Finite Group Databasebeta

← #7622797

Subgroups — #7622797

Order 512.

1181 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60330C211yesmaximal, characteristic
2#33509C212yesmaximal, complemented
3#33509C212yesmaximal, complemented
4#33508C211yesmaximal, characteristic, complemented
5#33507C211yesmaximal, characteristic, complemented
6#33507C212yesmaximal, complemented
7#33505C211yesmaximal, characteristic, complemented
8#33503C211yesmaximal, characteristic, complemented
9#33500C211yesmaximal, characteristic, complemented
10#33499C211yesmaximal, characteristic, complemented
11#33499C212yesmaximal, complemented
12#33498C211yesmaximal, characteristic, complemented
13#33484C211yesmaximal, characteristic, complemented
14#33483C211yesmaximal, characteristic, complemented
15#33483C212yesmaximal, complemented
16#33482C212yesmaximal, complemented
17#33481C212yesmaximal, complemented
18#33480C211yesmaximal, characteristic, complemented
19#33479C211yesmaximal, characteristic, complemented
20Q8×M32C211yesmaximal, characteristic, complemented
21#33476C211yesmaximal, characteristic, complemented
22#33475C212yesmaximal, complemented
23#33474C211yesmaximal, characteristic, complemented
24#3461C411yescharacteristic
25#2993C411yescharacteristic
26#2993C412yes—
27#2993C411yescharacteristic
28#2992C412yes—
29#2992C412yes—
30#2989C411yescharacteristic
31#2989C411yescharacteristic
32#2985C411yescharacteristic
33#2985C412yes—
34#2985C411yescharacteristic
35#2983C411yescharacteristic
36#2966C2211yescharacteristic
37#2966C2212yes—
38#2966C2212yes—
39#2966C2211yescharacteristic
40#2966C2212yes—
41C8×#41C2211yescharacteristic
42C8×#41C2211yescharacteristic
43#2960C2211yescharacteristic
44#2960C2212yes—
45#2960C2211yescharacteristic
46C2×C8×Q8C2211yescharacteristic
47#2183C2212yes—
48#2183C2211yescharacteristic
49#2183C2211yescharacteristic
50#2183C2211yescharacteristic
51#2183C2212yes—
52#2183C2212yes—
53#2183C2212yes—
54#2183C2212yes—
55#2183C2212yes—
56#2183C2212yes—
57#2183C2211yescharacteristic
58#2183C2212yes—
59#2183C2211yescharacteristic
60#2183C2212yes—
61#2183C2211yescharacteristic
62#2183C2211yescharacteristic
63#2183C2212yes—
64#2183C2212yes—
65#2183C2211yescharacteristic
66Q8×C16C2211yescharacteristic
67Q8×C16C2212yes—
68Q8×C16C2211yescharacteristic
69Q8×C16C2211yescharacteristic
70Q8×C16C2211yescharacteristic
71Q8×C16C2211yescharacteristic
72Q8×C16C2211yescharacteristic
73Q8×C16C2212yes—
74#2169C2211yescharacteristic
75#2169C2211yescharacteristic
76#2169C2211yescharacteristic
77#2169C2212yes—
78#2169C2212yes—
79#2169C2211yescharacteristic
80#2169C2212yes—
81#2169C2212yes—
82#2169C2212yes—
83#2168C2211yescharacteristic
84#2168C2211yescharacteristic
85#2168C2211yescharacteristic
86#2168C2211yescharacteristic
87#2168C2212yes—
