Finite Group Databasebeta

← C2×#22625696 #34020085

Subgroups — C2×#22625696 #34020085

Order 18688.

1662 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×#64408C211yesmaximal, characteristic
2C2×D73⋊#104C211yesmaximal, characteristic
3C2×M16×#64408C211yesmaximal, characteristic, complemented
4C2×#17989523C211yesmaximal, characteristic, complemented
5#22625696C218yesmaximal, direct product factor
6C2×#17989459C211yesmaximal, characteristic, complemented
7C2×#17989458C211yesmaximal, characteristic, complemented
8C2×#104×D73C211yesmaximal, characteristic
9C2×D73⋊M16C2211yescharacteristic
10#41×#64408—22no—
11#41×#64408—22no—
12#41×#64408C414yescomplemented
13#41×#64408C2214yes—
14C2×Q8×#64408C412yescomplemented
15C2×D4×#64408—22no—
16C2×D4×#64408C412yescomplemented
17C2×#14556670—21no—
18C2×#14556670C2211yescharacteristic
19C22×C4×#64408—21no—
20C22×C4×#64408C2211yescharacteristic
21C22×C4×#64408C2211yescharacteristic
22C2×#14556656C412yescomplemented
23D73⋊#104C414yescomplemented
24D73⋊#104C2214yes—
25C2×#14556655C412yescomplemented
26M16×#64408—22no—
27M16×#64408C2214yescomplemented
28C2×#14556645—21no—
29C2×C8×#64408—21no—
30#17989523—22no—
31#17989523C2214yescomplemented
32C2×(C2×#64408)⋊C4—22no—
33#17989459C2214yescomplemented
34#17989458C2214yescomplemented
35C2×#41×D73C2211yescharacteristic
36C2×M16×D73C2211yescharacteristic
37C2×C42×D73C2211yescharacteristic
38C2×#14556519C411yescharacteristic, complemented
39C2×#14556518C411yescharacteristic, complemented
40C2×#14556517C411yescharacteristic, complemented
41#104×D73C414yescomplemented
42#104×D73C2214yes—
43C2×#104×C73C411yescharacteristic, complemented
44C23×#64408—22no—
45C23×#64408—21no—
46C23×#64408D412yes—
47C2×#11924038C2×C412yescomplemented
48D73⋊M16—21no—
49D73⋊M16—21no—
50D73⋊M16C2×C412yescomplemented
51D73⋊M16C2312yes—
52C2×#11924037—21no—
53C2×#11924036—21no—
54Q8×#64408—24no—
55Q8×#64408C2×C418yescomplemented
56D4×#64408—28no—
57D4×#64408—28no—
58D4×#64408—24no—
59D4×#64408C2×C418yescomplemented
60#14556670—24no—
61#14556670—24no—
62#14556670—21no—
63#14556670—21no—
64#14556670C2×C412yes—
65#14556670C2312yes—
66C2×C4⋊#64408—22no—
67C2×C4⋊#64408C2×C412yes—
68C2×C22⋊#64408—22no—
69C2×C22⋊#64408—21no—
70C2×C4×#64408—22no—
71C2×C4×#64408—24no—
72C2×C4×#64408—24no—
73C2×C4×#64408—21no—
74C2×C4×#64408—21no—
75C2×C4×#64408—21no—
76C2×C4×#64408—21no—
77C2×C4×#64408C2×C412yes—
78C2×C4×#64408C2×C412yes—
79C2×C4×#64408C2×C412yescomplemented
80C2×C4×#64408C2×C412yescomplemented
81C2×C4×#64408D412yes—
82C2×C4×#64408D411yescharacteristic
83C2×C4×#64408D411yescharacteristic
84C2×C4×#64408D412yes—
