Finite Group Databasebeta

← C2×#10586020 #72304173

Subgroups — C2×#10586020 #72304173

Order 1024.

817801 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#585C212yesmaximal, complemented
2#10586020C21128yesmaximal, direct product factor
3C2×#62859C2116yesmaximal, complemented
4C2×#62853C2116yesmaximal, complemented
5C2×#62852C2116yesmaximal, complemented
6C2×#62848C214yesmaximal, complemented
7C2×#62842C2112yesmaximal, complemented
8C2×#62812C2116yesmaximal, complemented
9C2×#62811C2132yesmaximal, complemented
10C22×#3449C2112yesmaximal, complemented
11C22×#3428C211yesmaximal, characteristic, complemented
12C22×#585—2128no—
13C22×#585C22116yescomplemented
14C22×#585C22116yescomplemented
15C22×#585C22116yescomplemented
16C22×#585C22116yescomplemented
17C22×#585C221128yescomplemented
18C23×2−1+4C2214yescomplemented
19C23×2−1+4C2218yescomplemented
20C23×H(5,𝔽2)C22112yescomplemented
21C23×H(5,𝔽2)C2218yescomplemented
22C24×#41C2211yescharacteristic
23C24×#41C22112yescomplemented
24C24×#41C22116yescomplemented
25#62859C2211024yescomplemented
26#62853C2211024yescomplemented
27#62852C2211024yescomplemented
28#62848C221256yescomplemented
29#62842C221768yescomplemented
30#62812C2211024yescomplemented
31#62811C2212048yescomplemented
32C2×#3500C221128yescomplemented
33C2×#3499C22164yescomplemented
34C2×#3489C221256yescomplemented
35C2×#3498C22164yescomplemented
36C2×#3488C221256yescomplemented
37C2×#3487C22164yescomplemented
38C2×#3497C22164yescomplemented
39C2×#3486C22164yescomplemented
40C2×#3485C221192yescomplemented
41C2×#3496C221192yescomplemented
42C2×#3484C221192yescomplemented
43C2×D4×#41C221256yescomplemented
44C2×#3449C22116yescomplemented
45C2×#3449C22148yescomplemented
46C2×#3449C22196yescomplemented
47C2×#3449C22196yescomplemented
48C2×#3449C22148yescomplemented
49C2×#3449C22148yescomplemented
50C2×#3449C221768yescomplemented
51C22×#536C22148yescomplemented
52C22×#537C22148yescomplemented
53C22×#535C22148yescomplemented
54C22×#534C22148yescomplemented
55C22×#532C22148yescomplemented
56C22×#525C22196yescomplemented
57C2×#3428C22116yescomplemented
58C2×#3428C22116yescomplemented
59C2×#3428C22164yescomplemented
60C22×#520C2218yescomplemented
61C22×#519C2212yescomplemented
62C22×#518C2216yescomplemented
63C22×C4×#41C2218yescomplemented
64C23×#117C2216yescomplemented
65C2×#585—2512no—
66C2×#585—2512no—
67C2×#585—2512no—
68C2×#585—2512no—
69C2×#585—24096no—
70C2×#585C231512yescomplemented
71C2×#585C231512yescomplemented
72C2×#585C231512yescomplemented
73C2×#585C231512yescomplemented
74C22×2−1+4—2256no—
75C22×2−1+4—2128no—
76C22×2−1+4C23132yes—
77C22×2−1+4C23132yescomplemented
78C22×2−1+4C23164yescomplemented
79C22×2−1+4C23164yescomplemented
80C22×2−1+4C231128yescomplemented
81C22×2−1+4C231256yescomplemented
82C22×H(5,𝔽2)—2256no—
83C22×H(5,𝔽2)—2384no—
84C22×H(5,𝔽2)C23196yes—
85C22×H(5,𝔽2)C23196yescomplemented
86C22×H(5,𝔽2)C23164yescomplemented
87C22×H(5,𝔽2)C23164yescomplemented
88C22×H(5,𝔽2)C231384yescomplemented
89C22×H(5,𝔽2)C231256yescomplemented
90C23×#41—2512no—
91C23×#41—2384no—
92C23×#41D4164yescomplemented
93C23×#41C2318yes—
94C23×#41C23124yes—
95C23×#41C23148yes—
96C23×#41C23148yes—
97C23×#41C2318yes—
98C23×#41C2318yes—
99C23×#41C2314yes—
100C23×#41C2314yes—
101C23×#41C23132yes—
102C23×#41C23148yescomplemented
103C23×#41C23116yescomplemented
104C23×#41C231128yescomplemented
105C23×#41C23124yescomplemented
106C23×#41C23124yescomplemented
107C23×#41C23148yescomplemented
108C23×#41C23148yescomplemented