88#2168C2212yes—
89#2168C2212yes—
90#2168C2212yes—
91#2168C2212yes—
92#2168C2212yes—
93#2168C2212yes—
94#2168C2212yes—
95D4×C16C2212yes—
96D4×C16C2211yescharacteristic
97D4×C16C2212yes—
98D4×C16C2211yescharacteristic
99#2164C2212yes—
100#2164C2212yes—
101#2164C2212yes—
102#2164C2212yes—
103#2164C2212yes—
104#2164C2212yes—
105#2164C2212yes—
106#2164C2212yes—
107#2163C2211yescharacteristic
108#2163C2212yes—
109#2163C2211yescharacteristic
110#2163C2212yes—
111#2162C2211yescharacteristic
112#2162C2211yescharacteristic
113#2162C2211yescharacteristic
114#2162C2212yes—
115#2162C2212yes—
116#2162C2211yescharacteristic
117#2151C2212yes—
118#2151C2212yes—
119#2151C2212yes—
120#2151C2212yes—
121#2150C2211yescharacteristic
122#2150C2212yes—
123#2150C2211yescharacteristic
124#2150C2212yes—
125C2×C4⋊C16C2211yescharacteristic
126#2108C2212yes—
127#2108C2212yes—
128#2108C2212yes—
129#2108C2212yes—
130C4×M32C2211yescharacteristic
131C4×M32C2211yescharacteristic
132C4×M32C2212yes—
133C2×#346C2212yes—
134C2×C4×C16C2211yescharacteristic
135#544C811yescharacteristic
136#542C811yescharacteristic
137#542C811yescharacteristic
138#542C812yes—
139#541C811yescharacteristic
140#541C811yescharacteristic
141#541C812yes—
142#539C812yes—
143#539C812yes—
144#537C811yescharacteristic
145#536C811yescharacteristic
146#536C811yescharacteristic
147#533C2×C411yescharacteristic
148#533C2×C412yes—
149#533C2×C411yescharacteristic
150#529C2×C412yes—
151#529C2×C412yes—
152#529C2×C411yescharacteristic
153#529C2×C412yes—
154#529C2×C411yescharacteristic
155C4×#41C2×C411yescharacteristic
156C4×#41C2×C411yescharacteristic
157C2×C4×Q8C2×C411yescharacteristic
158C2×M32C2311yescharacteristic
159C2×M32C2311yescharacteristic
160C2×M32C2311yescharacteristic
161C2×M32C2312yes—
162C2×M32C2311yescharacteristic
163C2×M32C2312yes—
164C2×M32C2312yes—
165C2×M32C2312yes—
166C22×C16C2311yescharacteristic
167C22×C16C2312yes—
168C22×C16C2311yescharacteristic
169C22×C16C2312yes—
170C22×C16C2312yes—
171#446C2×C411yescharacteristic
172#446C2×C412yes—
173#446C2×C411yescharacteristic
174#446C2×C411yescharacteristic
175#446C2×C412yes—
176#446C2×C411yescharacteristic
177#446C2×C412yes—
178#446C2×C412yes—
179#446C2×C412yes—
180#446C2×C412yes—
181#446C2×C411yescharacteristic
182#446C2×C412yes—
183#446C2×C411yescharacteristic
184#446C2×C412yes—
185#446C2×C412yes—
186C8×Q8C2×C411yescharacteristic
187C8×Q8C2×C411yescharacteristic
188C8×Q8C2×C412yes—
189C8×Q8C2×C411yescharacteristic
190C8×Q8C2×C411yescharacteristic
191C8×Q8C2311yescharacteristic
192C8×Q8C2311yescharacteristic
193C8×Q8C2311yescharacteristic
194C8×Q8C2312yes—
195C8×Q8C2312yes—
196C8×Q8C2312yes—
197C8×Q8C2311yescharacteristic
198#436C2×C411yescharacteristic
199#436C2×C412yes—
200#436C2×C411yescharacteristic
201#436C2×C412yes—
