Finite Group Databasebeta

← C2×#19144961 #25965846

Subgroups — C2×#19144961 #25965846

Order 11008.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583529C211yesmaximal, characteristic, complemented
2C2×#14583474C211yesmaximal, characteristic
3#19144961C2116yesmaximal, direct product factor
4C2×#14583266C211yesmaximal, characteristic, complemented
5C2×#14583260C211yesmaximal, characteristic, complemented
6C2×#14583259C211yesmaximal, characteristic, complemented
7C2×#14583256C211yesmaximal, characteristic, complemented
8C2×#14583255C211yesmaximal, characteristic, complemented
9C2×#14583249C211yesmaximal, characteristic, complemented
10C2×#14583248C211yesmaximal, characteristic, complemented
11C2×#14582899C211yesmaximal, characteristic
12C2×#14582906C211yesmaximal, characteristic, complemented
13C2×#14582894C211yesmaximal, characteristic
14C2×#103×D43C211yesmaximal, characteristic, complemented
15C2×#14582856C211yesmaximal, characteristic, complemented
16C2×C43×#491C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583529—24no—
22#14583529C2218yescomplemented
23#14583474—24no—
24#14583474C2218yes—
25C2×#13063325C2211yescharacteristic
26C2×#13063324—21no—
27C2×#13063324C2211yescharacteristic
28C2×#13063323C2211yescharacteristic
29C2×#13063316C2211yescharacteristic
30C2×#13063315—21no—
31C2×#13063314C2211yescharacteristic
32C2×#13063313C2211yescharacteristic
33C2×#13063310—21no—
34C2×#13063310—21no—
35C2×#13063305—21no—
36C2×#13063303—21no—
37C2×#13063303—21no—
38C2×#13063303—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063282C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583266C2218yescomplemented
43#14583260C2218yescomplemented
44#14583259C2218yescomplemented
45#14583256C2218yescomplemented
46#14583255C2218yescomplemented
47#14583249C2218yescomplemented
48#14583248C2218yescomplemented
49#14582906C2218yescomplemented
50#14582899C2218yes—
51#14582894C2218yes—
52C2×#13063250C2211yescharacteristic
53C2×#13063250C2211yescharacteristic
54C2×#13063249C2211yescharacteristic
55C2×#13063249C2211yescharacteristic
56C2×#13063249C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063248C2211yescharacteristic
59C2×#13063248C2211yescharacteristic
60#103×D43C2218yescomplemented
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65#14582856C2218yescomplemented
66C2×#13063235C2211yescharacteristic
67C2×C4×C43⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×#125×C43C2211yescharacteristic
71C43×#491C2218yescomplemented
72C2×#103×C43C2211yescharacteristic
73C2×#103×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—24no—
80C2×#10621902C2314yes—
81C22×Dic86—21no—
82C22×Dic86—21no—
83C22×Dic86—21no—
84C22×Dic86C2311yescharacteristic
85C2×Q8×D43—22no—
86C2×Q8×D43—24no—
87C2×Q8×D43—24no—
88C2×Q8×D43C2314yes—
89C22×D172—21no—
90C22×D172C2311yescharacteristic
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43C2311yescharacteristic
95C2×#10621872—24no—
96C2×#10621872C2314yes—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C2×C8×D43—24no—
100C2×C8×D43C2314yes—
101#13063325—22no—
102#13063325C2314yes—
103#13063324—28no—
104#13063324—22no—
105#13063324C2314yes—
106#13063323—22no—
107#13063323C2314yes—
108#13063316—22no—
109#13063316C2314yes—
110#13063315—28no—
111#13063314—22no—
112#13063314C2314yes—
113#13063313—22no—
114#13063313C2314yes—
115#13063310—28no—
116#13063310—28no—
117#13063305—28no—
118#13063303—28no—
119#13063303—28no—
120#13063303—28no—
121#13063283—22no—
122#13063283C2314yes—
123#13063282D414yes—
124#13063282C2314yes—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4D411yescharacteristic
135C2×Dic43⋊C4D411yescharacteristic
136C4⋊C4×D43—22no—