109C23×#41C231128yescomplemented
110C23×#41C231384yescomplemented
111C23×#41C231512yescomplemented
112C24×Q8C2311yescharacteristic
113C24×Q8C23116yescomplemented
114C24×Q8C23112yescomplemented
115C24×D4C23124yes—
116C24×D4C2313yes—
117C24×D4C23148yescomplemented
118C24×D4C23112yescomplemented
119C25×C4C2313yes—
120C25×C4C23124yescomplemented
121#3500C2314096yescomplemented
122#3499C2312048yescomplemented
123#3498C2312048yescomplemented
124#3497C2312048yescomplemented
125#3496C2316144yescomplemented
126#3489C2318192yescomplemented
127#3488C2318192yescomplemented
128#3487C2312048yescomplemented
129#3486C2312048yescomplemented
130#3485C2316144yescomplemented
131#3484C2316144yescomplemented
132D4×#41C2318192yescomplemented
133C2×#550C231256yescomplemented
134C2×D4×Q8C231256yescomplemented
135C2×#548C231512yescomplemented
136C2×#547C231768yescomplemented
137C2×#546C2311536yescomplemented
138C2×D42C231768yescomplemented
139#3449C2311536yescomplemented
140#3449C231512yescomplemented
141#3449C2313072yescomplemented
142#3449C2313072yescomplemented
143#3449C2311536yescomplemented
144#3449C2311536yescomplemented
145C2×#537C231192yescomplemented
146C2×#537C231384yescomplemented
147C2×#537C23164yescomplemented
148C2×#537C2311536yescomplemented
149C2×#536C231192yescomplemented
150C2×#536C231192yescomplemented
151C2×#536C231192yescomplemented
152C2×#536C23164yescomplemented
153C2×#536C2311536yescomplemented
154C2×#535C231192yescomplemented
155C2×#535C231192yescomplemented
156C2×#535C231192yescomplemented
157C2×#535C23164yescomplemented
158C2×#535C2311536yescomplemented
159C2×#534C23164yes—
160C2×#534C231384yescomplemented
161C2×#534C231192yescomplemented
162C2×#534C2311536yescomplemented
163C2×#532C231192yescomplemented
164C2×#532C231192yescomplemented
165C2×#532C23164yescomplemented
166C2×#532C231192yescomplemented
167C2×#532C2311536yescomplemented
168C22×C4⋊Q8C23148yescomplemented
169C22×#127C23148yescomplemented
170C22×#124C23196yescomplemented
171C2×#525C231384yescomplemented
172C2×#525C231384yescomplemented
173C2×#525C231128yescomplemented
174C2×#525C231384yescomplemented
175C2×#525C2313072yescomplemented
176C22×#123C231192yescomplemented
177C22×C22⋊Q8C231192yescomplemented
178C22×#121C231192yescomplemented
179C22×#121C231192yescomplemented
180C22×#120C231192yescomplemented
181#3428C231512yescomplemented
182#3428C231512yescomplemented
183C2×#520C231128yescomplemented
184C2×#520C231256yescomplemented
185C2×#519C23132yescomplemented
186C2×#519C23164yescomplemented
187C2×#518C23196yescomplemented
188C2×#518C231192yescomplemented
189C2×C4×#41C23164yescomplemented
190C2×C4×#41C23164yescomplemented
191C2×C4×#41C231256yescomplemented
192C22×C4×Q8C23116yescomplemented
193C22×C4×D4C23148yescomplemented
194C22×C4×D4C231192yescomplemented
195C22×#117C2314yes—
196C22×#117C23112yes—
197C22×#117C23112yescomplemented
198C22×#117C23112yescomplemented
199C22×#117C23148yescomplemented
200C22×#117C23148yescomplemented
201C22×#117C231192yescomplemented
202C23×C4⋊C4C23112yescomplemented
203C23×C22⋊C4C23112yes—
204C23×C42C23112yescomplemented
205C26C24124yes—
206C26C2413yes—
207#585—28192no—
208#585—28192no—
209#585—28192no—
210#585—28192no—
211C2×2−1+4—21024no—
212C2×2−1+4—21024no—
213C2×2−1+4—24096no—
214C2×2−1+4—2512no—
215C2×2−1+4—2512no—
216C2×2−1+4—22048no—
217C2×2−1+4C241512yes—
218C2×2−1+4C2411024yescomplemented
219C2×2−1+4C241512yescomplemented
220C2×2−1+4C2411024yescomplemented
221C2×H(5,𝔽2)—21024no—