202#436C2×C412yes—
203#435C2×C412yes—
204#435C2×C412yes—
205#435C2×C412yes—
206#435C2×C412yes—
207#435C2×C412yes—
208#435C2×C412yes—
209#435C2×C412yes—
210#435C2×C412yes—
211C8×D4C2×C411yescharacteristic
212C8×D4C2×C411yescharacteristic
213C8×D4C2×C412yes—
214C8×D4C2×C411yescharacteristic
215C8×D4C2×C411yescharacteristic
216C8×D4C2311yescharacteristic
217C8×D4C2312yes—
218C8×D4C2312yes—
219C8×D4C2311yescharacteristic
220C8×D4C2311yescharacteristic
221C8×D4C2312yes—
222C8×D4C2311yescharacteristic
223#433C2×C412yes—
224#433C2×C412yes—
225#433C2×C412yes—
226#433C2×C412yes—
227#433C2×C412yes—
228#433C2×C412yes—
229#433C2×C412yes—
230#433C2×C412yes—
231#432C2×C412yes—
232#432C2×C412yes—
233#432C2×C411yescharacteristic
234#432C2×C412yes—
235#432C2×C411yescharacteristic
236#431C2×C411yescharacteristic
237#431C2×C411yescharacteristic
238#431C2×C411yescharacteristic
239#431C2×C411yescharacteristic
240#431C2×C412yes—
241#424C2×C412yes—
242#424C2×C412yes—
243#424C2×C412yes—
244#424C2×C412yes—
245#423C2×C411yescharacteristic
246#423C2×C412yes—
247#423C2×C411yescharacteristic
248C2×C4⋊C8C2×C411yescharacteristic
249C2×C4⋊C8C2×C412yes—
250#405C2312yes—
251#405C2312yes—
252#405C2312yes—
253#405C2312yes—
254C2×C4×C8C2311yescharacteristic
255C2×C4×C8C2312yes—
256C2×C4×C8C2311yescharacteristic
257C2×C4×C8C2311yescharacteristic
258C2×C4×C8C2312yes—
259C4⋊C16C2311yescharacteristic
260C4⋊C16C2311yescharacteristic
261C4⋊C16C2312yes—
262C4⋊C16C2311yescharacteristic
263C4⋊C16C2312yes—
264C4⋊C16C2311yescharacteristic
265C4⋊C16C2312yes—
266C4⋊C16C2312yes—
267C4⋊C16C2312yes—
268C4⋊C16C2312yes—
269C4⋊C16C2312yes—
270C4⋊C16C2312yes—
271C4⋊C16C2312yes—
272C4⋊C16C2311yescharacteristic
273C4⋊C16C2311yescharacteristic
274C4⋊C16C2312yes—
275C4⋊C16C2312yes—
276C4⋊C16C2312yes—
277C4⋊C16C2311yescharacteristic
278C4⋊C16C2311yescharacteristic
279C4⋊C16C2312yes—
280C4⋊C16C2311yescharacteristic
281C4⋊C16C2311yescharacteristic
282C4⋊C16C2312yes—
283C4⋊C16C2312yes—
284C22⋊C16C2311yescharacteristic
285C22⋊C16C2312yes—
286C22⋊C16C2311yescharacteristic
287C22⋊C16C2311yescharacteristic
288C22⋊C16C2312yes—
289C22⋊C16C2311yescharacteristic
290C22⋊C16C2311yescharacteristic
291C22⋊C16C2312yes—
292C22⋊C16C2311yescharacteristic
293C22⋊C16C2312yes—
294C22⋊C16C2312yes—
295C22⋊C16C2312yes—
296C22⋊C16C2312yes—
297#346C2311yescharacteristic
298#346C2312yes—
299#346C2312yes—
300#346C2312yes—
301#346C2311yescharacteristic
302#346C2312yes—
303#346C2311yescharacteristic
304#346C2311yescharacteristic
305#346C2312yes—
306#346C2312yes—
307#346C2312yes—
308#346C2312yes—
309C4×C16C2311yescharacteristic
310C4×C16C2311yescharacteristic
311C4×C16C2311yescharacteristic
312C4×C16C2311yescharacteristic
313C4×C16C2312yes—
314C4×C16C2311yescharacteristic
315C4×C16C2311yescharacteristic
316C4×C16C2312yes—
