Finite Group Databasebeta

← C2×#19145489 #25967296

Subgroups — C2×#19145489 #25967296

Order 11008.

2122 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583475C211yesmaximal, characteristic
2C2×#14583472C211yesmaximal, characteristic
3#19145489C2116yesmaximal, direct product factor
4C2×#14583243C211yesmaximal, characteristic, complemented
5C2×#14583242C211yesmaximal, characteristic, complemented
6C2×#14583240C211yesmaximal, characteristic, complemented
7C2×#14583158C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic, complemented
9C2×#14583141C211yesmaximal, characteristic, complemented
10C2×#14583139C211yesmaximal, characteristic, complemented
11C2×#14583057C211yesmaximal, characteristic, complemented
12C2×#14583056C211yesmaximal, characteristic, complemented
13C2×#14583056C211yesmaximal, characteristic, complemented
14C2×#14583054C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic
16C2×C43×#485C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C22×Dic172C2211yescharacteristic
21C22×Dic172C2211yescharacteristic
22C22×#10621885C2211yescharacteristic
23C22×#10621885C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583475—24no—
27#14583475C2218yes—
28#14583472—24no—
29#14583472C2218yes—
30C2×#13063325—21no—
31C2×#13063324—21no—
32C2×#13063313—21no—
33C2×#13063311—21no—
34C2×#13063310—21no—
35C2×#13063309—21no—
36C2×#13063309—21no—
37C2×#13063307—21no—
38C2×#13063305C2211yescharacteristic
39C2×#13063305C2211yescharacteristic
40C2×#13063305C2211yescharacteristic
41C2×#13063305C2211yescharacteristic
42C2×#13063305C2211yescharacteristic
43C2×#13063304C2211yescharacteristic
44C2×#13063301C2211yescharacteristic
45C2×#13063283C2211yescharacteristic
46#14583243C2218yescomplemented
47#14583242C2218yescomplemented
48#14583240C2218yescomplemented
49#14583158C2218yescomplemented
50#14583156C2218yescomplemented
51#14583141C2218yescomplemented
52#14583139C2218yescomplemented
53#14583057C2218yescomplemented
54#14583056C2218yescomplemented
55#14583056C2218yescomplemented
56#14583054C2218yescomplemented
57C2×#13063258C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65#14582864C2218yes—
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#485C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—42no—
78C2×#10621898—42no—
79C2×#10621898D414yes—
80C2×#10621898C2314yes—
81C22×Dic86—21no—
82C22×Dic86—22no—
83C22×Dic86—21no—
84C22×Dic86—42no—
85C22×Dic86—42no—
86C22×Dic86D411yescharacteristic
87C22×Dic86C2311yescharacteristic
88C22×Dic86C2311yescharacteristic
89C22×Dic86C2311yescharacteristic
90C22×Dic86C2314yes—
91C2×Q8×D43—22no—
92C2×Q8×D43—42no—
93C2×Q8×D43—42no—
94C2×Q8×D43C2314yes—
95C22×D172D411yescharacteristic
96C22×C22⋊D43D411yescharacteristic
97C22×C22⋊D43D411yescharacteristic
98C23×Dic43—21no—
99C22×C4×D43—21no—
100C22×C4×D43C2311yescharacteristic
101C22×C4×D43C2311yescharacteristic
102C2×Dic172—42no—
103C2×Dic172—42no—
104C2×Dic172C2314yes—
105C2×Dic172C2314yes—
106C2×#10621885—42no—
107C2×#10621885—42no—
108C2×#10621885C2314yes—
109C2×#10621885C2314yes—
110C2×#10621872—42no—
111C2×#10621872C2314yes—
112C22×C43⋊C8C2311yescharacteristic
113C22×C43⋊C8C2311yescharacteristic