222C2×H(5,𝔽2)—21024no—
223C2×H(5,𝔽2)—24096no—
224C2×H(5,𝔽2)—21536no—
225C2×H(5,𝔽2)—21536no—
226C2×H(5,𝔽2)—26144no—
227C2×H(5,𝔽2)C2411536yes—
228C2×H(5,𝔽2)C2411024yescomplemented
229C2×H(5,𝔽2)C2411536yescomplemented
230C2×H(5,𝔽2)C2411024yescomplemented
231C22×#41—22048no—
232C22×#41—22048no—
233C22×#41—28192no—
234C22×#41—2256no—
235C22×#41—2768no—
236C22×#41—2128no—
237C22×#41—2384no—
238C22×#41—2384no—
239C22×#41—2768no—
240C22×#41—2768no—
241C22×#41—2384no—
242C22×#41—2768no—
243C22×#41—2768no—
244C22×#41—26144no—
245C22×#41C2×D41256yescomplemented
246C22×#41C2×D41256yescomplemented
247C22×#41C2×D41128yescomplemented
248C22×#41C2×D41128yescomplemented
249C22×#41C2×D411024yescomplemented
250C22×#41C24116yes—
251C22×#41C24116yes—
252C22×#41C24196yes—
253C22×#41C24196yes—
254C22×#41C24116yes—
255C22×#41C24196yes—
256C22×#41C24116yes—
257C22×#41C241128yes—
258C22×#41C24196yes—
259C22×#41C24196yes—
260C22×#41C24196yes—
261C22×#41C241384yes—
262C22×#41C241768yes—
263C22×#41C241768yes—
264C22×#41C241384yes—
265C22×#41C241128yes—
266C22×#41C24116yes—
267C22×#41C24132yes—
268C22×#41C24116yes—
269C22×#41C241128yes—
270C22×#41C241128yes—
271C22×#41C24164yes—
272C22×#41C24164yes—
273C22×#41C241384yescomplemented
274C22×#41C241384yescomplemented
275C22×#41C241768yescomplemented
276C22×#41C241256yescomplemented
277C22×#41C241768yescomplemented
278C22×#41C241768yescomplemented
279C22×#41C2412048yescomplemented
280C22×#41C2412048yescomplemented
281C23×Q8—2256no—
282C23×Q8—2192no—
283C23×Q8C2×D4132yescomplemented
284C23×Q8C2418yes—
285C23×Q8C24124yes—
286C23×Q8C24148yes—
287C23×Q8C24148yes—
288C23×Q8C241128yes—
289C23×Q8C2418yes—
290C23×Q8C2414yes—
291C23×Q8C24116yes—
292C23×Q8C241192yescomplemented
293C23×Q8C241256yescomplemented
294C23×D4—2384no—
295C23×D4—2768no—
296C23×D4—2192no—
297C23×D4C2×D4196yescomplemented
298C23×D4C24116yes—
299C23×D4C24148yes—
300C23×D4C24196yes—
301C23×D4C24196yes—
302C23×D4C241384yes—
303C23×D4C2418yes—
304C23×D4C24124yes—
305C23×D4C24148yes—
306C23×D4C24148yes—
307C23×D4C241384yes—
308C23×D4C241192yes—
309C23×D4C24124yes—
310C23×D4C24112yes—
311C23×D4C24148yes—
312C23×D4C241192yescomplemented
313C23×D4C241768yescomplemented
314C24×C4—2384no—
315C24×C4C2×D4196yescomplemented
316C24×C4C24116yes—
317C24×C4C24124yes—
318C24×C4C24148yes—
319C24×C4C24196yes—
320C24×C4C24196yes—
321C24×C4C24124yes—
322C24×C4C2411yescharacteristic
323C24×C4C24112yes—
324C24×C4C2413yes—
325C24×C4C24112yes—
326C24×C4C2416yes—
327C24×C4C2416yes—
328C24×C4C24148yes—
329C24×C4C241384yescomplemented
330#550C2414096yescomplemented
331D4×Q8C2414096yescomplemented
332#548C2418192yescomplemented
333#547C24112288yescomplemented
334#546C24124576yescomplemented
335D42C24112288yescomplemented
336#537C2411024yescomplemented
337#537C2416144yescomplemented
338#537C2413072yescomplemented
339#536C2411024yescomplemented
340#536C2413072yescomplemented
341#536C2413072yescomplemented
342#536C2413072yescomplemented
343#535C2411024yescomplemented
344#535C2413072yescomplemented
345#535C2413072yescomplemented
346#535C2413072yescomplemented
347#534C2411024yes—
348#534C2416144yescomplemented
349#534C2413072yescomplemented
350#532C2411024yescomplemented
351#532C2413072yescomplemented
352#532C2413072yescomplemented
353#532C2413072yescomplemented
354C2×C4⋊Q8C24164yes—
355C2×C4⋊Q8C241192yes—
356C2×C4⋊Q8C241768yescomplemented
357C2×#127C24164yes—
358C2×#127C241192yes—
359C2×#127C241768yescomplemented
360C2×#124C241128yes—
361C2×#124C241384yes—