317C4×C16C2312yes—
318C4×C16C2312yes—
319C4×C16C2312yes—
320C4×C16C2312yes—
321C4×C16C2312yes—
322C2×#41C2×C811yescharacteristic
323C2×#41C2×C811yescharacteristic
324C22×Q8C2×C811yescharacteristic
325C2×M16C22×C412yes—
326C2×M16C22×C412yes—
327C2×M16C22×C412yes—
328C2×M16C22×C412yes—
329C22×C8C22×C411yescharacteristic
330C22×C8C22×C412yes—
331C22×C8C22×C411yescharacteristic
332C22×C8C22×C412yes—
333C22×C8C22×C411yescharacteristic
334C22×C8C2411yescharacteristic
335C22×C8C2412yes—
336C22×C8C2411yescharacteristic
337C22×C8C2411yescharacteristic
338C4⋊Q8C2×C811yescharacteristic
339C4⋊Q8C2×C811yescharacteristic
340C4⋊Q8C2×C812yes—
341C4⋊Q8C2×C812yes—
342C4⋊Q8C2×C811yescharacteristic
343C4⋊Q8C2×C811yescharacteristic
344#126C2×C812yes—
345#126C2×C812yes—
346#126C2×C812yes—
347#126C2×C812yes—
348#126C2×C812yes—
349#126C2×C812yes—
350#126C2×C812yes—
351#126C2×C812yes—
352#125C2×C812yes—
353#125C2×C812yes—
354#125C2×C812yes—
355#125C2×C811yescharacteristic
356#125C2×C811yescharacteristic
357#125C2×C812yes—
358#125C2×C812yes—
359#125C2×C812yes—
360#125C2×C812yes—
361#124C2×C811yescharacteristic
362#124C2×C811yescharacteristic
363#124C2×C812yes—
364#124C2×C812yes—
365#124C2×C812yes—
366#123C2×C812yes—
367#123C2×C812yes—
368#123C2×C812yes—
369#123C2×C812yes—
370#123C2×C812yes—
371#123C2×C812yes—
372#123C2×C812yes—
373#123C2×C812yes—
374C22⋊Q8C2×C811yescharacteristic
375C22⋊Q8C2×C811yescharacteristic
376C22⋊Q8C2×C812yes—
377C22⋊Q8C2×C812yes—
378C22⋊Q8C2×C812yes—
379C22⋊Q8C2×C811yescharacteristic
380C22⋊Q8C2×C811yescharacteristic
381C22⋊Q8C2×C812yes—
382C22⋊Q8C2×C811yescharacteristic
383C22⋊Q8C2×C811yescharacteristic
384C22⋊Q8C2×C812yes—
385C22⋊Q8C2×C812yes—
386C22⋊Q8C2×C812yes—
387C22⋊Q8C2×C812yes—
388C22⋊Q8C2×C812yes—
389#121C2×C812yes—
390#121C2×C812yes—
391#121C2×C811yescharacteristic
392#121C2×C811yescharacteristic
393#121C2×C812yes—
394C4×Q8C2×C811yescharacteristic
395C4×Q8C2×C811yescharacteristic
396C4×Q8C2×C812yes—
397C4×Q8C2×C811yescharacteristic
398C4×Q8C2×C811yescharacteristic
399C4×Q8C22×C411yescharacteristic
400C4×Q8C22×C411yescharacteristic
401C4×Q8C22×C412yes—
402C4×Q8C22×C411yescharacteristic
403C4×Q8C22×C411yescharacteristic
404C4×Q8C22×C412yes—
405C4×Q8C22×C412yes—
406C4×D4C2×C811yescharacteristic
407C4×D4C2×C811yescharacteristic
408C4×D4C2×C812yes—
409C4×D4C2×C811yescharacteristic
410C4×D4C2×C811yescharacteristic
411C4×D4C22×C411yescharacteristic
412C4×D4C22×C411yescharacteristic
413C4×D4C22×C412yes—
414C4×D4C22×C411yescharacteristic
415C4×D4C22×C411yescharacteristic
416C4×D4C22×C412yes—
417C4×D4C22×C412yes—
418#117C2×C811yescharacteristic
419#117C2×C811yescharacteristic
420#117C2×C811yescharacteristic
421#117C2×C811yescharacteristic
422#117C2×C812yes—
423#117C22×C412yes—
424#117C22×C412yes—
425#117C22×C412yes—
