C414yescomplemented
19#2905C2214yes—
20C2×#424—22no—
21C2×#424C414yescomplemented
22C2×#423—22no—
23C2×#344—22no—
24C2×#344—22no—
25C2×#344C2214yes—
26#1742—22no—
27#1742C2214yes—
28C2×#343—22no—
29#1733—22no—
30#1733C2214yes—
31C2×#339—22no—
32C2×#338—22no—
33C2×#338—22no—
34C2×#338C2214yes—
35C2×H(3,ℤ/4)—22no—
36C2×H(3,ℤ/4)—22no—
37C2×H(3,ℤ/4)—22no—
38C2×H(3,ℤ/4)—22no—
39C2×H(3,ℤ/4)C2214yes—
40C2×H(3,ℤ/4)C2214yes—
41C24×C4C2311yescharacteristic
42C22×M16—21no—
43C22×M16—21no—
44C22×M16—21no—
45C22×M16—21no—
46C22×M16—21no—
47C22×M16—21no—
48C22×M16—21no—
49C22×M16—21no—
50C22×M16—21no—
51C22×M16—21no—
52C22×M16—21no—
53C22×M16—21no—
54C22×M16—21no—
55C22×M16—21no—
56C22×M16—21no—
57C22×M16—21no—
58C22×M16—21no—
59C22×M16—21no—
60C22×M16—21no—
61C22×M16—21no—
62C22×M16—21no—
63C22×M16—21no—
64C22×M16—21no—
65C22×M16—21no—
66C22×M16—21no—
67C22×M16—21no—
68C22×M16—21no—
69C22×M16—21no—
70C22×M16—21no—
71C22×M16—21no—
72C22×M16—21no—
73C22×M16—21no—
74C22×M16—21no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—21no—
84C22×M16—21no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16C2×C412yes—
89C22×M16C2×C412yes—
90C22×M16C2×C412yes—
91C22×M16D412yes—
92C22×M16D412yes—
93C22×M16Q812yes—
94C22×M16C2312yes—
95C22×M16C2312yes—
96C22×M16C2312yes—
97C22×M16C2312yes—
98C23×C8—21no—
99C23×C8—21no—
100C23×C8C2×C412yes—
101C23×C8Q812yes—
102C2×#117—21no—
103C2×#117—21no—
104C2×#117—21no—
105C2×#117—21no—
106C2×#117—21no—
107C2×#117—21no—
108C2×#117—21no—
109C2×#117—21no—
110C2×#117—21no—
111C2×#117—21no—
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117C2×C412yes—
128C2×#117C2×C412yes—
129C2×#117D412yes—
130C2×#117D412yes—
131C2×#117D412yes—
132C2×#117D412yes—
133C2×#117D412yes—
134C2×#117Q812yes—
135C2×#117C2312yes—
136C2×#117C2312yes—
137C2×#117C2312yes—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C42—21no—
145C22×C42D412yes—
146C22×C42Q812yes—
147#424—28no—
148#424—28no—
149#424—28no—
150#424C2×C4116yescomplemented
151#423—28no—
152#423—28no—
153C2×C4⋊C8—28no—
154#344—28no—
155#343—28no—
156#339—28no—
157#338—28no—
158H(3,ℤ/4)—28no—
159H(3,ℤ/4)—28no—
160C25#4111yescharacteristic
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—41no—
164C23×C4C22×C411yescharacteristic
165C23×C4C22×C411yescharacteristic
166C23×C4C2×D411yescharacteristic
167C23×C4C2×D411yescharacteristic
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D411yescharacteristic
173C23×C4C2×D411yescharacteristic
174C23×C4C2×Q811yescharacteristic
175C23×C4C2×Q811yescharacteristic
176C23×C4C2×Q811yescharacteristic
177C23×C4C2×Q811yescharacteristic
178C23×C4#4111yescharacteristic
179C23×C4#4111yescharacteristic
180C23×C4#4111yescharacteristic
181C23×C4#4111yescharacteristic
182C23×C4#4111yescharacteristic
183C23×C4#4111yescharacteristic
184C23×C4#4111yescharacteristic
185C23×C4#4111yescharacteristic
186C23×C4#4111yescharacteristic
187C23×C4#4111yescharacteristic
188C23×C4#4111yescharacteristic
189C23×C4#4111yescharacteristic
190C23×C4#4111yescharacteristic
191C23×C4#4111yescharacteristic
192C23×C4#4111yescharacteristic
193C23×C4C2411yescharacteristic
194C2×M16—22no—
195C2×M16—22no—
196C2×M16—22no—
197C2×M16—22no—
198C2×M16—22no—
199C2×M16—22no—
200C2×M16—22no—