85C2×C4×#64408C2312yes—
86C2×C4×#64408C2312yes—
87#14556656C2×C418yescomplemented
88#14556655C2×C418yescomplemented
89#14556645—24no—
90C8×#64408—24no—
91(C2×#64408)⋊C4—28no—
92C2×#11924029C2×C411yescharacteristic
93C2×#11924028—21no—
94C2×#11924028C2×C411yescharacteristic
95C2×#11924027—21no—
96C2×#11924027C2×C411yescharacteristic
97#41×D73—21no—
98#41×D73—21no—
99#41×D73—21no—
100#41×D73—21no—
101#41×D73C2×C412yes—
102#41×D73C2×C412yes—
103#41×D73C2×C412yes—
104#41×D73C2312yes—
105C2×Q8×D73C2×C411yescharacteristic
106C2×D4×D73—21no—
107C2×D4×D73C2×C411yescharacteristic
108C22×C4×D73—21no—
109C22×C4×D73—21no—
110C22×C4×D73C2311yescharacteristic
111C2×#11924012C2×C411yescharacteristic, complemented
112C2×#11924011—21no—
113M16×D73—21no—
114M16×D73—21no—
115M16×D73C2×C412yescomplemented
116M16×D73C2312yes—
117C2×C8×D73—21no—
118C2×C4×Dic73—21no—
119C2×C4×Dic73C2×C411yescharacteristic, complemented
120C42×D73—21no—
121C42×D73—21no—
122C42×D73C2×C412yescomplemented
123C42×D73C2312yes—
124#14556519C2×C414yescomplemented
125#14556518C2×C414yescomplemented
126#14556517C2×C414yescomplemented
127C2×#41×C73C2×C411yescharacteristic
128C2×M16×C73C2×C411yescharacteristic, complemented
129C2×C42×C73C2×C411yescharacteristic, complemented
130#104×C73C2×C414yescomplemented
131C22×#64408—22no—
132C22×#64408—22no—
133C22×#64408—22no—
134C22×#64408—22no—
135C22×#64408—28no—
136C22×#64408—44no—
137C22×#64408—48no—
138C22×#64408—44no—
139C22×#64408C22⋊C412yes—
140C22×#64408C22⋊C412yes—
141C22×#64408C22⋊C414yes—
142C22×#64408C2×D414yes—
143#11924038—22no—
144#11924038C22×C414yescomplemented
145#11924037—22no—
146#11924037—22no—
147#11924036—22no—
148#11924036—22no—
149C2×#10596833—22no—
150C4⋊#64408—28no—
151C4⋊#64408—22no—
152C4⋊#64408C22×C414yes—
153C22⋊#64408—22no—
154C22⋊#64408—22no—
155C22⋊#64408—28no—
156C4×#64408—28no—
157C4×#64408—22no—
158C4×#64408—22no—
159C4×#64408—22no—
160C4×#64408—22no—
161C4×#64408—22no—
162C4×#64408C22⋊C414yes—
163C4×#64408C22⋊C412yes—
164C4×#64408C22⋊C412yes—
165C4×#64408C22×C414yes—
166C4×#64408C22×C414yescomplemented
167C4×#64408C2×D412yes—
168C4×#64408C2×D412yes—
169C23×D73—21no—
170C23×D73C2×D411yescharacteristic
171#11924029—21no—
172#11924029—21no—
173#11924029C4212yes—
174#11924029C22×C412yes—
175#11924028—21no—
176#11924028—21no—
177#11924028—22no—
178#11924028—22no—
179#11924028—22no—
180#11924028—22no—
181#11924028C4212yes—
182#11924028C22×C412yes—
183#11924027—22no—
184#11924027—22no—
185#11924027—22no—
186#11924027—22no—
187#11924027—21no—
188#11924027—21no—
189#11924027C4212yes—
190#11924027C22×C412yes—
191C2×Dic146—21no—
192C2×Dic146C4211yescharacteristic