362C2×#124C2411536yescomplemented
363#525C2412048yescomplemented
364#525C2416144yescomplemented
365#525C2416144yescomplemented
366#525C2416144yescomplemented
367C2×#123C241256yes—
368C2×#123C241768yes—
369C2×#123C2413072yescomplemented
370C2×C22⋊Q8C241256yes—
371C2×C22⋊Q8C241768yes—
372C2×C22⋊Q8C2413072yescomplemented
373C2×#121C241256yes—
374C2×#121C241256yes—
375C2×#121C241768yes—
376C2×#121C241768yes—
377C2×#121C2413072yescomplemented
378C2×#121C2413072yescomplemented
379C2×#120C241256yes—
380C2×#120C241768yes—
381C2×#120C2413072yescomplemented
382#520C2412048yescomplemented
383#519C241512yescomplemented
384#518C2411536yescomplemented
385C4×#41C2411024yescomplemented
386C4×#41C2411024yescomplemented
387C2×C4×Q8C241128yes—
388C2×C4×Q8C241256yescomplemented
389C2×C4×D4C241256yes—
390C2×C4×D4C241384yes—
391C2×C4×D4C241768yes—
392C2×C4×D4C241768yescomplemented
393C2×C4×D4C2413072yescomplemented
394C2×#117C24116yes—
395C2×#117C24116yes—
396C2×#117C24164yes—
397C2×#117C24196yes—
398C2×#117C241192yes—
399C2×#117C24148yes—
400C2×#117C24148yes—
401C2×#117C24196yes—
402C2×#117C241192yescomplemented
403C2×#117C241192yescomplemented
404C2×#117C241768yescomplemented
405C2×#117C241768yescomplemented
406C22×C4⋊C4C2418yes—
407C22×C4⋊C4C24124yes—
408C22×C4⋊C4C24196yes—
409C22×C4⋊C4C241192yes—
410C22×C4⋊C4C241192yescomplemented
411C22×C22⋊C4C2418yes—
412C22×C22⋊C4C24124yes—
413C22×C22⋊C4C24196yes—
414C22×C22⋊C4C241192yes—
415C22×C22⋊C4C241384yes—
416C22×C42C2418yes—
417C22×C42C24124yes—
418C22×C42C24148yes—
419C22×C42C24148yes—
420C22×C42C241192yescomplemented
421C25—2192no—
422C25—812no—
423C25—896no—
424C25C22×D4148yes—
425C25C25196yes—
426C25C25116yes—
427C25C251192yes—
428C25C25112yes—
429C25C2511yescharacteristic
430C25C2516yes—
431C25C25124yes—
4322−1+4—28192no—
4332−1+4—28192no—
4342−1+4—24096no—
4352−1+4—24096no—
436H(5,𝔽2)—28192no—
437H(5,𝔽2)—28192no—
438H(5,𝔽2)—212288no—
439H(5,𝔽2)—212288no—
440C2×#41—216384no—
441C2×#41—216384no—
442C2×#41—21024no—
443C2×#41—22048no—
444C2×#41—23072no—
445C2×#41—26144no—
446C2×#41—2128no—
447C2×#41—2768no—
448C2×#41—2768no—
449C2×#41—2128no—
450C2×#41—2128no—
451C2×#41—2128no—
452C2×#41—21024no—
453C2×#41—23072no—
454C2×#41—2768no—
455C2×#41—2768no—
456C2×#41—2768no—
457C2×#41—2768no—
458C2×#41—23072no—
459C2×#41—26144no—
460C2×#41—26144no—
461C2×#41—23072no—
462C2×#41—26144no—
463C2×#41—26144no—
464C2×#41C22×D41256yes—
465C2×#41C22×D41512yes—
466C2×#41C22×D41256yes—
467C2×#41C22×D412048yescomplemented
468C2×#41C22×D412048yescomplemented
469C2×#41C22×D411024yescomplemented
470C2×#41C22×D411024yescomplemented
471C2×#41C251128yes—
472C2×#41C251768yes—
473C2×#41C251768yes—
474C2×#41C251768yes—
475C2×#41C251128yes—
476C2×#41C251768yes—
477C2×#41C251768yes—
478C2×#41C251128yes—
479C2×#41C251768yes—
480C2×#41C251128yes—
481C2×#41C2513072yes—
482C2×#41C2511024yes—
483C2×#41C251128yes—
484C2×#41C251128yes—
485C2×#41C251256yes—
486C22×Q8—21024no—
487C22×Q8—22048no—
488C22×Q8—2192no—
489C22×Q8—264no—
490C22×Q8—2384no—
491C22×Q8—2384no—
492C22×Q8—21536no—
493C22×Q8C22×D41128yes—
494C22×Q8C22×D4164yes—
495C22×Q8C22×D41256yescomplemented
496C22×Q8C25116yes—
497C22×Q8C25196yes—
498C22×Q8C251384yes—
499C22×Q8C25116yes—
500C22×Q8C251384yes—
501C22×Q8C25164yes—
502C22×Q8C251192yes—
503C22×Q8C2511024yes—
504C22×Q8C25116yes—
505C22×Q8C25132yes—
506C22×Q8C25164yes—
507C22×D4—2384no—
508C22×D4—2128no—
509C22×D4—2768no—
510C22×D4—2768no—
511C22×D4—23072no—
512C22×D4—23072no—
513C22×D4—26144no—
