Finite Group Databasebeta

← #7625911

Subgroups — #7625911

Order 512.

7762 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#553C211yesmaximal, characteristic
2#34319C218yesmaximal, complemented
3#34305C218yesmaximal, complemented
4#34301C218yesmaximal, complemented
5#34247C214yesmaximal, complemented
6#34246C214yesmaximal, complemented
7#34238C214yesmaximal, complemented
8#34217C212yesmaximal, complemented
9#34204C212yesmaximal, complemented
10#34204C212yesmaximal, complemented
11#34186C211yesmaximal, characteristic, complemented
12#34179C211yesmaximal, characteristic, complemented
13#34178C211yesmaximal, characteristic, complemented
14C4×#553C218yesmaximal, complemented
15#34126C214yesmaximal, complemented
16D4×#117C212yesmaximal, complemented
17C4×#518C211yesmaximal, characteristic, complemented
18#33996C211yesmaximal, characteristic, complemented
19C2×#2274C211yesmaximal, characteristic, complemented
20C2×#553C4132yescomplemented
21C2×#553C2214yes—
22C2×#553C2214yes—
23C2×#553C2214yes—
24C2×#553C2214yes—
25C22×#126C2212yes—
26C22×#125C2211yescharacteristic
27C22×#123C2212yes—
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×#121C2212yes—
31C2×#518C2212yes—
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2212yes—
34C22×C4×D4C2211yescharacteristic
35C22×#117C2212yes—
36C22×#117C2212yes—
37C22×#117C2211yescharacteristic
38C23×C4⋊C4C2211yescharacteristic
39#2374C22116yescomplemented
40#2373C22116yescomplemented
41#2373C22116yescomplemented
42#2370C2218yescomplemented
43#2370C2218yescomplemented
44#2364C22116yescomplemented
45#2363C2218yescomplemented
46#2363C22116yescomplemented
47#2363C2218yescomplemented
48#2361C2218yescomplemented
49#2361C2218yescomplemented
50#2359C22116yescomplemented
51#2357C2218yescomplemented
52#2357C2218yescomplemented
53#2354C2218yescomplemented
54#2354C2214yescomplemented
55#2353C2218yescomplemented
56#2353C2218yescomplemented
57#2352C2214yescomplemented
58#2352C2214yescomplemented
59#2349C2218yescomplemented
60D4×C4⋊C4C2214yescomplemented
61#2347C2218yescomplemented
62#2346C2218yescomplemented
63#2345C2218yes—
64#2345C2218yes—
65#2345C2218yescomplemented
66#2344C2214yes—
67#2344C2218yescomplemented
68#2342C2214yes—
69#2342C2214yes—
70#2342C2218yes—
71#2342C2218yes—
72D4×C22⋊C4C2214yes—
73D4×C22⋊C4C2218yes—
74D4×C22⋊C4C2218yes—
75#2335C22116yescomplemented
76#2334C22116yescomplemented
77#2333C22116yescomplemented
78#2330C2218yescomplemented
79#2324C2218yescomplemented
80#2324C2218yescomplemented
81#2316C2212yes—
82#2316C2212yes—
83#2313C2214yes—
84#2312C2214yes—
85#2312C2214yes—
86#2309C2212yes—
87C4×#125C2218yescomplemented
88C4×#126C22116yescomplemented
89C4×#123C22116yescomplemented
90C4×#121C2218yescomplemented