137C4⋊C4×D43C2314yes—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063250C2314yes—
148#13063250C2314yes—
149#13063249C2314yes—
150#13063249C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063248C2314yes—
154#13063248C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063245C2314yes—
158#13063245C2314yes—
159#13063235C2314yes—
160C4×C43⋊C8C2314yes—
161C8×Dic43C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C22×Q8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C4⋊Q8×C43—22no—
167C4⋊Q8×C43C2314yes—
168#125×C43—22no—
169#125×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C42×C43C2311yescharacteristic
177#103×C43C2314yes—
178#103×C43C2314yes—
179#103×C43C2314yes—
180#103×C43C2314yes—
181#97×C43C2314yes—
182C23×D43—21no—
183C23×D43C2×D411yescharacteristic
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43—22no—
190C2×Q8×C43C2412yes—
191C2×Q8×C43C2412yes—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205#10621902—28no—
206#10621902—28no—
207#10621902—48no—
208Q8×D43—28no—
209Q8×D43—28no—
210Q8×D43—48no—
211C2×D172—21no—
212C2×D172—24no—
213C2×D172—22no—
214C2×D172—22no—
215C2×D172—44no—
216C2×D172C2412yes—
217C2×C4×D43—24no—
218C2×C4×D43—24no—
219C2×C4×D43—24no—
220C2×C4×D43—44no—
221C2×C4×D43—44no—
222C2×C4×D43—82no—
223C2×C4×D43C2×D412yes—
224C2×C4×D43#4114yes—
225C2×C4×D43#4114yes—
226C2×C4×D43C2412yes—
227C2×Dic86—22no—
228C2×Dic86—22no—
229C2×Dic86—21no—
230C2×Dic86—24no—
231C2×Dic86—24no—
232C2×Dic86—24no—
233C2×Dic86—44no—
234C2×Dic86—82no—
235C2×Dic86—82no—
236C2×Dic86C2412yes—
237C2×C8×C43—22no—
238C2×C8×C43—22no—
239C2×C8×C43C2412yes—
240C2×C8×C43C2412yes—
241C4⋊C4×C43—24no—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—24no—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43C2412yes—
248C4⋊C4×C43C2412yes—
249C42×C43C2×D412yes—
250C42×C43C2412yes—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4C2×D414yes—
257(C2×D43)⋊C4C2×D414yes—
258C4⋊Dic43—21no—
259C4⋊Dic43—24no—
260C4⋊Dic43—21no—
261C4⋊Dic43—24no—
262C4⋊Dic43C2412yes—
263C4⋊Dic43C2412yes—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4C2×D414yes—
270Dic43⋊C4C2×D414yes—
271C4×Dic43—24no—
272C4×Dic43C2×D412yes—
273C4×Dic43C2412yes—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—22no—
276C2×C43⋊C8C2412yes—
277C2×C43⋊C8C2412yes—
278#10621872—28no—
279C8×D43—28no—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43#12414yes—
288C22×D43C22×D412yes—
289Q8×C43—22no—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—42no—
294Q8×C43—42no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4112yes—
309C2×C4×C43C2×#4112yes—
310C2×C4×C43C2511yescharacteristic
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43#12414yes—
320C2×Dic43C22×D412yes—
321C2×Dic43C22×D412yes—
322C2×Dic43C22×D412yes—
323D172—22no—
324D172—22no—
325D172—48no—
326D172—42no—
327C4×D43—48no—
328C4×D43—48no—
329C4×D43—84no—
330C4×D43#12418yes—
331C4×D43C2×#4114yes—
332C4×D43C2×#4114yes—
333Dic86—22no—
334Dic86—22no—
335Dic86—42no—
336Dic86—48no—
337Dic86—84no—
338Dic86—84no—
339C8×C43—22no—
340C8×C43—22no—
341C43⋊C8—22no—
342C43⋊C8—22no—
343C2×#3137—431nomaximal, Sylow
344C22×C43C2×#12412yes—
345C22×C43#57712yes—
346C22×C43#57812yes—
347C22×C43C23×D411yescharacteristic
348C2×D43—28no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—84no—
355C2×D43C2×#12414yes—
356C4×C43—22no—
357C4×C43—22no—
358C4×C43—42no—
359C4×C43—42no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43C2×#12412yes—
363C4×C43C22×#4111yescharacteristic
364C4×C43C22×#4111yescharacteristic
365Dic43—22no—
366Dic43—22no—
367Dic43—42no—
368Dic43—42no—
369Dic43—42no—
370Dic43C2×#12414yes—
371C2×#544—431no—
372C2×#536—431no—
373#3137—4316no—
374C2×#491—431no—
375C2×#491D4311yescharacteristic, complemented
