Finite Group Databasebeta

← C2×#19148674 #26004804

Subgroups — C2×#19148674 #26004804

Order 11008.

7758 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148674C2132yesmaximal, direct product factor
2C2×#14583632C213yesmaximal, complemented
3C2×Q8×Dic86C211yesmaximal, characteristic, complemented
4C2×#14583604C213yesmaximal, complemented
5C2×#14583568C211yesmaximal, characteristic, complemented
6C2×#14583561C211yesmaximal, characteristic, complemented
7C2×#14583556C211yesmaximal, characteristic, complemented
8C2×#14583554C213yesmaximal, complemented
9C2×#14583550C213yesmaximal, complemented
10C2×#14583520C213yesmaximal, complemented
11C2×#14583514C213yesmaximal, complemented
12C2×#14583446C213yesmaximal, complemented
13C2×#14583427C213yesmaximal, complemented
14C2×#14583381C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
16C2×C43×#520C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621898C2216yes—
19C22×Q8×D43C2211yescharacteristic
20#14583632C22148yescomplemented
21Q8×Dic86C22116yescomplemented
22#14583604C22148yescomplemented
23#14583568C22116yescomplemented
24#14583561C22116yescomplemented
25#14583556C22116yescomplemented
26#14583554C22148yescomplemented
27#14583550C22148yescomplemented
28#14583520C22148yescomplemented
29#14583514C22148yescomplemented
30#14583446C22148yescomplemented
31C2×#13063325C2213yes—
32C2×#13063324C2213yes—
33C2×#13063324C2213yes—
34C2×#13063321C2213yes—
35#14583427C22148yescomplemented
36C2×#13063320C2213yes—
37C2×#13063318C2213yes—
38C2×#13063315C2213yes—
39C2×#13063313C2213yes—
40C2×#13063312C2213yes—
41C2×#13063311C2213yes—
42C2×#13063311C2216yes—
43C2×#13063310C2213yes—
44C2×#13063308C2216yes—
45C2×#13063307C2213yes—
46C2×#13063307C2216yes—
47C2×#13063305C2213yes—
48C2×#13063304C2216yes—
49C2×#13063304C2213yes—
50C2×#13063303C2216yes—
51C2×#13063303C2211yescharacteristic
52C2×#13063300C2213yes—
53C2×#13063299C2213yes—
54C2×#13063298C2213yes—
55C2×#13063296C2213yes—
56C2×#13063296C2213yes—
57#14583381C22116yescomplemented
58C2×Q8×Dic43C2211yescharacteristic
59C2×Q8×Dic43C2211yescharacteristic
60C2×C4×Dic86C2213yes—
61C2×C4×Dic86C2213yes—
62C2×#13063290C2213yes—
63C4×Q8×D43C22116yescomplemented
64C2×C4×D172C2213yes—
65C2×C4×D172C2213yes—
66C2×#13063287C2213yes—
67C2×C4×C22⋊D43C2213yes—
68C2×C4×C22⋊D43C2213yes—
69C2×C4×C22⋊D43C2216yes—
70C2×#13063282C2213yes—
71C2×C4⋊C4×D43C2213yes—
72C2×C4⋊C4×D43C2213yes—
73C2×C42×D43C2213yes—
74C22×#41×C43C2211yescharacteristic
75C43×#520C22116yescomplemented
76C2×C4×Q8×C43C2211yescharacteristic
77C2×C4×Q8×C43C2211yescharacteristic
78C2×C4×D4×C43C2213yes—
79C2×C4×D4×C43C2213yes—
80C2×#117×C43C2213yes—
81C22×C4⋊C4×C43C2213yes—
82C2×#10621902—28no—
83C2×#10621902C2318yes—
84C2×#10621898—424no—
85C2×#10621898C23148yes—
86C22×Dic86C2313yes—
87C22×Dic86C2311yescharacteristic
88C22×Dic86C2316yes—
89C2×Q8×D43—28no—
90C2×Q8×D43C2318yes—
91C22×D172C2313yes—
92C22×D172C2313yes—