91C4×#121C22116yescomplemented
92C4×#121C2218yescomplemented
93#2293C2214yescomplemented
94#2293C2218yescomplemented
95#2290C2214yescomplemented
96#2290C2218yescomplemented
97#2290C2218yescomplemented
98#2290C2214yescomplemented
99#2285C2212yes—
100#2283C2214yes—
101#2280C2212yes—
102#2280C2212yes—
103#2280C2214yes—
104#2280C2214yes—
105#2275C2218yescomplemented
106#2274C2211yescharacteristic
107#2274C2211yescharacteristic
108#2274C2211yescharacteristic
109#2274C2212yes—
110#2274C2212yes—
111#2274C2214yes—
112#2274C2211yescharacteristic
113#2274C2218yescomplemented
114#2274C2218yescomplemented
115#2273C2214yes—
116#2273C2214yes—
117C42×D4C2218yescomplemented
118C42×D4C2214yescomplemented
119C42×D4C2218yescomplemented
120C4×#117C2212yes—
121C4×#117C2214yes—
122C4×#117C2218yescomplemented
123C2×C4×C4⋊C4C2218yescomplemented
124C2×C4×C22⋊C4C2214yes—
125C2×C4×C22⋊C4C2214yes—
126C23×D4C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C23×D4C2312yes—
129C23×D4C2312yes—
130C24×C4C2311yescharacteristic
131C24×C4C2311yescharacteristic
132C24×C4C2312yes—
133C24×C4C2312yes—
134#553C2×C4164yescomplemented
135#553C2×C4164yescomplemented
136#553C2×C4164yescomplemented
137#553C2×C4164yescomplemented
138C2×#126C2×C4132yescomplemented
139C2×#126C2318yes—
140C2×#126C2318yes—
141C2×#125C2×C4116yescomplemented
142C2×#125C2314yes—
143C2×#125C2314yes—
144C2×#123C2×C4132yescomplemented
145C2×#123C2318yes—
146C2×#123C2318yes—
147C2×#121C2×C4132yescomplemented
148C2×#121C2×C4116yescomplemented
149C2×#121C2×C4116yescomplemented
150C2×#121C2314yes—
151C2×#121C2314yes—
152C2×#121C2318yes—
153C2×#121C2314yes—
154C2×#121C2314yes—
155C2×#121C2318yes—
156#518—216no—
157C2×C4×D4C2×C4132yescomplemented
158C2×C4×D4C2×C4116yescomplemented
159C2×C4×D4C2×C4116yescomplemented
160C2×C4×D4C2318yes—
161C2×C4×D4C2318yes—
162C2×C4×D4C2318yes—
163C2×C4×D4C23116yes—
164C2×C4×D4C23116yes—
165C2×C4×D4C2312yes—
166C2×C4×D4C2314yes—
167C2×C4×D4C2312yes—
168C2×C4×D4C2312yes—
169C2×C4×D4C2314yes—
170C2×C4×D4C2314yes—
171C2×C4×D4C2314yes—
172C2×C4×D4C2312yes—
173C2×C4×D4C2314yes—
174C2×C4×D4C2314yes—
175C2×#117—216no—
176C2×#117—216no—
177C2×#117C2×C4116yescomplemented
178C2×#117C2312yes—
179C2×#117C2312yes—
180C2×#117C2312yes—
181C2×#117C2314yes—
182C2×#117C2314yes—
183C2×#117C2314yes—
184C2×#117C2314yes—
185C2×#117C2314yes—
186C2×#117C2314yes—
187C2×#117C2318yes—
188C2×#117C2318yes—
189C2×#117C2314yes—
190C2×#117C2314yes—
191C2×#117C2312yes—
192C22×C4⋊C4C2×C4116yescomplemented
193C22×C4⋊C4C2314yes—
194C22×C4⋊C4C2314yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2314yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2314yes—
203C22×C4⋊C4C2311yescharacteristic
204C22×C22⋊C4C2314yes—
205C22×C22⋊C4C2314yes—