114C2×C8×D43—42no—
115C2×C8×D43C2314yes—
116#13063325—28no—
117#13063324—28no—
118#13063313—28no—
119#13063311—28no—
120#13063310—28no—
121#13063309—28no—
122#13063309—28no—
123#13063307—28no—
124#13063305—22no—
125#13063305—22no—
126#13063305—22no—
127#13063305—22no—
128#13063305—22no—
129#13063305C2314yes—
130#13063305C2314yes—
131#13063305C2314yes—
132#13063305C2314yes—
133#13063305C2314yes—
134#13063304—22no—
135#13063304C2314yes—
136#13063301—22no—
137#13063301C2314yes—
138#13063283—22no—
139#13063283C2314yes—
140C2×C4⋊Dic43—21no—
141C2×C4⋊Dic43—21no—
142C2×C4⋊Dic43—21no—
143C2×C4⋊Dic43—21no—
144C2×C4⋊Dic43—21no—
145C2×C4⋊Dic43C2311yescharacteristic
146C2×Dic43⋊C4—21no—
147C2×Dic43⋊C4—21no—
148C2×C22⋊Dic43—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4—21no—
156C2×C4×Dic43—21no—
157#13063258C2314yes—
158#13063256C2314yes—
159#13063250C2314yes—
160#13063250C2314yes—
161#13063248C2314yes—
162#13063248C2314yes—
163#13063248C2314yes—
164#13063248C2314yes—
165C22⋊(C43⋊C8)C2314yes—
166(C2×D43)⋊C8C2314yes—
167(C2×D43)⋊C8C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C23×C4×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22⋊Q8×C43—22no—
173C22⋊Q8×C43C2314yes—
174#117×C43—22no—
175#117×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C42×C43—21no—
183#107×C43C2314yes—
184#106×C43C2314yes—
185#103×C43C2314yes—
186#103×C43C2314yes—
187C22⋊C8×C43C2314yes—
188C24×C43C2×D411yescharacteristic
189C23×D43C2×D411yescharacteristic
190C23×D43C2×D411yescharacteristic
191C2×Q8×C43—21no—
192C2×Q8×C43—22no—
193C2×Q8×C43—22no—
194C2×Q8×C43C2412yes—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D412yes—
203C22×C4×C43C2412yes—
204C22×C4×C43C2411yescharacteristic
205C2×C22⋊D43—42no—
206C2×C22⋊D43—42no—
207C2×C22⋊D43C2×D414yes—
208C2×C22⋊D43C2×D414yes—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—24no—
214C22×Dic43—44no—
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217Q8×D43—44no—
218Q8×D43—44no—
219Q8×D43—48no—
220#10621898—48no—
221#10621898—44no—
222#10621898—44no—
223C2×D172—42no—
224C2×D172C2×D414yes—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—24no—
230C2×C4×D43—44no—
231C2×C4×D43C2×D412yes—
232C2×C4×D43C2×D412yes—
233C2×C4×D43C2412yes—
234C2×C4×D43C2412yes—
235C2×Dic86—22no—
236C2×Dic86—22no—
237C2×Dic86—22no—
238C2×Dic86—22no—
239C2×Dic86—22no—
240C2×Dic86—22no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—24no—
245C2×Dic86—24no—
246C2×Dic86—44no—
247C2×Dic86—44no—
248C2×Dic86—42no—
249C2×Dic86—44no—
250C2×Dic86—44no—
251C2×Dic86—48no—
252C2×Dic86C2×D414yes—
253C2×Dic86C2412yes—
254C2×Dic86C2412yes—
255C2×Dic86C2412yes—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43C2412yes—
259C2×C8×C43C2412yes—
260C4⋊C4×C43—24no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43C2412yes—
265C4⋊C4×C43C2412yes—
266C4⋊C4×C43C2412yes—
267C22⋊C4×C43—24no—
268C22⋊C4×C43—24no—
269C42×C43—24no—
270C22⋊Dic43—24no—
271#10621885—44no—
272#10621885—44no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—24no—
280C4⋊Dic43—21no—
281C4⋊Dic43—24no—
282C4⋊Dic43—24no—
283C4⋊Dic43—24no—
284C4⋊Dic43—24no—
285C4⋊Dic43—24no—