201C2×M16—22no—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—22no—
205C2×M16—22no—
206C2×M16—22no—
207C2×M16—22no—
208C2×M16—22no—
209C2×M16—22no—
210C2×M16—22no—
211C2×M16—22no—
212C2×M16—22no—
213C2×M16—22no—
214C2×M16—22no—
215C2×M16—22no—
216C2×M16—22no—
217C2×M16—22no—
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—22no—
221C2×M16—22no—
222C2×M16—22no—
223C2×M16—22no—
224C2×M16—22no—
225C2×M16—22no—
226C2×M16—22no—
227C2×M16—22no—
228C2×M16—22no—
229C2×M16—22no—
230C2×M16—22no—
231C2×M16—22no—
232C2×M16—22no—
233C2×M16—22no—
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—22no—
239C2×M16—22no—
240C2×M16—22no—
241C2×M16—22no—
242C2×M16—22no—
243C2×M16—22no—
244C2×M16—22no—
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—22no—
248C2×M16—41no—
249C2×M16—41no—
250C2×M16—41no—
251C2×M16—41no—
252C2×M16—41no—
253C2×M16—41no—
254C2×M16—41no—
255C2×M16—41no—
256C2×M16—41no—
257C2×M16—41no—
258C2×M16—41no—
259C2×M16—41no—
260C2×M16—41no—
261C2×M16—41no—
262C2×M16—41no—
263C2×M16—41no—
264C2×M16—41no—
265C2×M16—41no—
266C2×M16—41no—
267C2×M16—41no—
268C2×M16—41no—
269C2×M16—41no—
270C2×M16—41no—
271C2×M16—41no—
272C2×M16—41no—
273C2×M16—41no—
274C2×M16—41no—
275C2×M16—41no—
276C2×M16—41no—
277C2×M16—41no—
278C2×M16—41no—
279C2×M16—41no—
280C2×M16—41no—
281C2×M16—41no—
282C2×M16—41no—
283C2×M16—41no—
284C2×M16—41no—
285C2×M16—41no—
286C2×M16—41no—
287C2×M16—41no—
288C2×M16—41no—
289C2×M16—41no—
290C2×M16—41no—
291C2×M16—41no—
292C2×M16—41no—
293C2×M16—41no—
294C2×M16—41no—
295C2×M16—41no—
296C2×M16—41no—
297C2×M16—41no—
298C2×M16—41no—
299C2×M16—41no—
300C2×M16—41no—
301C2×M16—41no—
302C2×M16—41no—
303C2×M16—41no—
304C2×M16C22×C414yes—
305C2×M16C2×D414yes—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—41no—
325C22×C8—41no—
326C22×C8—41no—
327C22×C8—41no—
328C22×C8—41no—
329C22×C8—41no—
330C22×C8—41no—
331C22×C8—41no—
332C22×C8C22×C414yes—
333C22×C8C2×Q814yes—
334#117—22no—
335#117—22no—
336#117—22no—
337#117—22no—
338#117—22no—
339#117—22no—
340#117—22no—
341#117—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117—22no—
347#117—22no—
348#117—22no—
349#117—22no—
350#117—22no—
351#117—22no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117—22no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—22no—
362#117—22no—
363#117—41no—
364#117—41no—
365#117—41no—
366#117—41no—
367#117—41no—
368#117—41no—
369#117—41no—
370#117—41no—
371#117—41no—
372#117—41no—
373#117—41no—
374#117—41no—
375#117—41no—
376#117—41no—
377#117C22⋊C414yes—
378#117C22⋊C414yes—
379#117C22×C414yes—
380#117C2×D414yes—
381#117C2×D414yes—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—41no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—41no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4—41no—
414C2×C22⋊C4—41no—
415C2×C22⋊C4—41no—
416C2×C22⋊C4—41no—
417C2×C22⋊C4—41no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—41no—
430C2×C42—41no—
431C2×C42—41no—
432C2×C42C22⋊C414yes—
433C2×C42C22⋊C414yes—
434C2×C42C2×D414yes—
435C2×C42C2×Q814yes—
436C4⋊C8—232no—
437C24—82no—
438C24#11711yescharacteristic
439C24#11711yescharacteristic
440C24C22⋊Q811yescharacteristic
441C24C22⋊Q811yescharacteristic
442C24#12311yescharacteristic
443C24#12311yescharacteristic
444C24#12311yescharacteristic