193Q8×D73—21no—
194Q8×D73—21no—
195Q8×D73C4212yes—
196Q8×D73C22×C412yes—
197C2×D292—21no—
198C2×D292C4211yescharacteristic
199C2×C22⋊D73—21no—
200C2×C22⋊D73—21no—
201C2×C22⋊D73—21no—
202D4×D73—22no—
203D4×D73—22no—
204D4×D73—22no—
205D4×D73—22no—
206D4×D73—21no—
207D4×D73—21no—
208D4×D73C4212yes—
209D4×D73C22×C412yes—
210C22×Dic73—21no—
211C22×Dic73—21no—
212C22×Dic73#4111yescharacteristic
213C2×C4×D73—21no—
214C2×C4×D73—21no—
215C2×C4×D73—21no—
216C2×C4×D73—22no—
217C2×C4×D73—22no—
218C2×C4×D73—22no—
219C2×C4×D73—22no—
220C2×C4×D73—22no—
221C2×C4×D73—22no—
222C2×C4×D73—44no—
223C2×C4×D73C22×C411yescharacteristic
224C2×C4×D73C22×C411yescharacteristic
225C2×C4×D73C22×C411yescharacteristic
226C2×C4×D73C22×C411yescharacteristic
227C2×C4×D73C22×C411yescharacteristic
228C2×C4×D73C2×D411yescharacteristic
229C2×C4×D73C2×D411yescharacteristic
230C2×C4×D73C2×D411yescharacteristic
231C2×C4×D73#4111yescharacteristic
232C2×C4×D73#4111yescharacteristic
233C2×C4×D73#4111yescharacteristic
234C2×C4×D73C2411yescharacteristic
235#11924012—21no—
236#11924012C22×C412yescomplemented
237#11924011—22no—
238#11924011—22no—
239C2×#10596831—21no—
240C8×D73—22no—
241C8×D73—22no—
242C4×Dic73—21no—
243C4×Dic73—22no—
244C4×Dic73—22no—
245C4×Dic73C22×C412yescomplemented
246#41×C73—21no—
247#41×C73—21no—
248#41×C73C4212yes—
249#41×C73C22×C412yes—
250C2×Q8×C73C4211yescharacteristic
251C2×D4×C73—21no—
252C2×D4×C73C4211yescharacteristic
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73C22×C411yescharacteristic
256M16×C73—21no—
257M16×C73C22×C412yescomplemented
258C2×C8×C73—21no—
259C42×C73—21no—
260C42×C73C22×C412yescomplemented
261C23×C73—21no—
262C23×C73C4×D411yescharacteristic
263C22×D73—24no—
264C22×D73—21no—
265C22×D73—22no—
266C22×D73—22no—
267C22×D73—44no—
268C22×D73C2×C22⋊C411yescharacteristic
269C22×D73C2×C22⋊C411yescharacteristic
270C22×D73C4×D411yescharacteristic
271C22×D73C4×D411yescharacteristic
272C22×D73C4×D411yescharacteristic
273C22×D73C22×D411yescharacteristic
274C2×#64408—24no—
275C2×#64408—24no—
276C2×#64408—24no—
277C2×#64408—24no—
278C2×#64408—44no—
279C2×#64408—44no—
280C2×#64408—416no—
281C2×#64408—44no—
282C2×#64408—44no—
283C2×#64408—44no—
284C2×#64408—44no—
285C2×#64408C2×C22⋊C414yes—
286C2×#64408C2×C22⋊C414yes—
287Q8×C73—21no—
288Q8×C73C2×C4212yes—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—21no—
292D4×C73C2×C4212yes—
293C2×C4×C73—21no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—42no—
298C2×C4×C73C2×C4211yescharacteristic
299C2×C4×C73C2×C4211yescharacteristic
300C2×C4×C73C4×D411yescharacteristic
301C2×C4×C73C4×D411yescharacteristic