93C22×C22⋊D43C2313yes—
94C22×C22⋊D43C2313yes—
95C22×C22⋊D43C2316yes—
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2313yes—
98C22×C4×D43C2313yes—
99C22×C4×D43C2313yes—
100C22×C4×D43C2316yes—
101#13063325C23124yes—
102#13063324C23124yes—
103#13063324C23124yes—
104#13063321C23124yes—
105#13063320C23124yes—
106#13063318C23124yes—
107#13063315C23124yes—
108#13063313C23124yes—
109#13063312C23124yes—
110#13063311C23124yes—
111#13063311C23148yes—
112#13063310C23124yes—
113#13063308C23148yes—
114#13063307C23124yes—
115#13063307C23148yes—
116#13063305C23124yes—
117#13063304C23148yes—
118#13063304C23124yes—
119#13063303C23148yes—
120#13063303C2318yes—
121#13063300C23124yes—
122#13063299C23124yes—
123#13063298C23124yes—
124#13063296C23124yes—
125#13063296C23124yes—
126Q8×Dic43C2318yes—
127Q8×Dic43C2318yes—
128C4×Dic86C23124yes—
129C4×Dic86C23124yes—
130#13063290C23124yes—
131C4×D172C23124yes—
132C4×D172C23124yes—
133#13063287C23124yes—
134C4×C22⋊D43C23124yes—
135C4×C22⋊D43C23124yes—
136C4×C22⋊D43C23148yes—
137#13063282C23124yes—
138C2×C4⋊Dic43C2313yes—
139C2×C4⋊Dic43C2313yes—
140C2×C4⋊Dic43C2313yes—
141C2×C4⋊Dic43C2313yes—
142C2×Dic43⋊C4C2313yes—
143C2×Dic43⋊C4C2316yes—
144C2×Dic43⋊C4C2311yescharacteristic
145C2×Dic43⋊C4C2311yescharacteristic
146C2×Dic43⋊C4C2313yes—
147C2×Dic43⋊C4C2313yes—
148C2×Dic43⋊C4C2313yes—
149C4⋊C4×D43C23124yes—
150C4⋊C4×D43C23124yes—
151C2×C22⋊Dic43C2313yes—
152C2×C22⋊Dic43C2316yes—
153C2×C22⋊Dic43C2313yes—
154C2×(C2×D43)⋊C4C2313yes—
155C2×(C2×D43)⋊C4C2313yes—
156C2×(C2×D43)⋊C4C2311yescharacteristic
157C2×(C2×D43)⋊C4C2313yes—
158C2×(C2×D43)⋊C4C2316yes—
159C2×(C2×D43)⋊C4C2311yescharacteristic
160C2×(C2×D43)⋊C4C2313yes—
161C2×C4×Dic43C2313yes—
162C2×C4×Dic43C2313yes—
163C2×C4×Dic43C2313yes—
164C2×C4×Dic43C2313yes—
165C42×D43C23124yes—
166C2×#41×C43—28no—
167C2×#41×C43C2318yes—
168C22×Q8×C43C2311yescharacteristic
169C22×D4×C43C2313yes—
170C23×C4×C43C2313yes—
171C23×C4×C43C2316yes—
172C4×Q8×C43C2318yes—
173C4×Q8×C43C2318yes—
174C4×D4×C43C23124yes—
175C4×D4×C43C23124yes—
176#117×C43C23124yes—
177C2×C4⋊C4×C43C2313yes—
178C2×C4⋊C4×C43C2313yes—
179C2×C4⋊C4×C43C2313yes—
180C2×C4⋊C4×C43C23124yes—
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C22⋊C4×C43C2313yes—
183C2×C22⋊C4×C43C2313yes—
184C2×C42×C43C2313yes—
185C2×C42×C43C2313yes—
186C24×C43C2413yes—
187C23×D43C2413yes—
188C23×D43C2411yescharacteristic
189#41×C43—232no—
190C2×Q8×C43#4118yescomplemented
191C2×Q8×C43C2414yes—
192C2×D4×C43—212no—
193C2×D4×C43C24112yes—
194C22×C4×C43—212no—
195C22×C4×C43—412no—
196C22×C4×C43C2411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C22×C4×C43C2413yes—
199C22×C4×C43C2413yes—
200C22×C4×C43C2411yescharacteristic
201C22×C4×C43C24112yes—
202C22×C4×C43C24124yes—
203C22×C4×C43C2413yes—
204C2×C22⋊D43—212no—
205C2×C22⋊D43—212no—
206C2×C22⋊D43—412no—
207C2×C22⋊D43C24112yes—
208C2×C22⋊D43C24112yes—
209C2×C22⋊D43C24124yes—