206C22×C22⋊C4C2318yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C42C2314yes—
214C22×C42C2314yes—
215C22×C42C2318yes—
216C22×C42C2318yes—
217C22×C42C2312yes—
218C22×C42C2311yescharacteristic
219#390C2318yes—
220#390C2318yes—
221#390C23116yes—
222#390C23116yes—
223#390C2318yes—
224#389C2318yes—
225#389C2318yes—
226#389C2318yes—
227#389C2318yes—
228#389C23116yes—
229#389C23116yes—
230#389C2318yes—
231#388C23116yes—
232#388C23116yes—
233#388C23116yes—
234#388C23116yes—
235#388C23116yes—
236#388C23116yes—
237#388C23116yes—
238#388C23116yes—
239#388C2318yes—
240#388C2318yes—
241#388C2318yes—
242#388C2318yes—
243#387C2318yes—
244#387C23116yes—
245#387C23116yes—
246#387C23116yes—
247#387C23116yes—
248#387C23116yes—
249#387C23116yes—
250#387C2318yes—
251#386C23116yes—
252#386C23116yes—
253#386C2318yes—
254#386C23116yes—
255#386C2318yes—
256#386C23116yes—
257#385C23116yes—
258#385C23116yes—
259#385C2318yes—
260#385C2318yes—
261#384C2314yes—
262#383C2318yes—
263#382C2314yes—
264#382C2318yes—
265#381C2314yes—
266#381C2318yes—
267#381C2314yes—
268#381C2318yes—
269#380C2314yes—
270#380C2318yes—
271#380C2318yes—
272#380C2314yes—
273#380C2314yes—
274#380C2318yes—
275#380C2314yes—
276#380C2314yes—
277#380C2318yes—
278#380C2314yes—
279#379C2318yes—
280#379C2314yes—
281#379C2314yes—
282C4×C4⋊C4C2318yes—
283C4×C4⋊C4C23116yes—
284C4×C4⋊C4C23116yes—
285C4×C4⋊C4C2318yes—
286C4×C4⋊C4C2318yes—
287C4×C4⋊C4C23116yes—
288C4×C4⋊C4C2318yes—
289C4×C4⋊C4C2318yes—
290C4×C4⋊C4C2318yes—
291C4×C4⋊C4C2318yes—
292C4×C4⋊C4C2318yes—
293C4×C4⋊C4C2314yes—
294C4×C4⋊C4C2318yes—
295C4×C4⋊C4C2314yes—
296C4×C4⋊C4C2314yes—
297C4×C4⋊C4C2314yes—
298C4×C4⋊C4C23116yes—
299C4×C4⋊C4C2318yes—
300C4×C4⋊C4C2318yes—
301C4×C4⋊C4C2318yes—
302C4×C22⋊C4C23116yes—
303C4×C22⋊C4C23116yes—
304C4×C22⋊C4C23116yes—
305C4×C22⋊C4C2314yes—
306C4×C22⋊C4C2314yes—
307C4×C22⋊C4C2314yes—
308C4×C22⋊C4C2318yes—
309C4×C22⋊C4C23116yes—
310C4×C22⋊C4C2318yes—
311C4×C22⋊C4C2318yes—
312C4×C22⋊C4C2318yes—
313C4×C22⋊C4C2314yes—
314C4×C22⋊C4C2314yes—
315C4×C22⋊C4C2318yes—
316C4×C22⋊C4C2318yes—
317C4×C22⋊C4C2314yes—
318C4×C22⋊C4C2314yes—
319C4×C22⋊C4C2318yes—
320C4×C22⋊C4C2314yes—
321C4×C22⋊C4C2314yes—
322C4×C22⋊C4C2318yes—
323C4×C22⋊C4C2318yes—
324C4×C22⋊C4C2318yes—
325C4×C22⋊C4C23116yes—
326C4×C22⋊C4C23116yes—
327C4×C22⋊C4C2314yes—
328#376C2314yes—
329#376C2318yes—
330#376C2318yes—
331C2×#95C2318yes—
332C2×#95C2318yes—
333C43C2318yes—
334C43C2314yes—
335C25C2411yescharacteristic
336C25C2411yescharacteristic
337C25C2412yes—
338C22×D4—28no—
339C22×D4—44no—
340C22×D4—48no—
341C22×D4—84no—
342C22×D4C22×C418yes—
343C22×D4C22×C4116yes—
344C22×D4C22×C418yes—
345C22×D4C22×C4116yes—
346C22×D4C2412yes—
347C22×D4C2414yes—
348C22×D4C2414yes—