426#117C22×C412yes—
427C2×C4⋊C4C2×C811yescharacteristic
428C2×C4⋊C4C2×C812yes—
429C2×C42C22×C411yescharacteristic
430C2×C42C22×C412yes—
431C2×C42C22×C411yescharacteristic
432C2×C42C22×C411yescharacteristic
433C2×C42C22×C412yes—
434M32—22no—
435M32—22no—
436M32—41no—
437M32—42no—
438M32—42no—
439M32—41no—
440M32—42no—
441M32—42no—
442C2×C16—22no—
443C2×C16—24no—
444C2×C16—42no—
445C2×C16—42no—
446C2×C16—41no—
447C2×C16C2411yescharacteristic
448C2×C16C2411yescharacteristic
449C2×C16C2411yescharacteristic
450C2×C16C2411yescharacteristic
451C2×C16C2412yes—
452C2×C16C2412yes—
453C2×C16C2411yescharacteristic
454C2×C16C2411yescharacteristic
455C2×C16C2412yes—
456C2×C16C2411yescharacteristic
457C2×C16C2412yes—
458C2×C16C2411yescharacteristic
459C4⋊C8C22×C411yescharacteristic
460C4⋊C8C22×C411yescharacteristic
461C4⋊C8C22×C412yes—
462C4⋊C8C22×C412yes—
463C4⋊C8C22×C412yes—
464C4⋊C8C22×C412yes—
465C4⋊C8C22×C412yes—
466C4⋊C8C22×C411yescharacteristic
467C4⋊C8C22×C411yescharacteristic
468C4⋊C8C22×C412yes—
469C4⋊C8C22×C412yes—
470C4⋊C8C22×C412yes—
471C4⋊C8C22×C412yes—
472C4⋊C8C22×C412yes—
473C4⋊C8C22×C411yescharacteristic
474C4⋊C8C22×C411yescharacteristic
475C4⋊C8C22×C412yes—
476C4⋊C8C22×C412yes—
477C4⋊C8C22×C411yescharacteristic
478C4⋊C8C22×C411yescharacteristic
479C4⋊C8C22×C411yescharacteristic
480C4⋊C8C22×C411yescharacteristic
481C4⋊C8C22×C412yes—
482C4⋊C8C22×C412yes—
483C4⋊C8C22×C412yes—
484C22⋊C8C22×C411yescharacteristic
485C22⋊C8C22×C411yescharacteristic
486C22⋊C8C22×C412yes—
487C22⋊C8C22×C412yes—
488C22⋊C8C22×C411yescharacteristic
489C22⋊C8C22×C411yescharacteristic
490C22⋊C8C22×C411yescharacteristic
491C22⋊C8C22×C411yescharacteristic
492C22⋊C8C22×C412yes—
493C22⋊C8C22×C412yes—
494C22⋊C8C22×C412yes—
495C22⋊C8C22×C412yes—
496C22⋊C8C22×C412yes—
497#97C22×C412yes—
498#97C22×C412yes—
499#97C22×C412yes—
500#97C22×C412yes—
501#97C22×C412yes—
502#97C22×C412yes—
503#97C22×C412yes—
504#97C22×C412yes—
505C4×C8C22×C411yescharacteristic
506C4×C8C22×C411yescharacteristic
507C4×C8C22×C411yescharacteristic
508C4×C8C22×C412yes—
509C4×C8C22×C411yescharacteristic
510C4×C8C22×C411yescharacteristic
511C4×C8C22×C412yes—
512C4×C8C22×C411yescharacteristic
513C4×C8C22×C412yes—
514C4×C8C22×C412yes—
515C4×C8C2411yescharacteristic
516C4×C8C2411yescharacteristic
517C4×C8C2412yes—
518C4×C8C2412yes—
519C4×C8C2412yes—
520C4×C8C2411yescharacteristic
521C4×C8C2411yescharacteristic
522#41—42no—
523#41—42no—
524C2×Q8—42no—
525C2×Q8C22×C811yescharacteristic
526C2×Q8C22×C811yescharacteristic
527C2×Q8C22×C811yescharacteristic
528C2×Q8C22×C812yes—
529C2×Q8C22×C811yescharacteristic
530C2×Q8C22×C812yes—
531C2×Q8C22×C812yes—
532C2×D4C22×C811yescharacteristic
533C2×D4C22×C811yescharacteristic
534C2×D4C22×C811yescharacteristic
535C2×D4C22×C812yes—