210C22×Dic43C2411yescharacteristic
211C22×Dic43C2413yes—
212C22×Dic43C2413yes—
213C22×Dic43C2413yes—
214C22×Dic43C2411yescharacteristic
215C22×Dic43C2411yescharacteristic
216#10621902—232no—
217Q8×D43—232no—
218#10621898—496no—
219C2×D172—212no—
220C2×D172—212no—
221C2×D172C24112yes—
222C2×D172C24112yes—
223C2×C4×D43—212no—
224C2×C4×D43—212no—
225C2×C4×D43—24no—
226C2×C4×D43—212no—
227C2×C4×D43—412no—
228C2×C4×D43C2414yes—
229C2×C4×D43C24112yes—
230C2×C4×D43C24112yes—
231C2×C4×D43C24112yes—
232C2×C4×D43C24124yes—
233C2×Dic86—212no—
234C2×Dic86—24no—
235C2×Dic86—412no—
236C2×Dic86C24112yes—
237C2×Dic86C2414yes—
238C2×Dic86C24124yes—
239C4⋊C4×C43C24112yes—
240C4⋊C4×C43C24112yes—
241C4⋊C4×C43C24112yes—
242C4⋊C4×C43C2414yes—
243C22⋊C4×C43C24112yes—
244C22⋊C4×C43C24112yes—
245C42×C43C24112yes—
246C42×C43C24112yes—
247C22⋊Dic43C24112yes—
248C22⋊Dic43C24124yes—
249C22⋊Dic43C24112yes—
250(C2×D43)⋊C4C24112yes—
251(C2×D43)⋊C4C24112yes—
252(C2×D43)⋊C4C2414yes—
253(C2×D43)⋊C4C24112yes—
254(C2×D43)⋊C4C24124yes—
255(C2×D43)⋊C4C2414yes—
256(C2×D43)⋊C4C24112yes—
257C4⋊Dic43C24112yes—
258C4⋊Dic43C24112yes—
259C4⋊Dic43C24112yes—
260C4⋊Dic43C24112yes—
261Dic43⋊C4C24112yes—
262Dic43⋊C4C24124yes—
263Dic43⋊C4C2414yes—
264Dic43⋊C4C2414yes—
265Dic43⋊C4C24112yes—
266Dic43⋊C4C24112yes—
267Dic43⋊C4C24112yes—
268C4×Dic43C24112yes—
269C4×Dic43C24112yes—
270C4×Dic43C24112yes—
271C4×Dic43C24112yes—
272C23×C43—26no—
273C23×C43—26no—
274C23×C43—26no—
275C23×C43C2516yes—
276C23×C43C2511yescharacteristic
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—26no—
280C22×D43—26no—
281C22×D43—26no—
282C22×D43H(5,𝔽2)14yes—
283C22×D43C2516yes—
284C22×D43C2512yes—
285Q8×C43C2×#41116yescomplemented
286D4×C43—224no—
287C2×C4×C43—22no—
288C2×C4×C43—26no—
289C2×C4×C43—26no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—224no—
293C2×C4×C43—424no—
294C2×C4×C43C2×#41112yes—
295C2×C4×C43C2512yes—
296C2×C4×C43C2516yes—
297C2×C4×C43C2512yes—
298C2×C4×C43C2516yes—
299C2×C4×C43C2512yes—
300C2×C4×C43C2516yes—
301C22⋊D43—224no—
302C22⋊D43—224no—
303C22⋊D43—424no—
304C2×Dic43—26no—
305C2×Dic43—22no—
306C2×Dic43—26no—
307C2×Dic43—26no—
308C2×Dic43—22no—
309C2×Dic432−1+414yes—
310C2×Dic43C2512yes—
311C2×Dic43C2516yes—
312C2×Dic43C2516yes—
313C2×Dic43C2516yes—
314C2×Dic43C2512yes—
315C2×Dic43C2512yes—
316D172—224no—
317D172—224no—
318C4×D43—224no—
319C4×D43—224no—
320C4×D43—224no—
321C4×D43—28no—
322C4×D43—424no—
323Dic86—224no—
324Dic86—28no—
325Dic86—424no—
326C2×#3522—431nomaximal, Sylow
327C22×C43—26no—
328C22×C43—26no—
329C22×C43—26no—
330C22×C43—412no—
331C22×C43C22×#4112yes—
332C22×C43C2×H(5,𝔽2)12yes—
333C22×C43C2×2−1+412yes—
334C22×C43C2611yescharacteristic
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—28no—
338C2×D43—26no—
339C2×D43—26no—
340C2×D43—26no—
341C2×D43—412no—
342C2×D43C2×H(5,𝔽2)14yes—
343C4×C43—22no—
344C4×C43—26no—
345C4×C43—26no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43C22×#41112yes—