376C2×#489—431no—
377C2×#489—431no—
378C2×#488—431no—
379C2×#488—431no—
380C2×#487—431no—
381C2×#487—431no—
382C2×#417—431no—
383C2×#419—431no—
384C2×#416—431no—
385C22×#103—431no—
386C2×#405—431no—
387C2×C43#313714yescomplemented
388C2×C43C22×#12411yescharacteristic
389C2×C43C2×#57711yescharacteristic
390C2×C43C2×#57811yescharacteristic
391D43—24no—
392D43—82no—
393C22×#41—431no—
394C23×Q8—431no—
395C22×M16—431no—
396C23×C8—431no—
397#544—438no—
398#544—864no—
399#536—438no—
400#536—864no—
401C2×C4⋊Q8—431no—
402C2×C4⋊Q8—431no—
403C2×C4⋊Q8—431no—
404C2×C4⋊Q8—861no—
405C2×C4⋊Q8C2×D4311yescharacteristic
406C2×#125—431no—
407C2×#125—861no—
408C2×#125C2×D4311yescharacteristic
409C2×#124—431no—
410C2×#124—431no—
411C2×#123—861no—
412C2×#123—861no—
413C2×C22⋊Q8—861no—
414C2×C22⋊Q8—861no—
415C2×C22⋊Q8—861no—
416C2×C22⋊Q8—861no—
417C2×#117—431no—
418C2×#117—431no—
419C22×C4⋊C4—431no—
420#491—438no—
421#491C2×D4318yescomplemented
422#489—438no—
423#489—438no—
424#488—438no—
425#488—438no—
426#487—438no—
427#487—438no—
428#419—438no—
429#417—438no—
430#416—438no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—438no—
440C2×#103C2×D4311yescharacteristic
441C2×#103C2×D4311yescharacteristic
442C2×#103C2×D4311yescharacteristic
443C2×#103C2×D4311yescharacteristic
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448#405—438no—
449C2×#97—431no—
450C2×#97C2×D4311yescharacteristic
451C2×C4×C8—431no—
452C2×C4×C8—431no—
453C43C2×#313711yescharacteristic, complemented, Sylow
454C2×#41—434no—
455C2×#41—862no—
456C2×#41—864no—
457C2×#41—864no—
458C22×Q8—434no—
459C22×Q8—431no—
460C22×Q8—861no—
461C22×Q8—861no—
462C22×Q8—862no—
463C22×Q8—864no—
464C22×Q8—864no—
465C22×Q8—861no—
466C22×Q8C22×D4311yescharacteristic
467C22×Q8C22×D4311yescharacteristic
468C22×D4—431no—
469C22×D4—861no—
470C23×C4—431no—
471C23×C4—861no—
472C23×C4—861no—
473C23×C4—861no—
474C2×M16—434no—
475C2×M16—864no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—434no—
479C22×C8—864no—
480C22×C8C22×D4311yescharacteristic
481C22×C8C22×D4311yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8—434no—
484C4⋊Q8—434no—
485C4⋊Q8—434no—
486C4⋊Q8—862no—
487C4⋊Q8—862no—
488C4⋊Q8—868no—
489C4⋊Q8—862no—
490C4⋊Q8C22×D4314yes—
491#125—22no—
492#125—434no—
493#125—862no—
494#125—868no—
495#125C22×D4314yes—
496#124—434no—
497#124—434no—
498#124—862no—
499#124—862no—
500#123—868no—
501#123—868no—
502C22⋊Q8—868no—
503C22⋊Q8—868no—
504C22⋊Q8—868no—
505C22⋊Q8—868no—
506#117—434no—
507#117—434no—
508#117—434no—
509#117—862no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—434no—
519C2×C4⋊C4—862no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C22⋊C4—431no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C42—431no—
537C2×C42—861no—
538C2×C42C22×D4311yescharacteristic
539#103—434no—
540#103—434no—
541#103—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#103—434no—
546#103—434no—
547#103C22×D4314yes—
548#103C22×D4314yes—
549#103C22×D4314yes—
550#103C22×D4314yes—
551#102—434no—
552#102—434no—
553#102—434no—
554#102—434no—
555#97—434no—
556#97C22×D4314yes—
557C4×C8—434no—
558C4×C8—434no—
559C24—431no—
560C24—861no—
561#41—868no—
562#41—868no—
563#41—1728no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—432no—
571C2×Q8—864no—
572C2×Q8—864no—
573C2×Q8—868no—
574C2×Q8—868no—
575C2×Q8—864no—
576C2×Q8—861no—
577C2×Q8—862no—
578C2×Q8—862no—
579C2×Q8—3442no—
580C2×Q8—3442no—
581C2×Q8—1724no—
582C2×Q8—1728no—
583C2×Q8C23×D4312yes—
584C2×Q8C23×D4312yes—
585C2×D4—432no—
586C2×D4—864no—
587C2×D4—861no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4—1724no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—431no—
596C22×C4—432no—
597C22×C4—434no—