514C22×D4—2192no—
515C22×D4—264no—
516C22×D4—2384no—
517C22×D4—2384no—
518C22×D4—21536no—
519C22×D4—8384no—
520C22×D4C22×D41384yes—
521C22×D4C22×D41192yes—
522C22×D4C22×D41768yescomplemented
523C22×D4C25132yes—
524C22×D4C251192yes—
525C22×D4C251768yes—
526C22×D4C25132yes—
527C22×D4C25116yes—
528C22×D4C25196yes—
529C22×D4C251768yes—
530C22×D4C251384yes—
531C22×D4C25116yes—
532C22×D4C251384yes—
533C22×D4C251128yes—
534C22×D4C251384yes—
535C22×D4C25164yes—
536C22×D4C251192yes—
537C22×D4C2513072yes—
538C22×D4C251256yes—
539C22×D4C2511536yes—
540C22×D4C25148yes—
541C22×D4C25196yes—
542C22×D4C251192yes—
543C23×C4—2192no—
544C23×C4—2128no—
545C23×C4—2384no—
546C23×C4—2768no—
547C23×C4—2768no—
548C23×C4—23072no—
549C23×C4—848no—
550C23×C4C22×D41192yes—
551C23×C4C22×D4116yes—
552C23×C4C22×D41192yes—
553C23×C4C22×D4148yes—
554C23×C4C22×D4196yes—
555C23×C4C22×D4196yes—
556C23×C4C22×D41768yescomplemented
557C23×C4C25196yes—
558C23×C4C251192yes—
559C23×C4C251768yes—
560C23×C4C25132yes—
561C23×C4C251768yes—
562C23×C4C25116yes—
563C23×C4C251192yes—
564C23×C4C251128yes—
565C23×C4C251384yes—
566C23×C4C25132yes—
567C23×C4C25196yes—
568C23×C4C25116yes—
569C23×C4C251192yes—
570C23×C4C2511yescharacteristic
571C23×C4C25124yes—
572C23×C4C2516yes—
573C23×C4C25148yes—
574C23×C4C25112yes—
575C23×C4C2512yes—
576C23×C4C2518yes—
577C23×C4C25124yes—
578C23×C4C25112yes—
579C23×C4C25196yes—
580C23×C4C25196yes—
581C23×C4C25148yes—
582C23×C4C2512yes—
583C23×C4C25112yes—
584C23×C4C2511yescharacteristic
585C4⋊Q8C251512yes—
586C4⋊Q8C2511536yes—
587#127C251512yes—
588#127C2511536yes—
589#124C2511024yes—
590#124C2513072yes—
591#123C2512048yes—
592#123C2516144yes—
593C22⋊Q8C2512048yes—
594C22⋊Q8C2516144yes—
595#121C2512048yes—
596#121C2512048yes—
597#121C2516144yes—
598#121C2516144yes—
599#120C2512048yes—
600#120C2516144yes—
601C4×Q8C2511024yes—
602C4×D4C2512048yes—
603C4×D4C2513072yes—
604C4×D4C2516144yes—
605#117C251128yes—
606#117C251128yes—
607#117C251768yes—
608#117C251384yes—
609#117C251384yes—
610#117C251768yes—
611C2×C4⋊C4C25132yes—
612C2×C4⋊C4C25196yes—
613C2×C4⋊C4C251256yes—
614C2×C4⋊C4C25164yes—
615C2×C4⋊C4C251192yes—
616C2×C4⋊C4C251768yes—
617C2×C4⋊C4C2511536yes—
618C2×C22⋊C4C25132yes—
619C2×C22⋊C4C25164yes—
620C2×C22⋊C4C25196yes—
621C2×C22⋊C4C251192yes—
622C2×C22⋊C4C251768yes—
623C2×C22⋊C4C251512yes—
624C2×C22⋊C4C2513072yes—
625C2×C42C25116yes—
626C2×C42C25196yes—
627C2×C42C25164yes—
628C2×C42C251192yes—
629C2×C42C251384yes—
630C2×C42C251384yes—
631C2×C42C25116yes—
632C24—264no—
633C24—2384no—
634C24—2768no—
635C24—424no—
636C24—44no—
637C24—448no—
638C24—464no—
639C24—4384no—
640C24—896no—
641C24—848no—
642C24—8384no—
643C24—8768no—
644C24C23×D4196yes—
645C24C23×D418yes—
646C24C23×D4148yes—
647C24C23×D41192yes—
648C24C26132yes—
649C24C2612yes—
650C24C26112yes—
651C24C2611yescharacteristic
652C24C261384yes—
653C24C26164yes—
654C24C26148yes—
655C24C2614yes—
656C24C26124yes—
657#41—24096no—
658#41—212288no—
659#41—2512no—
660#41—23072no—
661#41—23072no—
662#41—2512no—
663#41—2512no—
664#41—2512no—
665#41—23072no—
666#41—23072no—
667#41—23072no—
668#41—23072no—
669#41C23×D411024yes—
670#41C23×D412048yes—
671#41C23×D411024yes—
672C2×Q8—24096no—
673C2×Q8—264no—
674C2×Q8—2384no—
675C2×Q8—2768no—
676C2×Q8—264no—
677C2×Q8—2256no—
678C2×Q8—21536no—
679C2×Q8—21536no—
680C2×Q8C23×D41128yes—
681C2×Q8C23×D41512yes—
682C2×Q8C23×D41256yes—
683C2×Q8C26164yes—
684C2×Q8C261384yes—
685C2×Q8C26164yes—
686C2×Q8C26164yes—
687C2×D4—2128no—