349C22×D4C2418yes—
350C22×D4C2412yes—
351C22×D4C2414yes—
352C23×C4—28no—
353C23×C4—28no—
354C23×C4—84no—
355C23×C4—84no—
356C23×C4C22×C418yes—
357C23×C4C22×C418yes—
358C23×C4C22×C4116yes—
359C23×C4C22×C4116yes—
360C23×C4C2418yes—
361C23×C4C2411yescharacteristic
362C23×C4C2411yescharacteristic
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2418yes—
368C23×C4C24116yes—
369C23×C4C2412yes—
370C23×C4C2411yescharacteristic
371C23×C4C2412yes—
372C23×C4C2411yescharacteristic
373C23×C4C2412yes—
374C23×C4C2414yes—
375C23×C4C2414yes—
376C23×C4C2414yes—
377C23×C4C2414yes—
378C23×C4C2411yescharacteristic
379#126C22×C4164yes—
380#126C22×C4164yes—
381#125C22×C4132yes—
382#125C22×C4132yes—
383#123C22×C4164yes—
384#123C22×C4164yes—
385#121C22×C4164yes—
386#121C22×C4164yes—
387#121C22×C4132yes—
388#121C22×C4132yes—
389#121C22×C4132yes—
390#121C22×C4132yes—
391C4×D4—232no—
392C4×D4—232no—
393C4×D4—416no—
394C4×D4—432no—
395C4×D4—816no—
396C4×D4C22×C4132yes—
397C4×D4C22×C4132yes—
398C4×D4C22×C4132yes—
399C4×D4C22×C4132yes—
400C4×D4C22×C4116yes—
401C4×D4C22×C4116yes—
402C4×D4C22×C4116yes—
403C4×D4C22×C4116yes—
404C4×D4C22×C4132yes—
405C4×D4C22×C4132yes—
406#117—28no—
407#117—28no—
408#117—28no—
409#117—216no—
410#117—216no—
411#117—216no—
412#117—216no—
413#117—216no—
414#117—216no—
415#117—88no—
416#117—88no—
417#117C22×C4132yes—
418#117C22×C4132yes—
419#117#41116yes—
420C2×C4⋊C4—216no—
421C2×C4⋊C4—216no—
422C2×C4⋊C4C22×C418yes—
423C2×C4⋊C4C22×C418yes—
424C2×C4⋊C4C22×C4116yes—
425C2×C4⋊C4C22×C4132yes—
426C2×C4⋊C4C22×C4132yes—
427C2×C4⋊C4C22×C418yes—
428C2×C4⋊C4C22×C4116yes—
429C2×C4⋊C4C22×C418yes—
430C2×C4⋊C4C22×C4116yes—
431C2×C4⋊C4C2414yes—
432C2×C4⋊C4C2414yes—
433C2×C4⋊C4C2418yes—
434C2×C4⋊C4C2418yes—
435C2×C4⋊C4C2414yes—
436C2×C4⋊C4C2418yes—
437C2×C4⋊C4C24116yes—
438C2×C4⋊C4C24116yes—
439C2×C4⋊C4C2418yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2414yes—
442C2×C4⋊C4C2418yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2414yes—
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2414yes—
450C2×C22⋊C4—216no—
451C2×C22⋊C4—216no—
452C2×C22⋊C4—232no—
453C2×C22⋊C4C22×C4116yes—
454C2×C22⋊C4C22×C418yes—
455C2×C22⋊C4C22×C4116yes—
456C2×C22⋊C4C22×C4116yes—
457C2×C22⋊C4C22×C418yes—
458C2×C22⋊C4C22×C4116yes—
459C2×C22⋊C4C2414yes—
460C2×C22⋊C4C2414yes—
461C2×C22⋊C4C2414yes—
462C2×C22⋊C4C2418yes—
463C2×C22⋊C4C2418yes—
464C2×C22⋊C4C24116yes—
465C2×C22⋊C4C2418yes—
466C2×C22⋊C4C2418yes—
467C2×C22⋊C4C24116yes—
468C2×C22⋊C4C2418yes—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C24116yes—
471C2×C22⋊C4C2418yes—
472C2×C22⋊C4C2411yescharacteristic
473C2×C22⋊C4C2411yescharacteristic
474C2×C22⋊C4C2411yescharacteristic
475C2×C22⋊C4C2411yescharacteristic
476C2×C22⋊C4C2414yes—