598C22×C4—434no—
599C22×C4—432no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—864no—
603C22×C4—864no—
604C22×C4—864no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—3442no—
609C22×C4—1724no—
610C22×C4—1724no—
611C22×C4D4×D4311yescharacteristic
612C22×C4D4×D4311yescharacteristic
613C22×C4C23×D4311yescharacteristic
614M16—868no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—432no—
618C2×C8—432no—
619C2×C8—868no—
620C2×C8—862no—
621C2×C8—862no—
622C2×C8C23×D4312yes—
623C2×C8C23×D4312yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—434no—
631C4⋊C4—434no—
632C4⋊C4—432no—
633C4⋊C4—432no—
634C4⋊C4—864no—
635C4⋊C4—864no—
636C4⋊C4—864no—
637C4⋊C4—864no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—864no—
643C4⋊C4C23×D4312yes—
644C4⋊C4C23×D4312yes—
645C22⋊C4—434no—
646C22⋊C4—434no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C22⋊C4—864no—
651C22⋊C4—864no—
652C42—432no—
653C42—432no—
654C42—864no—
655C42D4×D4312yes—
656C42C23×D4312yes—
657C23—434no—
658C23—432no—
659C23—862no—
660C23—862no—
661C23—862no—
662C23—1722no—
663C23—1722no—
664C23—1722no—
665C23C2×D4×D4311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—42no—
672Q8—862no—
673Q8—862no—
674Q8—3444no—
675Q8—3444no—
676Q8—1728no—
677Q8—1722no—
678D4—862no—
679D4—862no—
680D4—1728no—
681D4—1722no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—434no—
693C2×C4—432no—
694C2×C4—438no—
695C2×C4—434no—
696C2×C4—434no—
697C2×C4—432no—
698C2×C4—432no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—3444no—
705C2×C4—1728no—
706C2×C4—1728no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4C2×D4×D4312yes—
711C2×C4C2×D4×D4312yes—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4#41×D4312yes—
714C2×C4#41×D4312yes—
715C2×C4C24×D4311yescharacteristic
716C8—22no—
717C8—22no—
718C8—862no—
719C8—862no—
720C22—434no—
721C22—868no—
722C22—862no—
723C22—862no—
724C22—3444no—
725C22—1722no—
726C22—1722no—
727C22—1722no—
728C22#124×D4312yes—
729C22#1458370812yes—
730C22#1458371512yes—
731C22C22×D4×D4311yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—434no—
739C4—862no—
740C4—862no—
741C4—1722no—
742C4—1722no—
743C4—1722no—
744C4#124×D4312yes—
745C4C2×#41×D4311yescharacteristic
746C4C2×#41×D4311yescharacteristic
747C2—864no—
748C2—3442no—
749C2#1914496114yesdirect product factor
750C2C2×#124×D4311yescharacteristic
751C2C2×#1458370811yescharacteristic
752C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#491C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
hypercenterC2×#491D43
hypocenterC43C2×#3137
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×#14583529C2semidirect
3. #19144961C2direct (N × H)
4. C2×#14583266C2semidirect
5. C2×#14583260C2semidirect
6. C2×#14583259C2semidirect
7. C2×#14583256C2semidirect
8. C2×#14583255C2semidirect
9. C2×#14583249C2semidirect
10. C2×#14583248C2semidirect
12. C2×#14582906C2semidirect
14. C2×#103×D43C2semidirect
15. C2×#14582856C2semidirect
16. C2×C43×#491C2semidirect
22. #14583529C22semidirect
42. #14583266C22semidirect
43. #14583260C22semidirect
44. #14583259C22semidirect
45. #14583256C22semidirect
46. #14583255C22semidirect
47. #14583249C22semidirect
48. #14583248C22semidirect
49. #14582906C22semidirect
60. #103×D43C22semidirect
65. #14582856C22semidirect
71. C43×#491C22semidirect
375. C2×#491D43semidirect
387. C2×C43#3137semidirect
421. #491C2×D43semidirect
453. C43C2×#3137semidirect
749. C2#19144961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835292
C2×#145834742
#191449612
C2×#145832662
C2×#145832602
C2×#145832592
C2×#145832562
C2×#145832552
C2×#145832492
C2×#145832482
C2×#145828992
C2×#145829062
C2×#145828942
C2×#103×D432
C2×#145828562
C2×C43×#4912
C2×#313743