302C2×C4×C73C4×D411yescharacteristic
303C2×C4×C73C23×C411yescharacteristic
304C22⋊D73—22no—
305C22⋊D73—22no—
306C22⋊D73—22no—
307C22⋊D73—22no—
308C22⋊D73—22no—
309C22⋊D73—22no—
310C2×Dic73—21no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—42no—
315C2×Dic73#11711yescharacteristic
316C2×Dic73#11711yescharacteristic
317C2×Dic73C4×D411yescharacteristic
318C2×Dic73C4×D411yescharacteristic
319C2×Dic73C4×D411yescharacteristic
320C2×Dic73C2×#4111yescharacteristic
321D292—22no—
322D292—22no—
323D292—21no—
324D292C2×C4212yes—
325C4×D73—22no—
326C4×D73—22no—
327C4×D73—22no—
328C4×D73—22no—
329C4×D73—22no—
330C4×D73—22no—
331C4×D73—44no—
332C4×D73—44no—
333C4×D73C2×C4211yescharacteristic
334C4×D73C2×C4211yescharacteristic
335C4×D73C2×C22⋊C411yescharacteristic
336C4×D73C2×C22⋊C411yescharacteristic
337C4×D73#11711yescharacteristic
338C4×D73#11711yescharacteristic
339C4×D73C4×D411yescharacteristic
340C4×D73C4×D411yescharacteristic
341C4×D73C4×D411yescharacteristic
342C4×D73C4×D411yescharacteristic
343C4×D73C4×D411yescharacteristic
344C4×D73C4×D411yescharacteristic
345C4×D73C23×C411yescharacteristic
346C4×D73C23×C411yescharacteristic
347C4×D73C22×D411yescharacteristic
348C4×D73C2×#4111yescharacteristic
349Dic146—21no—
350Dic146—22no—
351Dic146—22no—
352Dic146C2×C4212yes—
353#10596833—24no—
354C8×C73—22no—
355#10596831—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—42no—
359C22×C73C4×C22⋊C411yescharacteristic
360C22×C73C4×C22⋊C411yescharacteristic
361C22×C73C2×C4×D411yescharacteristic
362C2×D73—22no—
363C2×D73—22no—
364C2×D73—22no—
365C2×D73—22no—
366C2×D73—22no—
367C2×D73—22no—
368C2×D73—42no—
369C2×D73—44no—
370C2×D73—44no—
371C2×D73C4×C22⋊C411yescharacteristic
372C2×D73C4×C22⋊C411yescharacteristic
373C2×D73#42114yes—
374C2×D73C22×C22⋊C411yescharacteristic
375C2×D73C2×C4×D411yescharacteristic
376#64408—24no—
377#64408—24no—
378#64408—44no—
379#64408—44no—
380C4×C73—22no—
381C4×C73—42no—
382C4×C73C4×C22⋊C411yescharacteristic
383C4×C73C4×C22⋊C411yescharacteristic
384C4×C73C22×C4211yescharacteristic
385C4×C73C2×C4×D411yescharacteristic
386Dic73—22no—
387Dic73—42no—
388Dic73C4×C22⋊C411yescharacteristic
389Dic73C4×C22⋊C411yescharacteristic
390Dic73C2×#11711yescharacteristic
391Dic73C2×C4×D411yescharacteristic
392C2×#1759—731nomaximal, Sylow
393C2×C73—21no—
394C2×C73—21no—
395C2×C73—42no—
396C2×C73#175912yescomplemented
397C2×C73C2×C4×C22⋊C411yescharacteristic
398D73—21no—
399D73—21no—
400D73—42no—
401D73#175912yescomplemented
402D73C2×#42112yes—
403C2×C4×#41—731no—
404C22×#104—731no—
405C22×#104—731no—
406C2×C4×M16—731no—
407C2×#376—731no—
408#1759—738no—
409C2×#339—731no—
410C2×#339—731no—