477C2×C22⋊C4C2418yes—
478C2×C22⋊C4C2414yes—
479C2×C22⋊C4C2412yes—
480C2×C22⋊C4C2412yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C2414yes—
483C2×C42—216no—
484C2×C42—216no—
485C2×C42—88no—
486C2×C42—88no—
487C2×C42C22×C4116yes—
488C2×C42C22×C418yes—
489C2×C42C2418yes—
490C2×C42C2418yes—
491C2×C42C2414yes—
492C2×C42C2414yes—
493C2×C42C2414yes—
494C2×C42C2418yes—
495C2×C42C2418yes—
496C2×C42C2418yes—
497C2×C42C2418yes—
498C2×C42C24116yes—
499C2×C42C24116yes—
500C2×C42C2418yes—
501C2×C42C2418yes—
502C2×C42C2414yes—
503C2×C42C2414yes—
504C2×C42C2412yes—
505C2×C42C2412yes—
506C2×C42C2414yes—
507#95C2418yes—
508#95C2418yes—
509#95C2418yes—
510#95C2418yes—
511#95C24116yes—
512#95C2418yes—
513#95C2418yes—
514#95C2418yes—
515#95C24116yes—
516#95C24116yes—
517#95C2418yes—
518#95C2418yes—
519#95C2418yes—
520#95C2418yes—
521#95C24116yes—
522#95C2418yes—
523C24—24no—
524C24—24no—
525C24—24no—
526C24—28no—
527C24—42no—
528C24—44no—
529C24—42no—
530C24—44no—
531C24—42no—
532C24C23×C414yes—
533C24C23×C414yes—
534C24C23×C418yes—
535C24C2511yescharacteristic
536C24C2512yes—
537C24C2514yes—
538C24C2511yescharacteristic
539C24C2511yescharacteristic
540C2×D4—28no—
541C2×D4—216no—
542C2×D4—232no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—416no—
546C2×D4—44no—
547C2×D4—48no—
548C2×D4—432no—
549C2×D4—416no—
550C2×D4—816no—
551C2×D4C23×C4116yes—
552C2×D4C23×C418yes—
553C2×D4C23×C4116yes—
554C2×D4C23×C4116yes—
555C2×D4C23×C418yes—
556C2×D4C23×C4132yes—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—232no—
560C22×C4—232no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—216no—
570C22×C4—216no—
571C22×C4—216no—
572C22×C4—232no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—44no—
579C22×C4—42no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—42no—
583C22×C4—416no—
584C22×C4—48no—
585C22×C4—416no—
586C22×C4—48no—
587C22×C4—816no—
588C22×C4—816no—
589C22×C4C23×C414yes—
590C22×C4C23×C414yes—
591C22×C4C23×C418yes—
592C22×C4C23×C418yes—
593C22×C4C23×C418yes—
594C22×C4C23×C418yes—
595C22×C4C23×C418yes—
596C22×C4C23×C414yes—
597C22×C4C23×C418yes—
598C22×C4C23×C414yes—
599C22×C4C23×C418yes—
600C22×C4C23×C4116yes—
601C22×C4C23×C4116yes—
602C22×C4C23×C4116yes—
603C22×C4C23×C4116yes—
604C22×C4C23×C414yes—
605C22×C4C2×#4118yes—
606C22×C4C2518yes—
607C22×C4C2518yes—
608C22×C4C2518yes—
609C22×C4C2511yescharacteristic
610C22×C4C2514yes—
611C22×C4C2511yescharacteristic
612C22×C4C2512yes—
613C22×C4C2514yes—
614C22×C4C2512yes—
615C22×C4C2511yescharacteristic
616C22×C4C2514yes—
617C22×C4C2511yescharacteristic
618C22×C4C2518yes—
619C22×C4C2512yes—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—48no—
626C4⋊C4—416no—
627C4⋊C4—48no—
628C4⋊C4—416no—
629C4⋊C4C23×C4116yes—