445C24#12311yescharacteristic
446C24#12311yescharacteristic
447C24#12311yescharacteristic
448C24#12511yescharacteristic
449C24#12511yescharacteristic
450C24#12611yescharacteristic
451C24#12611yescharacteristic
452C24C2×#4111yescharacteristic
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—84no—
463C22×C4—84no—
464C22×C4—84no—
465C22×C4C2×C22⋊C411yescharacteristic
466C22×C4C2×C22⋊C411yescharacteristic
467C22×C4C2×C22⋊C411yescharacteristic
468C22×C4C2×C22⋊C411yescharacteristic
469C22×C4#11711yescharacteristic
470C22×C4#11711yescharacteristic
471C22×C4#11711yescharacteristic
472C22×C4#11711yescharacteristic
473C22×C4#11711yescharacteristic
474C22×C4#11711yescharacteristic
475C22×C4C4×D411yescharacteristic
476C22×C4C4×D411yescharacteristic
477C22×C4C4×D411yescharacteristic
478C22×C4C4×D411yescharacteristic
479C22×C4C4×D411yescharacteristic
480C22×C4C4×D411yescharacteristic
481C22×C4C4×D411yescharacteristic
482C22×C4C4×D411yescharacteristic
483C22×C4C4×Q811yescharacteristic
484C22×C4C4×Q811yescharacteristic
485C22×C4C4×Q811yescharacteristic
486C22×C4C4×Q811yescharacteristic
487C22×C4C4×Q811yescharacteristic
488C22×C4C4×Q811yescharacteristic
489C22×C4C4×Q811yescharacteristic
490C22×C4C4×Q811yescharacteristic
491C22×C4#12111yescharacteristic
492C22×C4#12111yescharacteristic
493C22×C4#12111yescharacteristic
494C22×C4#12111yescharacteristic
495C22×C4#12111yescharacteristic
496C22×C4#12111yescharacteristic
497C22×C4#12111yescharacteristic
498C22×C4#12111yescharacteristic
499C22×C4C22⋊Q811yescharacteristic
500C22×C4C22⋊Q811yescharacteristic
501C22×C4C22⋊Q811yescharacteristic
502C22×C4C22⋊Q811yescharacteristic
503C22×C4C22⋊Q811yescharacteristic
504C22×C4C22⋊Q811yescharacteristic
505C22×C4C22⋊Q811yescharacteristic
506C22×C4C22⋊Q811yescharacteristic
507C22×C4C22⋊Q811yescharacteristic
508C22×C4C22⋊Q811yescharacteristic
509C22×C4C22⋊Q811yescharacteristic
510C22×C4C22⋊Q811yescharacteristic
511C22×C4C22⋊Q811yescharacteristic
512C22×C4C22⋊Q811yescharacteristic
513C22×C4C22⋊Q811yescharacteristic
514C22×C4C22⋊Q811yescharacteristic
515C22×C4C22⋊Q811yescharacteristic
516C22×C4C22⋊Q811yescharacteristic
517C22×C4C22⋊Q811yescharacteristic
518C22×C4C22⋊Q811yescharacteristic
519C22×C4C22⋊Q811yescharacteristic
520C22×C4C22⋊Q811yescharacteristic
521C22×C4#12311yescharacteristic
522C22×C4#12311yescharacteristic
523C22×C4#12311yescharacteristic
524C22×C4#12311yescharacteristic
525C22×C4#12311yescharacteristic
526C22×C4#12311yescharacteristic
527C22×C4#12311yescharacteristic
528C22×C4#12311yescharacteristic
529C22×C4#12311yescharacteristic
530C22×C4#12311yescharacteristic
531C22×C4#12311yescharacteristic
532C22×C4#12311yescharacteristic
533C22×C4#12311yescharacteristic
534C22×C4#12311yescharacteristic
535C22×C4#12311yescharacteristic
536C22×C4#12311yescharacteristic
537C22×C4#12311yescharacteristic
538C22×C4#12311yescharacteristic
539C22×C4#12311yescharacteristic
540C22×C4#12311yescharacteristic
541C22×C4#12311yescharacteristic
542C22×C4#12311yescharacteristic
543C22×C4#12311yescharacteristic
544C22×C4#12311yescharacteristic
545C22×C4#12311yescharacteristic
546C22×C4#12311yescharacteristic
547C22×C4#12411yescharacteristic
548C22×C4#12411yescharacteristic
549C22×C4#12411yescharacteristic
550C22×C4#12411yescharacteristic