688C2×D4—2768no—
689C2×D4—2128no—
690C2×D4—21536no—
691C2×D4—2512no—
692C2×D4—23072no—
693C2×D4—23072no—
694C2×D4—212288no—
695C2×D4—264no—
696C2×D4—2384no—
697C2×D4—2768no—
698C2×D4—264no—
699C2×D4—2256no—
700C2×D4—21536no—
701C2×D4—21536no—
702C2×D4—4512no—
703C2×D4—81536no—
704C2×D4C23×D41384yes—
705C2×D4C23×D411536yes—
706C2×D4C23×D41768yes—
707C2×D4C261128yes—
708C2×D4C261768yes—
709C2×D4C261128yes—
710C2×D4C26164yes—
711C2×D4C261384yes—
712C2×D4C26164yes—
713C2×D4C2611024yes—
714C2×D4C261192yes—
715C22×C4—264no—
716C22×C4—2384no—
717C22×C4—2768no—
718C22×C4—2128no—
719C22×C4—2128no—
720C22×C4—2512no—
721C22×C4—2768no—
722C22×C4—21536no—
723C22×C4—23072no—
724C22×C4—23072no—
725C22×C4—432no—
726C22×C4—4192no—
727C22×C4—8192no—
728C22×C4C23×D4116yes—
729C22×C4C23×D4196yes—
730C22×C4C23×D4196yes—
731C22×C4C23×D41192yes—
732C22×C4C23×D41768yes—
733C22×C4C23×D4116yes—
734C22×C4C23×D418yes—
735C22×C4C23×D418yes—
736C22×C4C23×D4196yes—
737C22×C4C23×D4148yes—
738C22×C4C23×D4164yes—
739C22×C4C23×D41768yes—
740C22×C4C23×D41192yes—
741C22×C4C23×D41384yes—
742C22×C4C23×D41384yes—
743C22×C4C26132yes—
744C22×C4C26132yes—
745C22×C4C261384yes—
746C22×C4C261128yes—
747C22×C4C261768yes—
748C22×C4C261128yes—
749C22×C4C26164yes—
750C22×C4C26164yes—
751C22×C4C261384yes—
752C22×C4C2611yescharacteristic
753C22×C4C2614yes—
754C22×C4C26112yes—
755C22×C4C26124yes—
756C22×C4C26148yes—
757C22×C4C26148yes—
758C22×C4C2612yes—
759C22×C4C2614yes—
760C22×C4C26196yes—
761C22×C4C2618yes—
762C22×C4C26148yes—
763C22×C4C2618yes—
764C22×C4C2611yescharacteristic
765C4⋊C4C261128yes—
766C4⋊C4C261384yes—
767C4⋊C4C2611024yes—
768C22⋊C4C261128yes—
769C22⋊C4C261384yes—
770C22⋊C4C2612048yes—
771C42C26164yes—
772C42C26164yes—
773C42C261384yes—
774C23—24no—
775C23—248no—
776C23—28no—
777C23—2128no—
778C23—264no—
779C23—2128no—
780C23—2768no—
781C23—448no—
782C23—416no—
783C23—4192no—
784C23—48no—
785C23—496no—
786C23—4128no—
787C23—496no—
788C23—4768no—
789C23—4256no—
790C23—8768no—
791C23—8192no—
792C23—81536no—
793C23C24×D418yes—
794C23C24×D4148yes—
795C23C24×D414yes—
796C23C24×D41192yes—
797C23C24×D4116yes—
798C23C24×D4196yes—
799C23C27164yes—
800C23C2714yes—
801C23C27124yes—
802C23C2712yes—
803C23C2711yescharacteristic
804Q8—2128no—
805Q8—2768no—
806Q8—2128no—
807Q8C24×D41256yes—
808D4—2256no—
809D4—21536no—
810D4—2256no—
811D4—2128no—
812D4—2768no—
813D4—2128no—
814D4—41024no—
815D4C24×D41768yes—
816C2×C4—2128no—
817C2×C4—264no—
818C2×C4—2768no—
819C2×C4—264no—
820C2×C4—2256no—
821C2×C4—2256no—
822C2×C4—21536no—
823C2×C4—464no—
824C2×C4—4384no—
825C2×C4C24×D414yes—
826C2×C4C24×D418yes—
827C2×C4C24×D4132yes—
828C2×C4C24×D4148yes—
829C2×C4C24×D41192yes—
830C2×C4C24×D41192yes—
831C2×C4C24×D41384yes—
832C2×C4C24×D414yes—
833C2×C4C24×D4132yes—
834C2×C4C24×D4116yes—
835C2×C4C24×D4116yes—
836C2×C4C24×D41192yes—
837C2×C4C24×D4196yes—
838C2×C4C27164yes—
839C2×C4C27164yes—
840C2×C4C2712yes—
841C2×C4C2712yes—
842C2×C4C27124yes—
843C2×C4C2714yes—
844C22—24no—
845C22—248no—
846C22—28no—
847C22—216no—
848C22—28no—
849C22—296no—
850C22—264no—
851C22—2128no—
852C22—416no—
853C22—4192no—
854C22—496no—
855C22—4256no—
856C22—4128no—
857C22—8768no—
858C22C25×D418yes—
859C22C25×D4148yes—
860C22C25×D414yes—
861C22C25×D412yes—
862C22#6310314yes—
863C22C2811yescharacteristic
864C4—264no—
865C4—264no—
866C4C25×D414yes—
867C4C25×D418yes—
868C4C25×D4148yes—
869C4C25×D414yes—
870C2—28no—
871C2—24no—
872C2—248no—
873C2—464no—
874C2#1058602014yesdirect product factor