349Dic43—26no—
350Dic43—22no—
351Dic43—26no—
352Dic43—26no—
353Dic43—22no—
354Dic43C2×2−1+414yes—
355#3522—4332no—
356C2×#559—433no—
357C2×Q82—431no—
358C2×#554—433no—
359C2×#550—431no—
360C2×#548—431no—
361C2×#548—431no—
362C2×#547—433no—
363C2×#547—433no—
364C2×#542—433no—
365C2×#542—433no—
366C2×#532—433no—
367C2×#529—433no—
368C2×#520—431no—
369C2×#520D4311yescharacteristic, complemented
370C22×C4×Q8—431no—
371C2×C43—46no—
372C2×C43#352214yescomplemented
373C2×C43C23×#4111yescharacteristic
374C2×C43C22×H(5,𝔽2)11yescharacteristic
375C2×C43C22×2−1+411yescharacteristic
376D43—24no—
377D43—46no—
378C22×#41—431no—
379C22×#41—436no—
380C22×#41C2×D4311yescharacteristic
381C23×Q8—431no—
382#559—4348no—
383Q82—4316no—
384#554—4348no—
385#550—4316no—
386#548—4316no—
387#548—4316no—
388#547—4348no—
389#547—4348no—
390#542—4348no—
391#542—4348no—
392#532—4348no—
393C2×C4⋊Q8—433no—
394C2×C4⋊Q8—433no—
395C2×C4⋊Q8—433no—
396C2×#127—433no—
397#529—4348no—
398C2×#126—433no—
399C2×#126—433no—
400C2×#125—433no—
401C2×#124—433no—
402C2×#124—433no—
403C2×#124—436no—
404C2×#124—433no—
405C2×#123—436no—
406C2×#123—433no—
407C2×#123—433no—
408C2×#123—436no—
409C2×C22⋊Q8—436no—
410C2×C22⋊Q8—433no—
411C2×C22⋊Q8—431no—
412C2×C22⋊Q8—436no—
413C2×C22⋊Q8—433no—
414C2×#121—433no—
415C2×#121—433no—
416C2×#121—433no—
417C2×#121—433no—
418C2×#121—433no—
419#520—4316no—
420#520C2×D43116yescomplemented
421C2×C4×Q8—431no—
422C2×C4×Q8—431no—
423C2×C4×Q8—4316no—
424C2×C4×Q8—433no—
425C2×C4×Q8—433no—
426C2×C4×Q8—433no—
427C2×C4×Q8C2×D4311yescharacteristic
428C2×C4×Q8C2×D4311yescharacteristic
429C2×C4×D4—433no—
430C2×C4×D4—433no—
431C2×C4×D4—436no—
432C2×C4×D4—433no—
433C2×C4×D4—433no—
434C2×C4×D4—433no—
435C2×C4×D4C2×D4313yes—
436C2×C4×D4C2×D4313yes—
437C2×#117—433no—
438C2×#117C2×D4313yes—
439C22×C4⋊C4—433no—
440C22×C4⋊C4—433no—
441C22×C4⋊C4C2×D4313yes—
442C22×C42—433no—
443C43C2×#352211yescharacteristic, complemented, Sylow
444C2×#41—28no—
445C2×#41—438no—
446C2×#41—4348no—
447C2×#41—868no—
448C2×#41—17224no—
449C2×#41C22×D4318yes—
450C22×Q8—438no—
451C22×Q8—431no—
452C22×Q8—433no—
453C22×Q8—436no—
454C22×Q8—868no—
455C22×Q8C22×D4311yescharacteristic
456C22×D4—433no—
457C22×D4—433no—
458C22×D4—436no—
459C22×D4—433no—
460C22×D4—433no—
461C22×D4C22×D4313yes—
462C23×C4—433no—
463C23×C4—433no—
464C23×C4—433no—
465C23×C4—431no—
466C23×C4—436no—
467C23×C4C22×D4313yes—
468C23×C4C22×D4316yes—
469C4⋊Q8—4324no—
470C4⋊Q8—4324no—
471C4⋊Q8—4324no—
472#127—4324no—
473#126—4324no—
474#126—4324no—
475#125—4324no—
476#124—4324no—
477#124—4324no—
478#124—4348no—
479#124—4324no—
480#123—4348no—
481#123—4324no—
482#123—4324no—
483#123—4348no—
484C22⋊Q8—4348no—
485C22⋊Q8—4324no—
486C22⋊Q8—438no—
487C22⋊Q8—4348no—
488C22⋊Q8—4324no—
489#121—4324no—
490#121—4324no—
491#121—4324no—
492#121—4324no—
493#121—4324no—
494C4×Q8—438no—
495C4×Q8—438no—
496C4×Q8—4324no—
497C4×Q8—4324no—