551C22×C4#12411yescharacteristic
552C22×C4#12411yescharacteristic
553C22×C4#12411yescharacteristic
554C22×C4#12411yescharacteristic
555C22×C4#12511yescharacteristic
556C22×C4#12511yescharacteristic
557C22×C4#12511yescharacteristic
558C22×C4#12511yescharacteristic
559C22×C4#12511yescharacteristic
560C22×C4#12511yescharacteristic
561C22×C4#12511yescharacteristic
562C22×C4#12511yescharacteristic
563C22×C4#12511yescharacteristic
564C22×C4#12511yescharacteristic
565C22×C4#12511yescharacteristic
566C22×C4#12511yescharacteristic
567C22×C4#12511yescharacteristic
568C22×C4#12511yescharacteristic
569C22×C4#12611yescharacteristic
570C22×C4#12611yescharacteristic
571C22×C4#12611yescharacteristic
572C22×C4#12611yescharacteristic
573C22×C4#12611yescharacteristic
574C22×C4#12611yescharacteristic
575C22×C4#12611yescharacteristic
576C22×C4#12611yescharacteristic
577C22×C4#12611yescharacteristic
578C22×C4#12611yescharacteristic
579C22×C4#12611yescharacteristic
580C22×C4#12611yescharacteristic
581C22×C4#12611yescharacteristic
582C22×C4#12611yescharacteristic
583C22×C4#12711yescharacteristic
584C22×C4#12711yescharacteristic
585C22×C4#12711yescharacteristic
586C22×C4#12711yescharacteristic
587C22×C4C4⋊Q811yescharacteristic
588C22×C4C4⋊Q811yescharacteristic
589C22×C4C4⋊Q811yescharacteristic
590C22×C4C4⋊Q811yescharacteristic
591C22×C4C23×C411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×Q811yescharacteristic
597C22×C4C22×Q811yescharacteristic
598C22×C4C2×#4111yescharacteristic
599C22×C4C2×#4111yescharacteristic
600C22×C4C2×#4111yescharacteristic
601C22×C4C2×#4111yescharacteristic
602C22×C4C2×#4111yescharacteristic
603C22×C4C2×#4111yescharacteristic
604C22×C4C2×#4111yescharacteristic
605M16—24no—
606M16—24no—
607M16—24no—
608M16—24no—
609M16—42no—
610M16—42no—
611M16—42no—
612M16—42no—
613M16—42no—
614M16—42no—
615M16—42no—
616M16—42no—
617M16—42no—
618M16—42no—
619M16—42no—
620M16—42no—
621M16—42no—
622M16—42no—
623M16—42no—
624M16—42no—
625M16—42no—
626M16—42no—
627M16—42no—
628M16—42no—
629M16—42no—
630M16—42no—
631M16—42no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16—42no—
636M16—42no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—24no—
641C2×C8—24no—
642C2×C8—24no—
643C2×C8—24no—
644C2×C8—24no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8—42no—
648C2×C8—42no—
649C2×C8—42no—
650C2×C8—42no—
651C2×C8—42no—
652C2×C8—42no—
653C2×C8—42no—
654C2×C8—42no—
655C2×C8—42no—
656C2×C8—42no—
657C2×C8—42no—
658C2×C8—42no—
659C2×C8—42no—
660C2×C8—42no—
661C2×C8—42no—
662C2×C8—42no—
663C2×C8—42no—
664C2×C8—42no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C42—24no—
690C42—24no—
691C42—24no—
692C42—24no—
693C42—24no—
694C42—24no—
695C42—42no—
696C42—42no—
697C42—42no—
698C42—42no—
699C42—42no—
700C42C2×C22⋊C418yes—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23#38111yescharacteristic
717C23#38111yescharacteristic
718C23#38111yescharacteristic
719C23#38111yescharacteristic
720C23#38711yescharacteristic
721C23#38711yescharacteristic
722C23#38711yescharacteristic
723C23#38711yescharacteristic
724C23#38711yescharacteristic
725C23#38711yescharacteristic
726C23#38711yescharacteristic
727C23#38711yescharacteristic
728C23#39711yescharacteristic