630C4⋊C4C23×C4116yes—
631C4⋊C4C23×C4132yes—
632C4⋊C4C23×C4116yes—
633C4⋊C4C23×C4116yes—
634C4⋊C4C23×C4116yes—
635C4⋊C4C23×C418yes—
636C4⋊C4C23×C418yes—
637C4⋊C4C23×C4132yes—
638C4⋊C4C2×#41116yes—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—216no—
643C22⋊C4—216no—
644C22⋊C4—216no—
645C22⋊C4—232no—
646C22⋊C4—48no—
647C22⋊C4—416no—
648C22⋊C4—416no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4C23×C4132yes—
652C22⋊C4C23×C414yes—
653C22⋊C4C23×C414yes—
654C22⋊C4C23×C414yes—
655C22⋊C4C23×C414yes—
656C22⋊C4C23×C4116yes—
657C22⋊C4C23×C4116yes—
658C22⋊C4C23×C4132yes—
659C22⋊C4C23×C418yes—
660C22⋊C4C23×C418yes—
661C22⋊C4C23×C4132yes—
662C22⋊C4C2×#41116yes—
663C42—216no—
664C42—216no—
665C42—28no—
666C42—28no—
667C42—28no—
668C42—48no—
669C42—48no—
670C42—48no—
671C42—48no—
672C42—416no—
673C42—48no—
674C42—416no—
675C42—48no—
676C42C23×C4116yes—
677C42C23×C4116yes—
678C42C23×C418yes—
679C42C23×C418yes—
680C42C2×#41116yes—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—28no—
688C23—22no—
689C23—24no—
690C23—28no—
691C23—22no—
692C23—22no—
693C23—28no—
694C23—24no—
695C23—28no—
696C23—28no—
697C23—28no—
698C23—216no—
699C23—44no—
700C23—48no—
701C23—44no—
702C23—48no—
703C23—44no—
704C23—416no—
705C23—88no—
706C23—816no—
707C23C24×C414yes—
708C23C24×C418yes—
709C23C24×C412yes—
710C23C24×C412yes—
711C23C24×C412yes—
712C23C22×#4114yes—
713C23#58514yes—
714C23C2611yescharacteristic
715D4—232no—
716D4—216no—
717D4—232no—
718D4—416no—
719D4—48no—
720D4—432no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—24no—
728C2×C4—28no—
729C2×C4—22no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—22no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—216no—
736C2×C4—216no—
737C2×C4—216no—
738C2×C4—216no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—48no—
749C2×C4—44no—
750C2×C4—416no—
751C2×C4—416no—
752C2×C4—416no—
753C2×C4—416no—
754C2×C4—48no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—432no—
758C2×C4—816no—
759C2×C4—832no—
760C2×C4C4×#41116yes—
761C2×C4C24×C412yes—
762C2×C4C24×C412yes—
763C2×C4C24×C418yes—
764C2×C4C24×C414yes—
765C2×C4C24×C418yes—
766C2×C4C24×C412yes—
767C2×C4C24×C412yes—
768C2×C4C24×C414yes—
769C2×C4C24×C418yes—
770C2×C4C24×C414yes—
771C2×C4C22×#41116yes—
772C2×C4C22×#4114yes—
773C2×C4C22×#4114yes—
774C22—28no—
775C22—28no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—24no—
782C22—28no—
783C22—24no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—28no—
788C22—24no—
789C22—416no—
790C22—44no—
791C22—416no—
792C22—44no—
793C22—44no—
794C22—88no—
795C22—816no—
796C22C2×C4×#4114yes—
797C22#342814yes—
798C22C25×C411yescharacteristic
799C22C23×#4112yes—
800C22C2×#58512yes—
801C22H(7,𝔽2)12yes—
802C4—216no—