411C73C2×#175911yescharacteristic, complemented, Sylow
412C22×#41—731no—
413C22×M16—731no—
414C22×M16—731no—
415C4×#41—734no—
416C4×#41—734no—
417C4×#41—1462no—
418C4×#41—1462no—
419C2×C4×Q8—732no—
420C2×C4×D4—732no—
421C2×C4×D4—1462no—
422C2×#117—731no—
423C2×#117—1461no—
424C22×C42—731no—
425C22×C42—731no—
426C22×C42—731no—
427C22×C42—1461no—
428C2×#104—732no—
429C2×#104—734no—
430C2×#104—734no—
431C2×#104—732no—
432C2×#104—731no—
433C2×#104—731no—
434C2×#104—731no—
435C2×#104—734no—
436C2×#104—734no—
437C2×#104#6440811yescharacteristic, complemented
438C4×M16—734no—
439C4×M16—1462no—
440C2×#97—1461no—
441C2×C4×C8—1461no—
442#376—734no—
443#376—1462no—
444C2×#95—1462no—
445#339—734no—
446#339—734no—
447C2×#41—732no—
448C2×#41—732no—
449C2×#41—732no—
450C2×#41—732no—
451C2×#41—731no—
452C2×#41—731no—
453C2×#41—731no—
454C2×#41—1461no—
455C2×#41—1461no—
456C2×#41—1461no—
457C2×#41—1461no—
458C2×#41—1461no—
459C2×#41—1461no—
460C2×#41C2×#6440811yescharacteristic
461C22×Q8—731no—
462C22×D4—731no—
463C22×D4—1461no—
464C23×C4—732no—
465C23×C4—731no—
466C23×C4—1461no—
467C23×C4—1461no—
468C23×C4—1462no—
469C23×C4—1461no—
470C2×M16—732no—
471C2×M16—732no—
472C2×M16—732no—
473C2×M16—731no—
474C2×M16—732no—
475C2×M16—732no—
476C2×M16—1461no—
477C2×M16—1461no—
478C2×M16—1461no—
479C2×M16—1461no—
480C2×M16—1461no—
481C2×M16—1461no—
482C2×M16C2×#6440811yescharacteristic, complemented
483C22×C8—1461no—
484C22×C8—1461no—
485C4×Q8—738no—
486C4×Q8—1464no—
487C4×D4—738no—
488C4×D4—1464no—
489C4×D4—1468no—
490C4×D4—1468no—
491#117—732no—
492#117—732no—
493#117—1464no—
494#117—1464no—
495#117—1461no—
496#117—1461no—
497C2×C4⋊C4—732no—
498C2×C4⋊C4—1462no—
499C2×C22⋊C4—1462no—
500C2×C22⋊C4—1461no—
501C2×C42—731no—
502C2×C42—732no—
503C2×C42—732no—
504C2×C42—732no—
505C2×C42—732no—
506C2×C42—732no—
507C2×C42—731no—
508C2×C42—732no—
509C2×C42—732no—
510C2×C42—732no—
511C2×C42—731no—
512C2×C42—732no—
513C2×C42—732no—
514C2×C42—1461no—
515C2×C42—1461no—
516C2×C42—1464no—
517C2×C42—1464no—
518C2×C42—1461no—
519C2×C42—1461no—
520C2×C42—1462no—
521C2×C42—1461no—
522C2×C42—1461no—
523C2×C42—1461no—
524C2×C42C2×#6440811yescharacteristic, complemented
525#104—738no—
526#104—738no—
527#104—734no—
528#104—734no—
529#104—734no—
530#104C2×#6440814yescomplemented
531#97—1464no—
532C4×C8—1464no—
533#95—1468no—
534C24—731no—
535C24—1461no—
536#41—21no—
537#41—21no—
538#41—732no—
539#41—732no—
540#41—732no—
541#41—732no—
542#41—732no—
543#41—732no—
544#41—1462no—
545#41—1462no—
546#41—1462no—
547#41—1462no—
548#41—1462no—
549#41—1462no—
550#41—1462no—
551#41—1462no—
552#41—1461no—
553#41—1461no—