536C2×D4C22×C811yescharacteristic
537C2×D4C22×C812yes—
538C2×D4C22×C812yes—
539C22×C4C22×C811yescharacteristic
540C22×C4C22×C811yescharacteristic
541C22×C4C22×C811yescharacteristic
542C22×C4C22×C811yescharacteristic
543C22×C4C22×C812yes—
544C22×C4C22×C812yes—
545C22×C4C22×C812yes—
546C22×C4C22×C811yescharacteristic
547C22×C4C22×C811yescharacteristic
548C22×C4C22×C812yes—
549C22×C4C23×C411yescharacteristic
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C412yes—
552C22×C4C23×C411yescharacteristic
553M16—42no—
554M16—42no—
555M16—42no—
556M16—42no—
557C2×C8—21no—
558C2×C8—22no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—22no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—42no—
568C2×C8—41no—
569C2×C8—42no—
570C2×C8C23×C411yescharacteristic
571C2×C8C23×C411yescharacteristic
572C2×C8C23×C411yescharacteristic
573C2×C8C23×C411yescharacteristic
574C2×C8C23×C412yes—
575C2×C8C23×C411yescharacteristic
576C2×C8C23×C411yescharacteristic
577C2×C8C23×C412yes—
578C2×C8C23×C411yescharacteristic
579C2×C8C23×C412yes—
580C2×C8C23×C412yes—
581C2×C8C2511yescharacteristic
582C4⋊C4C22×C812yes—
583C4⋊C4C22×C811yescharacteristic
584C4⋊C4C22×C811yescharacteristic
585C4⋊C4C22×C812yes—
586C4⋊C4C22×C812yes—
587C4⋊C4C22×C812yes—
588C4⋊C4C22×C812yes—
589C4⋊C4C22×C811yescharacteristic
590C4⋊C4C22×C811yescharacteristic
591C4⋊C4C22×C812yes—
592C4⋊C4C22×C811yescharacteristic
593C4⋊C4C22×C811yescharacteristic
594C4⋊C4C22×C811yescharacteristic
595C4⋊C4C22×C811yescharacteristic
596C4⋊C4C22×C811yescharacteristic
597C4⋊C4C22×C811yescharacteristic
598C4⋊C4C22×C812yes—
599C4⋊C4C22×C812yes—
600C4⋊C4C22×C812yes—
601C4⋊C4C22×C812yes—
602C4⋊C4C22×C812yes—
603C4⋊C4C22×C812yes—
604C4⋊C4C22×C812yes—
605C4⋊C4C22×C812yes—
606C4⋊C4C22×C812yes—
607C4⋊C4C22×C812yes—
608C4⋊C4C22×C812yes—
609C4⋊C4C22×C812yes—
610C4⋊C4C22×C812yes—
611C4⋊C4C22×C812yes—
612C4⋊C4C22×C812yes—
613C4⋊C4C22×C812yes—
614C4⋊C4C22×C812yes—
615C22⋊C4C22×C812yes—
616C22⋊C4C22×C811yescharacteristic
617C22⋊C4C22×C811yescharacteristic
618C22⋊C4C22×C811yescharacteristic
619C22⋊C4C22×C811yescharacteristic
620C22⋊C4C22×C812yes—
621C22⋊C4C22×C811yescharacteristic
622C22⋊C4C22×C811yescharacteristic
623C22⋊C4C22×C812yes—
624C22⋊C4C22×C812yes—
625C22⋊C4C22×C812yes—
626C22⋊C4C22×C812yes—
627C22⋊C4C22×C812yes—
628C22⋊C4C22×C812yes—
629C22⋊C4C22×C812yes—
630C22⋊C4C22×C812yes—
631C22⋊C4C22×C812yes—
632C22⋊C4C22×C812yes—
633C22⋊C4C22×C812yes—
634C22⋊C4C22×C812yes—
635C22⋊C4C22×C812yes—
636C42C22×C811yescharacteristic
637C42C22×C811yescharacteristic
638C42C22×C812yes—
639C42C22×C811yescharacteristic
640C42C22×C811yescharacteristic
641C42C22×C811yescharacteristic
642C42C22×C811yescharacteristic
643C42C22×C812yes—
644C42C22×C812yes—
645C42C22×C812yes—
646C42C23×C411yescharacteristic
647C42C23×C411yescharacteristic