729C23#39711yescharacteristic
730C23#39711yescharacteristic
731C23#39711yescharacteristic
732C23#39811yescharacteristic
733C23#39811yescharacteristic
734C23#39811yescharacteristic
735C23#39811yescharacteristic
736C23#39911yescharacteristic
737C23#39911yescharacteristic
738C23#39911yescharacteristic
739C23#39911yescharacteristic
740C23#40011yescharacteristic
741C23#40011yescharacteristic
742C23#40011yescharacteristic
743C23#40011yescharacteristic
744C23C2×#11711yescharacteristic
745C23C2×C22⋊Q811yescharacteristic
746C23C2×#12311yescharacteristic
747C23C2×#12311yescharacteristic
748C23C2×#12311yescharacteristic
749C23C2×#12511yescharacteristic
750C23C2×#12611yescharacteristic
751C2×C4—28no—
752C2×C4—48no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4—84no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4#38111yescharacteristic
764C2×C4#38111yescharacteristic
765C2×C4#38111yescharacteristic
766C2×C4#38111yescharacteristic
767C2×C4#38711yescharacteristic
768C2×C4#38711yescharacteristic
769C2×C4#38711yescharacteristic
770C2×C4#38711yescharacteristic
771C2×C4#38711yescharacteristic
772C2×C4#38711yescharacteristic
773C2×C4#38711yescharacteristic
774C2×C4#38711yescharacteristic
775C2×C4#38711yescharacteristic
776C2×C4#38711yescharacteristic
777C2×C4#38711yescharacteristic
778C2×C4#38711yescharacteristic
779C2×C4#38711yescharacteristic
780C2×C4#38711yescharacteristic
781C2×C4#38711yescharacteristic
782C2×C4#38711yescharacteristic
783C2×C4#38711yescharacteristic
784C2×C4#38711yescharacteristic
785C2×C4#38711yescharacteristic
786C2×C4#38711yescharacteristic
787C2×C4#38711yescharacteristic
788C2×C4#38711yescharacteristic
789C2×C4#38711yescharacteristic
790C2×C4#38711yescharacteristic
791C2×C4#39011yescharacteristic
792C2×C4#39011yescharacteristic
793C2×C4#39011yescharacteristic
794C2×C4#39011yescharacteristic
795C2×C4#39011yescharacteristic
796C2×C4#39011yescharacteristic
797C2×C4#39011yescharacteristic
798C2×C4#39011yescharacteristic
799C2×C4#39111yescharacteristic
800C2×C4#39111yescharacteristic
801C2×C4#39111yescharacteristic
802C2×C4#39111yescharacteristic
803C2×C4#39111yescharacteristic
804C2×C4#39111yescharacteristic
805C2×C4#39111yescharacteristic
806C2×C4#39111yescharacteristic
807C2×C4#39711yescharacteristic
808C2×C4#39711yescharacteristic
809C2×C4#39711yescharacteristic
810C2×C4#39711yescharacteristic
811C2×C4#39711yescharacteristic
812C2×C4#39711yescharacteristic
813C2×C4#39711yescharacteristic
814C2×C4#39711yescharacteristic
815C2×C4#39711yescharacteristic
816C2×C4#39711yescharacteristic
817C2×C4#39711yescharacteristic
818C2×C4#39711yescharacteristic
819C2×C4#39811yescharacteristic
820C2×C4#39811yescharacteristic
821C2×C4#39811yescharacteristic
822C2×C4#39811yescharacteristic
823C2×C4#39811yescharacteristic
824C2×C4#39811yescharacteristic
825C2×C4#39811yescharacteristic
826C2×C4#39811yescharacteristic
827C2×C4#39811yescharacteristic
828C2×C4#39811yescharacteristic
829C2×C4#39811yescharacteristic
830C2×C4#39811yescharacteristic
831C2×C4#39911yescharacteristic
832C2×C4#39911yescharacteristic
833C2×C4#39911yescharacteristic
834C2×C4#39911yescharacteristic
835C2×C4#39911yescharacteristic
836C2×C4#39911yescharacteristic
837C2×C4#39911yescharacteristic
838C2×C4#39911yescharacteristic