875C2C26×D411yescharacteristic
876C2C2×#6310312yes—
subgroupG/H
center, socleC22×C4C26
commutator, Frattini, cosocleC22C28
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×#585C2semidirect
2. #10586020C2direct (N × H)
3. C2×#62859C2semidirect
4. C2×#62853C2semidirect
5. C2×#62852C2semidirect
6. C2×#62848C2semidirect
7. C2×#62842C2semidirect
8. C2×#62812C2semidirect
9. C2×#62811C2semidirect
10. C22×#3449C2semidirect
11. C22×#3428C2semidirect
13. C22×#585C22semidirect
14. C22×#585C22semidirect
15. C22×#585C22semidirect
16. C22×#585C22semidirect
17. C22×#585C22semidirect
18. C23×2−1+4C22semidirect
19. C23×2−1+4C22semidirect
20. C23×H(5,𝔽2)C22semidirect
21. C23×H(5,𝔽2)C22semidirect
23. C24×#41C22semidirect
24. C24×#41C22semidirect
25. #62859C22semidirect
26. #62853C22semidirect
27. #62852C22semidirect
28. #62848C22semidirect
29. #62842C22semidirect
30. #62812C22semidirect
31. #62811C22semidirect
32. C2×#3500C22semidirect
33. C2×#3499C22semidirect
34. C2×#3489C22semidirect
35. C2×#3498C22semidirect
36. C2×#3488C22semidirect
37. C2×#3487C22semidirect
38. C2×#3497C22semidirect
39. C2×#3486C22semidirect
40. C2×#3485C22semidirect
41. C2×#3496C22semidirect
42. C2×#3484C22semidirect
43. C2×D4×#41C22semidirect
44. C2×#3449C22semidirect
45. C2×#3449C22semidirect
46. C2×#3449C22semidirect
47. C2×#3449C22semidirect
48. C2×#3449C22semidirect
49. C2×#3449C22semidirect
50. C2×#3449C22semidirect
51. C22×#536C22semidirect
52. C22×#537C22semidirect
53. C22×#535C22semidirect
54. C22×#534C22semidirect
55. C22×#532C22semidirect
56. C22×#525C22semidirect
57. C2×#3428C22semidirect
58. C2×#3428C22semidirect
59. C2×#3428C22semidirect
60. C22×#520C22semidirect
61. C22×#519C22semidirect
62. C22×#518C22semidirect
63. C22×C4×#41C22semidirect
64. C23×#117C22semidirect
70. C2×#585C23semidirect
71. C2×#585C23semidirect
72. C2×#585C23semidirect
73. C2×#585C23semidirect
77. C22×2−1+4C23semidirect
78. C22×2−1+4C23semidirect
79. C22×2−1+4C23semidirect
80. C22×2−1+4C23semidirect
81. C22×2−1+4C23semidirect
85. C22×H(5,𝔽2)C23semidirect
86. C22×H(5,𝔽2)C23semidirect
87. C22×H(5,𝔽2)C23semidirect
88. C22×H(5,𝔽2)C23semidirect
89. C22×H(5,𝔽2)C23semidirect
92. C23×#41D4semidirect
102. C23×#41C23semidirect
103. C23×#41C23semidirect
104. C23×#41C23semidirect
105. C23×#41C23semidirect
106. C23×#41C23semidirect
107. C23×#41C23semidirect
108. C23×#41C23semidirect
109. C23×#41C23semidirect
110. C23×#41C23semidirect
111. C23×#41C23semidirect
113. C24×Q8C23semidirect
114. C24×Q8C23semidirect
117. C24×D4C23semidirect
118. C24×D4C23semidirect
120. C25×C4C23semidirect
121. #3500C23semidirect
122. #3499C23semidirect
123. #3498C23semidirect
124. #3497C23semidirect
125. #3496C23semidirect
126. #3489C23semidirect
127. #3488C23semidirect
128. #3487C23semidirect
129. #3486C23semidirect
130. #3485C23semidirect
131. #3484C23semidirect
132. D4×#41C23semidirect
133. C2×#550C23semidirect
134. C2×D4×Q8C23semidirect
135. C2×#548C23semidirect
136. C2×#547C23semidirect
137. C2×#546C23semidirect
138. C2×D42C23semidirect
139. #3449C23semidirect
140. #3449C23semidirect
141. #3449C23semidirect
142. #3449C23semidirect
143. #3449C23semidirect
144. #3449C23semidirect
145. C2×#537C23semidirect
146. C2×#537C23semidirect
147. C2×#537C23semidirect
148. C2×#537C23semidirect
149. C2×#536C23semidirect
150. C2×#536C23semidirect
151. C2×#536C23semidirect
152. C2×#536C23semidirect
153. C2×#536C23semidirect
154. C2×#535C23semidirect
155. C2×#535C23semidirect
156. C2×#535C23semidirect