803C4—22no—
804C4—24no—
805C4—22no—
806C4—28no—
807C4—24no—
808C4—22no—
809C4—28no—
810C4—22no—
811C4—28no—
812C4—48no—
813C4—48no—
814C4—48no—
815C4C2×C4×#4118yes—
816C2—24no—
817C2—24no—
818C2—42no—
819C2—44no—
820C2—48no—
821C2C22×C4×#4111yescharacteristic
822C2C2×#342811yescharacteristic
823C2#6265211yescharacteristic
824C2#6300814yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC22×#553C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34319C2semidirect
3. #34305C2semidirect
4. #34301C2semidirect
5. #34247C2semidirect
6. #34246C2semidirect
7. #34238C2semidirect
8. #34217C2semidirect
9. #34204C2semidirect
10. #34204C2semidirect
11. #34186C2semidirect
12. #34179C2semidirect
13. #34178C2semidirect
14. C4×#553C2semidirect
15. #34126C2semidirect
16. D4×#117C2semidirect
17. C4×#518C2semidirect
18. #33996C2semidirect
19. C2×#2274C2semidirect
20. C2×#553C4semidirect
39. #2374C22semidirect
40. #2373C22semidirect
41. #2373C22semidirect
42. #2370C22semidirect
43. #2370C22semidirect
44. #2364C22semidirect
45. #2363C22semidirect
46. #2363C22semidirect
47. #2363C22semidirect
48. #2361C22semidirect
49. #2361C22semidirect
50. #2359C22semidirect
51. #2357C22semidirect
52. #2357C22semidirect
53. #2354C22semidirect
54. #2354C22semidirect
55. #2353C22semidirect
56. #2353C22semidirect
57. #2352C22semidirect
58. #2352C22semidirect
59. #2349C22semidirect
60. D4×C4⋊C4C22semidirect
61. #2347C22semidirect
62. #2346C22semidirect
65. #2345C22semidirect
67. #2344C22semidirect
75. #2335C22semidirect
76. #2334C22semidirect
77. #2333C22semidirect
78. #2330C22semidirect
79. #2324C22semidirect
80. #2324C22semidirect
87. C4×#125C22semidirect
88. C4×#126C22semidirect
89. C4×#123C22semidirect
90. C4×#121C22semidirect
91. C4×#121C22semidirect
92. C4×#121C22semidirect
93. #2293C22semidirect
94. #2293C22semidirect
95. #2290C22semidirect
96. #2290C22semidirect
97. #2290C22semidirect
98. #2290C22semidirect
105. #2275C22semidirect
113. #2274C22semidirect
114. #2274C22semidirect
117. C42×D4C22semidirect
118. C42×D4C22semidirect
119. C42×D4C22semidirect
122. C4×#117C22semidirect
123. C2×C4×C4⋊C4C22semidirect
134. #553C2×C4semidirect
135. #553C2×C4semidirect
136. #553C2×C4semidirect
137. #553C2×C4semidirect
138. C2×#126C2×C4semidirect
141. C2×#125C2×C4semidirect
144. C2×#123C2×C4semidirect
147. C2×#121C2×C4semidirect
148. C2×#121C2×C4semidirect
149. C2×#121C2×C4semidirect
157. C2×C4×D4C2×C4semidirect
158. C2×C4×D4C2×C4semidirect
159. C2×C4×D4C2×C4semidirect
177. C2×#117C2×C4semidirect
192. C22×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5532
#343192
#343052
#343012
#342472
#342462
#342382
#342172
#342042
#341862
#341792
#341782
C4×#5532
#341262
D4×#1172
C4×#5182
#339962
C2×#22742