839C2×C4#39911yescharacteristic
840C2×C4#39911yescharacteristic
841C2×C4#39911yescharacteristic
842C2×C4#39911yescharacteristic
843C2×C4#40011yescharacteristic
844C2×C4#40011yescharacteristic
845C2×C4#40011yescharacteristic
846C2×C4#40011yescharacteristic
847C2×C4#40011yescharacteristic
848C2×C4#40011yescharacteristic
849C2×C4#40011yescharacteristic
850C2×C4#40011yescharacteristic
851C2×C4#40011yescharacteristic
852C2×C4#40011yescharacteristic
853C2×C4#40011yescharacteristic
854C2×C4#40011yescharacteristic
855C2×C4C22×C22⋊C411yescharacteristic
856C2×C4C2×#11711yescharacteristic
857C2×C4C2×C4×D411yescharacteristic
858C2×C4C2×C4×D411yescharacteristic
859C2×C4C2×C4×Q811yescharacteristic
860C2×C4C2×C4×Q811yescharacteristic
861C2×C4C2×#12111yescharacteristic
862C2×C4C2×#12111yescharacteristic
863C2×C4C2×C22⋊Q811yescharacteristic
864C2×C4C2×C22⋊Q811yescharacteristic
865C2×C4C2×C22⋊Q811yescharacteristic
866C2×C4C2×C22⋊Q811yescharacteristic
867C2×C4C2×C22⋊Q811yescharacteristic
868C2×C4C2×#12311yescharacteristic
869C2×C4C2×#12311yescharacteristic
870C2×C4C2×#12311yescharacteristic
871C2×C4C2×#12311yescharacteristic
872C2×C4C2×#12311yescharacteristic
873C2×C4C2×#12411yescharacteristic
874C2×C4C2×#12411yescharacteristic
875C2×C4C2×#12511yescharacteristic
876C2×C4C2×#12511yescharacteristic
877C2×C4C2×#12511yescharacteristic
878C2×C4C2×#12611yescharacteristic
879C2×C4C2×#12611yescharacteristic
880C2×C4C2×#12611yescharacteristic
881C2×C4C2×#12711yescharacteristic
882C2×C4C2×C4⋊Q811yescharacteristic
883C8—44no—
884C8—44no—
885C8—44no—
886C8—44no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22#144511yescharacteristic
923C22#144511yescharacteristic
924C22#144511yescharacteristic
925C22#144511yescharacteristic
926C22#144511yescharacteristic
927C22#144511yescharacteristic
928C22#144511yescharacteristic
929C22#144511yescharacteristic
930C22C2×#38111yescharacteristic
931C22C2×#38711yescharacteristic
932C22C2×#38711yescharacteristic
933C22C2×#39711yescharacteristic
934C22C2×#39811yescharacteristic
935C22C2×#39911yescharacteristic
936C22C2×#40011yescharacteristic
937C4—48no—
938C4—84no—
939C4—84no—
940C4#144511yescharacteristic
941C4#144511yescharacteristic
942C4#144511yescharacteristic
943C4#144511yescharacteristic
944C4#144511yescharacteristic
945C4#144511yescharacteristic
946C4#144511yescharacteristic
947C4#144511yescharacteristic
948C4C2×#38711yescharacteristic
949C4C2×#38711yescharacteristic
950C4C2×#39011yescharacteristic
951C4C2×#39111yescharacteristic
952C4C2×#39711yescharacteristic
953C4C2×#39811yescharacteristic
954C4C2×#39911yescharacteristic
955C4C2×#40011yescharacteristic
956C2—21no—
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—21no—
962C2—21no—
963C2—21no—
964C2—21no—
965C2—21no—
966C2—21no—
967C2—21no—
968C2—21no—
969C2—21no—
970C2#1134912yesdirect product factor
971C2C2×#144511yescharacteristic
subgroupG/H
centerC2×C4#391
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC22#1445
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11349C2direct (N × H)
18. #2905C4semidirect
21. C2×#424C4semidirect
150. #424C2×C4semidirect
970. C2#11349direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29052
C22×#3442
C2×#17422
C2×#17332
C22×#3382
C22×H(3,ℤ/4)2
#113492