157. C2×#535C23semidirect
158. C2×#535C23semidirect
160. C2×#534C23semidirect
161. C2×#534C23semidirect
162. C2×#534C23semidirect
163. C2×#532C23semidirect
164. C2×#532C23semidirect
165. C2×#532C23semidirect
166. C2×#532C23semidirect
167. C2×#532C23semidirect
168. C22×C4⋊Q8C23semidirect
169. C22×#127C23semidirect
170. C22×#124C23semidirect
171. C2×#525C23semidirect
172. C2×#525C23semidirect
173. C2×#525C23semidirect
174. C2×#525C23semidirect
175. C2×#525C23semidirect
176. C22×#123C23semidirect
177. C22×C22⋊Q8C23semidirect
178. C22×#121C23semidirect
179. C22×#121C23semidirect
180. C22×#120C23semidirect
181. #3428C23semidirect
182. #3428C23semidirect
183. C2×#520C23semidirect
184. C2×#520C23semidirect
185. C2×#519C23semidirect
186. C2×#519C23semidirect
187. C2×#518C23semidirect
188. C2×#518C23semidirect
189. C2×C4×#41C23semidirect
190. C2×C4×#41C23semidirect
191. C2×C4×#41C23semidirect
192. C22×C4×Q8C23semidirect
193. C22×C4×D4C23semidirect
194. C22×C4×D4C23semidirect
197. C22×#117C23semidirect
198. C22×#117C23semidirect
199. C22×#117C23semidirect
200. C22×#117C23semidirect
201. C22×#117C23semidirect
202. C23×C4⋊C4C23semidirect
204. C23×C42C23semidirect
218. C2×2−1+4C24semidirect
219. C2×2−1+4C24semidirect
220. C2×2−1+4C24semidirect
228. C2×H(5,𝔽2)C24semidirect
229. C2×H(5,𝔽2)C24semidirect
230. C2×H(5,𝔽2)C24semidirect
245. C22×#41C2×D4semidirect
246. C22×#41C2×D4semidirect
247. C22×#41C2×D4semidirect
248. C22×#41C2×D4semidirect
249. C22×#41C2×D4semidirect
273. C22×#41C24semidirect
274. C22×#41C24semidirect
275. C22×#41C24semidirect
276. C22×#41C24semidirect
277. C22×#41C24semidirect
278. C22×#41C24semidirect
279. C22×#41C24semidirect
280. C22×#41C24semidirect
283. C23×Q8C2×D4semidirect
292. C23×Q8C24semidirect
293. C23×Q8C24semidirect
297. C23×D4C2×D4semidirect
312. C23×D4C24semidirect
313. C23×D4C24semidirect
315. C24×C4C2×D4semidirect
329. C24×C4C24semidirect
330. #550C24semidirect
331. D4×Q8C24semidirect
332. #548C24semidirect
333. #547C24semidirect
334. #546C24semidirect
335. D42C24semidirect
336. #537C24semidirect
337. #537C24semidirect
338. #537C24semidirect
339. #536C24semidirect
340. #536C24semidirect
341. #536C24semidirect
342. #536C24semidirect
343. #535C24semidirect
344. #535C24semidirect
345. #535C24semidirect
346. #535C24semidirect
348. #534C24semidirect
349. #534C24semidirect
350. #532C24semidirect
351. #532C24semidirect
352. #532C24semidirect
353. #532C24semidirect
356. C2×C4⋊Q8C24semidirect
359. C2×#127C24semidirect
362. C2×#124C24semidirect
363. #525C24semidirect
364. #525C24semidirect
365. #525C24semidirect
366. #525C24semidirect
369. C2×#123C24semidirect
372. C2×C22⋊Q8C24semidirect
377. C2×#121C24semidirect
378. C2×#121C24semidirect
381. C2×#120C24semidirect
382. #520C24semidirect
383. #519C24semidirect
384. #518C24semidirect
385. C4×#41C24semidirect
386. C4×#41C24semidirect
388. C2×C4×Q8C24semidirect
392. C2×C4×D4C24semidirect
393. C2×C4×D4C24semidirect
402. C2×#117C24semidirect
403. C2×#117C24semidirect
404. C2×#117C24semidirect
405. C2×#117C24semidirect
410. C22×C4⋊C4C24semidirect
420. C22×C42C24semidirect
467. C2×#41C22×D4semidirect
468. C2×#41C22×D4semidirect
469. C2×#41C22×D4semidirect
470. C2×#41C22×D4semidirect
495. C22×Q8C22×D4semidirect
522. C22×D4C22×D4semidirect
556. C23×C4C22×D4semidirect
874. C2#10586020direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5852
#105860202
C2×#628592
C2×#628532
C2×#628522
C2×#628482
C2×#628422
C2×#628122
C2×#628112
C22×#34492
C22×#34282