286C4⋊Dic43C2412yes—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289C4×Dic43—24no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8—22no—
292C2×C43⋊C8C2412yes—
293C2×C43⋊C8C2412yes—
294Dic172—44no—
295Dic172—44no—
296#10621872—44no—
297C8×D43—44no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43C22×D412yes—
302C23×C43C22×D411yescharacteristic
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43C22×D412yes—
310C22×D43C22×D412yes—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—42no—
314C2×C4×C43—22no—
315C2×C4×C43—24no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43C22×D412yes—
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43H(5,𝔽2)12yes—
329C2×C4×C43H(5,𝔽2)12yes—
330C2×C4×C43C2511yescharacteristic
331C22⋊D43—44no—
332C22⋊D43—44no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—48no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43C22×D412yes—
345C2×Dic43C22×D412yes—
346D172—44no—
347C4×D43—24no—
348C4×D43—24no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—48no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—22no—
358Dic86—22no—
359Dic86—22no—
360Dic86—44no—
361Dic86—48no—
362Dic86—48no—
363Dic86—42no—
364Dic86—42no—
365Dic86—42no—
366C8×C43—22no—
367C8×C43—22no—
368C43⋊C8—22no—
369C43⋊C8—22no—
370C2×#3202—431nomaximal, Sylow
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—44no—
375C22×C43#53412yes—
376C22×C43#57812yes—
377C22×C43#57812yes—
378C22×C43C23×D411yescharacteristic
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—44no—
386C2×D43—44no—
387C4×C43—22no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43#53412yes—
393C4×C43C2×H(5,𝔽2)11yescharacteristic
394C4×C43C2×H(5,𝔽2)11yescharacteristic
395Dic43—22no—
396Dic43—22no—
397Dic43—42no—
398Dic43—42no—
399Dic43—42no—
400Dic43—42no—
401C2×#536—431no—
402C2×#536—431no—
403#3202—4316no—
404C2×#485—431no—
405C2×#485—431no—
406C2×#485—431no—
407C2×#485D4311yescharacteristic, complemented
408C2×#470—431no—
409C2×#470—431no—
410C2×#467—431no—
411C2×#467—431no—
412C2×#451—431no—
413C2×#451—431no—
414C2×#451—431no—
415C2×#451—431no—
416C2×#408—431no—
417C2×C43—42no—
418C2×C43#320214yescomplemented
419C2×C43C2×#53411yescharacteristic
420C2×C43C2×#57811yescharacteristic
421C2×C43C2×#57811yescharacteristic
422D43—42no—
423D43—42no—
424C22×#41—431no—
425C23×Q8—431no—
426C23×Q8—431no—
427C22×Q16—431no—
428C22×Q16—431no—
429C22×Q16—431no—
430C22×Q16—431no—
431C22×M16—431no—
432C23×C8—431no—
433#536—438no—
434#536—438no—
435#536—864no—
436#536—864no—
437C2×C4⋊Q8—861no—
438C2×C4⋊Q8—861no—
439C2×#124—861no—
440C2×#124—861no—
441C2×#123—861no—
442C2×#123—861no—
443C2×#123—861no—
444C2×#123—861no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—431no—
447C2×C22⋊Q8—431no—
448C2×C22⋊Q8—431no—
449C2×C22⋊Q8—431no—
450C2×C22⋊Q8—431no—
451C2×C22⋊Q8—431no—
452C2×C22⋊Q8C2×D4311yescharacteristic
453C2×#117—431no—
454C2×#117C2×D4311yescharacteristic
455#485—438no—
456#485—438no—
457#485—438no—
458#485C2×D4318yescomplemented
459#470—438no—
460#470—438no—
461#467—438no—
462#467—438no—
463#451—438no—
464#451—438no—
465#451—438no—
466#451—438no—
467C2×#107—431no—
468C2×#107C2×D4311yescharacteristic
469C2×#106—431no—
470C2×#106C2×D4311yescharacteristic