498C4×Q8—4324no—
499C4×Q8C22×D4318yes—
500C4×Q8C22×D4318yes—
501C4×D4—4324no—
502C4×D4—4324no—
503C4×D4—4348no—
504C4×D4—4324no—
505C4×D4—4324no—
506C4×D4—4324no—
507C4×D4C22×D43124yes—
508C4×D4C22×D43124yes—
509#117—4324no—
510#117C22×D43124yes—
511C2×C4⋊C4—433no—
512C2×C4⋊C4—433no—
513C2×C4⋊C4—433no—
514C2×C4⋊C4—436no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—433no—
518C2×C4⋊C4—433no—
519C2×C4⋊C4—433no—
520C2×C4⋊C4—433no—
521C2×C4⋊C4—433no—
522C2×C4⋊C4—4324no—
523C2×C4⋊C4—4324no—
524C2×C4⋊C4C22×D4313yes—
525C2×C4⋊C4C22×D4313yes—
526C2×C4⋊C4C22×D4313yes—
527C2×C4⋊C4C22×D43124yes—
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C22⋊C4—433no—
530C2×C22⋊C4—436no—
531C2×C22⋊C4—433no—
532C2×C22⋊C4—433no—
533C2×C22⋊C4—433no—
534C2×C22⋊C4—431no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—433no—
537C2×C22⋊C4—436no—
538C2×C22⋊C4—433no—
539C2×C22⋊C4C22×D4313yes—
540C2×C22⋊C4C22×D4313yes—
541C2×C42—433no—
542C2×C42—433no—
543C2×C42—433no—
544C2×C42—433no—
545C2×C42—4324no—
546C2×C42C22×D4313yes—
547C2×C42C22×D4313yes—
548C24—431no—
549C24—433no—
550C24C23×D4313yes—
551#41—232no—
552#41—8632no—
553#41—17296no—
554C2×Q8—434no—
555C2×Q8—4312no—
556C2×Q8—4324no—
557C2×Q8—864no—
558C2×Q8—8632no—
559C2×Q8—8612no—
560C2×Q8—17212no—
561C2×Q8#1062189818yescomplemented
562C2×Q8C23×D4314yes—
563C2×D4—212no—
564C2×D4—4312no—
565C2×D4—4312no—
566C2×D4—4324no—
567C2×D4—4312no—
568C2×D4—4312no—
569C2×D4—8612no—
570C2×D4—8612no—
571C2×D4—8612no—
572C2×D4—8612no—
573C2×D4—17212no—
574C2×D4C23×D43112yes—
575C22×C4—212no—
576C22×C4—412no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—433no—
580C22×C4—433no—
581C22×C4—433no—
582C22×C4—431no—
583C22×C4—434no—
584C22×C4—4312no—
585C22×C4—4312no—
586C22×C4—4312no—
587C22×C4—4324no—
588C22×C4—864no—
589C22×C4—8612no—
590C22×C4—8612no—
591C22×C4—8612no—
592C22×C4—17212no—
593C22×C4C23×D43112yes—
594C22×C4C23×D4311yescharacteristic
595C22×C4C23×D4313yes—
596C22×C4C23×D4311yescharacteristic
597C22×C4C23×D4313yes—
598C22×C4C23×D4311yescharacteristic
599C22×C4C23×D43124yes—
600C22×C4C23×D4313yes—
601C4⋊C4—4312no—
602C4⋊C4—4312no—
603C4⋊C4—4312no—
604C4⋊C4—4324no—
605C4⋊C4—434no—
606C4⋊C4—434no—
607C4⋊C4—4312no—
608C4⋊C4—4312no—
609C4⋊C4—4312no—
610C4⋊C4—4312no—
611C4⋊C4—4312no—
612C4⋊C4C23×D43112yes—
613C4⋊C4C23×D43112yes—
614C4⋊C4C23×D43112yes—
615C4⋊C4C23×D4314yes—
616C22⋊C4—4312no—
617C22⋊C4—4324no—
618C22⋊C4—4312no—
619C22⋊C4—4312no—
620C22⋊C4—4312no—
621C22⋊C4—434no—
622C22⋊C4—434no—
623C22⋊C4—4312no—
624C22⋊C4—4324no—
625C22⋊C4—4312no—
626C22⋊C4C23×D43112yes—
627C22⋊C4C23×D43112yes—
628C42—4312no—
629C42—4312no—
630C42—4312no—
631C42—4312no—
632C42C23×D43112yes—
633C42C23×D43112yes—
634C23—26no—
635C23—26no—
636C23—26no—
637C23—434no—
638C23—432no—
639C23—436no—
640C23—862no—
641C23—862no—
642C23—866no—
643C23—866no—
644C23—866no—
645C23C24×D4316yes—
646C23C24×D4311yescharacteristic
647Q8—868no—