648C42C23×C411yescharacteristic
649C42C23×C411yescharacteristic
650C42C23×C412yes—
651C42C23×C412yes—
652C42C23×C412yes—
653C16—21no—
654C16—22no—
655C16—21no—
656C16—21no—
657C16—21no—
658C16—22no—
659C16—22no—
660C16—21no—
661C16—21no—
662C16—21no—
663C16—22no—
664C162−1+412yes—
665C23C23×C811yescharacteristic
666C23C23×C811yescharacteristic
667C23C23×C812yes—
668C23C23×C811yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—42no—
673Q8—42no—
674Q8—42no—
675Q8—41no—
676D4—22no—
677D4—42no—
678D4—42no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4C23×C811yescharacteristic
702C2×C4C23×C811yescharacteristic
703C2×C4C23×C811yescharacteristic
704C2×C4C23×C811yescharacteristic
705C2×C4C23×C812yes—
706C2×C4C23×C811yescharacteristic
707C2×C4C23×C811yescharacteristic
708C2×C4C23×C812yes—
709C2×C4C23×C812yes—
710C2×C4C23×C812yes—
711C2×C4C23×C811yescharacteristic
712C2×C4C23×C811yescharacteristic
713C2×C4C23×C811yescharacteristic
714C2×C4C23×C811yescharacteristic
715C2×C4C23×C812yes—
716C2×C4C23×C812yes—
717C2×C4C23×C812yes—
718C2×C4C23×C811yescharacteristic
719C2×C4C24×C411yescharacteristic
720C8—21no—
721C8—22no—
722C8—21no—
723C8—21no—
724C8—21no—
725C8—21no—
726C8—21no—
727C8—22no—
728C8—21no—
729C8—22no—
730C8—22no—
731C8C2×2−1+411yescharacteristic
732C8#58511yescharacteristic
733C22—21no—
734C22—21no—
735C22—21no—
736C22—22no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—22no—
745C22C24×C811yescharacteristic
746C4—21no—
747C4—21no—
748C4—21no—
749C4—22no—
750C4—22no—
751C4—22no—
752C4—21no—
753C4—21no—
754C4—22no—
755C4—22no—
756C4—22no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—22no—
761C4—21no—
762C4—21no—
763C4#340712yes—
764C4C4×2−1+411yescharacteristic
765C4#357311yescharacteristic
766C2—41no—
767C2—41no—
768C2—41no—
769C2—42no—
770C2C8×2−1+411yescharacteristic
771C2C2×#340711yescharacteristic
772C2#6262411yescharacteristic
subgroupG/H
center, Frattini, cosocleC2×C8C25
commutator, socleC22C24×C8
prime radical#537C8
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #33509C2semidirect
3. #33509C2semidirect
4. #33508C2semidirect
5. #33507C2semidirect
6. #33507C2semidirect
7. #33505C2semidirect
8. #33503C2semidirect
9. #33500C2semidirect
10. #33499C2semidirect
11. #33499C2semidirect
12. #33498C2semidirect
13. #33484C2semidirect
14. #33483C2semidirect
15. #33483C2semidirect
16. #33482C2semidirect
17. #33481C2semidirect
18. #33480C2semidirect
19. #33479C2semidirect
20. Q8×M32C2semidirect
21. #33476C2semidirect
22. #33475C2semidirect
23. #33474C2semidirect

Maximal subgroups

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

subgroupindex
#603302
#335092
#335082
#335072
#335052
#335032
#335002
#334992
#334982
#334842
#334832
#334822
#334812
#334802
#334792
Q8×M322
#334762
#334752
#334742