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103—431no—
477C2×#103C2×D4311yescharacteristic
478C2×#103C2×D4311yescharacteristic
479#408—438no—
480C2×C22⋊C8—431no—
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×C22⋊C8C2×D4311yescharacteristic
484C43C2×#320211yescharacteristic, complemented, Sylow
485C2×#41—434no—
486C2×#41—434no—
487C2×#41—1722no—
488C2×#41—1722no—
489C22×Q8—431no—
490C22×Q8—434no—
491C22×Q8—431no—
492C22×Q8—431no—
493C22×Q8—431no—
494C22×Q8—434no—
495C22×Q8—861no—
496C22×Q8—862no—
497C22×Q8—861no—
498C22×Q8—862no—
499C22×Q8—1722no—
500C22×Q8—1722no—
501C22×Q8—1722no—
502C22×Q8—1722no—
503C22×Q8C22×D4311yescharacteristic
504C22×D4—431no—
505C22×D4—431no—
506C22×D4—431no—
507C23×C4—431no—
508C23×C4—431no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4C22×D4311yescharacteristic
512C2×Q16—434no—
513C2×Q16—434no—
514C2×Q16—434no—
515C2×Q16—434no—
516C2×Q16—1722no—
517C2×Q16—1722no—
518C2×Q16—1722no—
519C2×Q16—1722no—
520C2×M16—434no—
521C2×M16—1722no—
522C22×C8—431no—
523C22×C8—431no—
524C22×C8—434no—
525C22×C8—1722no—
526C22×C8C22×D4311yescharacteristic
527C22×C8C22×D4311yescharacteristic
528C4⋊Q8—868no—
529C4⋊Q8—868no—
530#124—868no—
531#124—868no—
532#123—868no—
533#123—868no—
534#123—868no—
535#123—868no—
536C22⋊Q8—22no—
537C22⋊Q8—434no—
538C22⋊Q8—434no—
539C22⋊Q8—434no—
540C22⋊Q8—434no—
541C22⋊Q8—434no—
542C22⋊Q8—434no—
543C22⋊Q8—434no—
544C22⋊Q8—862no—
545C22⋊Q8—862no—
546C22⋊Q8—862no—
547C22⋊Q8—862no—
548C22⋊Q8—862no—
549C22⋊Q8—862no—
550C22⋊Q8—862no—
551C22⋊Q8C22×D4314yes—
552#117—22no—
553#117—434no—
554#117—862no—
555#117C22×D4314yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4C22×D4311yescharacteristic
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C42—21no—
579C2×C42—861no—
580#107—434no—
581#107C22×D4314yes—
582#106—434no—
583#106C22×D4314yes—
584#103—434no—
585#103—434no—
586#103—434no—
587#103—434no—
588#103—434no—
589#103—434no—
590#103C22×D4314yes—
591#103C22×D4314yes—
592C22⋊C8—434no—
593C22⋊C8—434no—
594C22⋊C8—434no—
595C22⋊C8C22×D4314yes—
596C24—431no—
597C24—431no—
598C24D4×D4311yescharacteristic
599#41—1728no—
600#41—1724no—
601#41—1724no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—434no—
606C2×Q8—432no—
607C2×Q8—432no—
608C2×Q8—432no—
609C2×Q8—864no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—864no—
614C2×Q8—862no—
615C2×Q8—862no—
616C2×Q8—862no—
617C2×Q8—862no—
618C2×Q8—862no—
619C2×Q8—862no—
620C2×Q8—1722no—
621C2×Q8—1724no—
622C2×Q8—1724no—
623C2×Q8—1724no—
624C2×Q8—1728no—
625C2×Q8—1724no—
626C2×Q8—1724no—
627C2×Q8—1724no—
628C2×Q8—1728no—
629C2×Q8C23×D4312yes—
630C2×D4—434no—
631C2×D4—434no—
632C2×D4—434no—
633C2×D4—1722no—
634C2×D4—1722no—
635C2×D4—1722no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—432no—
645C22×C4—432no—
646C22×C4—432no—
647C22×C4—432no—
648C22×C4—864no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—864no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—1724no—
659C22×C4—1724no—
660C22×C4D4×D4312yes—
661C22×C4D4×D4311yescharacteristic
662C22×C4C23×D4312yes—
663C22×C4C23×D4311yescharacteristic
664Q16—1724no—
665Q16—1724no—
666Q16—1724no—
667Q16—1724no—