648Q8—8624no—
649Q8—17224no—
650Q8C2×#10621898116yescomplemented
651D4—224no—
652D4—8624no—
653D4—8624no—
654D4—8624no—
655D4—8624no—
656D4—17224no—
657C2×C4—22no—
658C2×C4—26no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—224no—
663C2×C4—424no—
664C2×C4—434no—
665C2×C4—432no—
666C2×C4—432no—
667C2×C4—436no—
668C2×C4—436no—
669C2×C4—436no—
670C2×C4—432no—
671C2×C4—868no—
672C2×C4—8624no—
673C2×C4—862no—
674C2×C4—866no—
675C2×C4—866no—
676C2×C4—866no—
677C2×C4—862no—
678C2×C4—8624no—
679C2×C4—8624no—
680C2×C4—17224no—
681C2×C4C2×#10621898112yes—
682C2×C4C24×D4312yes—
683C2×C4C24×D4316yes—
684C2×C4C24×D4312yes—
685C2×C4C24×D4316yes—
686C2×C4C24×D4312yes—
687C2×C4C24×D4316yes—
688C22—26no—
689C22—26no—
690C22—26no—
691C22—412no—
692C22—434no—
693C22—862no—
694C22—862no—
695C22—868no—
696C22—866no—
697C22—866no—
698C22—866no—
699C22—17212no—
700C22C22×#1062189812yes—
701C22H(5,𝔽2)×D4312yes—
702C222−1+4×D4312yes—
703C22C25×D4311yescharacteristic
704C4—22no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—22no—
709C4—434no—
710C4—862no—
711C4—866no—
712C4—866no—
713C4—866no—
714C4—862no—
715C4C22×#10621898112yes—
716C2—46no—
717C2—864no—
718C2—1726no—
719C2#1914867414yesdirect product factor
720C2C23×#1062189811yescharacteristic
721C2C2×H(5,𝔽2)×D4311yescharacteristic
722C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#520C2
socleC23×C43C25
hypercenterC2×#520D43
hypocenterC43C2×#3522
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #19148674C2direct (N × H)
2. C2×#14583632C2semidirect
3. C2×Q8×Dic86C2semidirect
4. C2×#14583604C2semidirect
5. C2×#14583568C2semidirect
6. C2×#14583561C2semidirect
7. C2×#14583556C2semidirect
8. C2×#14583554C2semidirect
9. C2×#14583550C2semidirect
10. C2×#14583520C2semidirect
11. C2×#14583514C2semidirect
12. C2×#14583446C2semidirect
13. C2×#14583427C2semidirect
14. C2×#14583381C2semidirect
15. C2×C4×Q8×D43C2semidirect
16. C2×C43×#520C2semidirect
20. #14583632C22semidirect
21. Q8×Dic86C22semidirect
22. #14583604C22semidirect
23. #14583568C22semidirect
24. #14583561C22semidirect
25. #14583556C22semidirect
26. #14583554C22semidirect
27. #14583550C22semidirect
28. #14583520C22semidirect
29. #14583514C22semidirect
30. #14583446C22semidirect
35. #14583427C22semidirect
57. #14583381C22semidirect
63. C4×Q8×D43C22semidirect
75. C43×#520C22semidirect
190. C2×Q8×C43#41semidirect
285. Q8×C43C2×#41semidirect
369. C2×#520D43semidirect
372. C2×C43#3522semidirect
420. #520C2×D43semidirect
443. C43C2×#3522semidirect
561. C2×Q8#10621898semidirect
650. Q8C2×#10621898semidirect
719. C2#19148674direct (N × H)

Maximal subgroups

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

subgroupindex
#191486742
C2×#145836322
C2×Q8×Dic862
C2×#145836042
C2×#145835682
C2×#145835612
C2×#145835562
C2×#145835542
C2×#145835502
C2×#145835202
C2×#145835142
C2×#145834462
C2×#145834272
C2×#145833812
C2×C4×Q8×D432
C2×C43×#5202
C2×#352243