668M16—1724no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—432no—
672C2×C8—432no—
673C2×C8—862no—
674C2×C8—862no—
675C2×C8—1724no—
676C2×C8C23×D4312yes—
677C2×C8C23×D4312yes—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—432no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—861no—
690C4⋊C4—864no—
691C4⋊C4C23×D4312yes—
692C4⋊C4C23×D4312yes—
693C4⋊C4C23×D4312yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C42—24no—
705C42—864no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—432no—
710C23—432no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23C2×D4×D4312yes—
718C23C2×D4×D4311yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—42no—
722Q8—862no—
723Q8—862no—
724Q8—862no—
725Q8—862no—
726Q8—862no—
727Q8—862no—
728Q8—1724no—
729Q8—1728no—
730Q8—1728no—
731Q8—1722no—
732Q8—1722no—
733Q8—1722no—
734D4—1724no—
735D4—1724no—
736D4—1724no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—864no—
754C2×C4—864no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—1728no—
764C2×C4—1728no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4C2×D4×D4312yes—
770C2×C4C2×D4×D4311yescharacteristic
771C2×C4#1306337112yes—
772C2×C4#1306337112yes—
773C2×C4C24×D4311yescharacteristic
774C8—22no—
775C8—22no—
776C8—862no—
777C8—862no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—862no—
783C22—862no—
784C22—862no—
785C22—862no—
786C22—862no—
787C22—862no—
788C22—1724no—
789C22—1724no—
790C22#1458346012yes—
791C22#1458371312yes—
792C22#1458371512yes—
793C22C22×D4×D4311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—862no—
800C4—862no—
801C4—1722no—
802C4—1722no—
803C4—1722no—
804C4—1722no—
805C4#1458346012yes—
806C4C2×#1306337111yescharacteristic
807C4C2×#1306337111yescharacteristic
808C2—42no—
809C2—1722no—
810C2—1722no—
811C2#1914548914yesdirect product factor
812C2C2×#1458346011yescharacteristic
813C2C2×#1458371311yescharacteristic
814C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#485C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenterC2×#485D43
hypocenterC43C2×#3202
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #19145489C2direct (N × H)
4. C2×#14583243C2semidirect
5. C2×#14583242C2semidirect
6. C2×#14583240C2semidirect
7. C2×#14583158C2semidirect
8. C2×#14583156C2semidirect
9. C2×#14583141C2semidirect
10. C2×#14583139C2semidirect
11. C2×#14583057C2semidirect
12. C2×#14583056C2semidirect
13. C2×#14583056C2semidirect
14. C2×#14583054C2semidirect
16. C2×C43×#485C2semidirect
46. #14583243C22semidirect
47. #14583242C22semidirect
48. #14583240C22semidirect
49. #14583158C22semidirect
50. #14583156C22semidirect
51. #14583141C22semidirect
52. #14583139C22semidirect
53. #14583057C22semidirect
54. #14583056C22semidirect
55. #14583056C22semidirect
56. #14583054C22semidirect
71. C43×#485C22semidirect
407. C2×#485D43semidirect
418. C2×C43#3202semidirect
458. #485C2×D43semidirect
484. C43C2×#3202semidirect
811. C2#19145489direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834752
C2×#145834722
#191454892
C2×#145832432
C2×#145832422
C2×#145832402
C2×#145831582
C2×#145831562
C2×#145831412
C2×#145831392
C2×#145830572
C2×#145830562
C2×#145830542
C2×#145828642
C2×C43×#4852
C2×#320243