554#41—1461no—
555#41—1461no—
556#41—1461no—
557#41—1461no—
558#41C4×#6440812yes—
559#41C22×#6440812yes—
560C2×Q8—732no—
561C2×Q8—732no—
562C2×Q8—731no—
563C2×Q8—1461no—
564C2×Q8—1461no—
565C2×Q8—1461no—
566C2×Q8C4×#6440811yescharacteristic
567C2×D4—21no—
568C2×D4—732no—
569C2×D4—732no—
570C2×D4—731no—
571C2×D4—1461no—
572C2×D4—1461no—
573C2×D4—1461no—
574C2×D4—1461no—
575C2×D4—1462no—
576C2×D4—1462no—
577C2×D4—1462no—
578C2×D4—1462no—
579C2×D4—1461no—
580C2×D4—1461no—
581C2×D4C4×#6440811yescharacteristic
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—2924no—
585C22×C4—2924no—
586C22×C4—2928no—
587C22×C4—2924no—
588C22×C4—734no—
589C22×C4—734no—
590C22×C4—731no—
591C22×C4—731no—
592C22×C4—731no—
593C22×C4—731no—
594C22×C4—731no—
595C22×C4—731no—
596C22×C4—731no—
597C22×C4—731no—
598C22×C4—731no—
599C22×C4—731no—
600C22×C4—731no—
601C22×C4—731no—
602C22×C4—731no—
603C22×C4—732no—
604C22×C4—732no—
605C22×C4—1462no—
606C22×C4—1462no—
607C22×C4—1462no—
608C22×C4—1462no—
609C22×C4—1461no—
610C22×C4—1462no—
611C22×C4—1462no—
612C22×C4—1461no—
613C22×C4—1468no—
614C22×C4—1462no—
615C22×C4—1462no—
616C22×C4—1462no—
617C22×C4—1462no—
618C22×C4—1461no—
619C22×C4—1461no—
620C22×C4—1461no—
621C22×C4C22×#6440811yescharacteristic
622M16—21no—
623M16—734no—
624M16—732no—
625M16—1462no—
626M16—1462no—
627M16—1462no—
628M16—1462no—
629M16—1462no—
630M16—1461no—
631M16C22×#6440812yescomplemented
632C2×C8—21no—
633C2×C8—1462no—
634C2×C8—1462no—
635C2×C8—1462no—
636C2×C8—1462no—
637C2×C8—1462no—
638C2×C8—1461no—
639C4⋊C4—734no—
640C4⋊C4—1462no—
641C4⋊C4—1468no—
642C22⋊C4—1468no—
643C22⋊C4—1462no—
644C22⋊C4—1462no—
645C42—21no—
646C42—732no—
647C42—732no—
648C42—734no—
649C42—734no—
650C42—732no—
651C42—732no—
652C42—734no—
653C42—732no—
654C42—1462no—
655C42—1462no—
656C42—1462no—
657C42—1462no—
658C42—1462no—
659C42—1462no—
660C42—1462no—
661C42—1468no—
662C42—1461no—
663C42C22×#6440812yescomplemented
664C23—21no—
665C23—2924no—
666C23—731no—
667C23—731no—
668C23—731no—
669C23—731no—
670C23—731no—
671C23—731no—
672C23—1462no—
673C23—1462no—
674C23—1464no—
675C23—1461no—
676C23D4×#6440811yescharacteristic
677Q8—21no—
678Q8—732no—
679Q8—1462no—
680Q8—1462no—
681Q8—1461no—
682Q8C2×C4×#6440812yes—
683D4—22no—
684D4—22no—
685D4—21no—
686D4—732no—
687D4—1462no—
688D4—1462no—
689D4—1462no—
690D4—1462no—
691D4—1462no—
692D4—1462no—
693D4—1462no—
694D4—1462no—
695D4—1461no—
696D4C2×C4×#6440812yes—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—2924no—
703C2×C4—2924no—
704C2×C4—2922no—
705C2×C4—2924no—
706C2×C4—2924no—
707C2×C4—2924no—
708C2×C4—2924no—
709C2×C4—29216no—
710C2×C4—2924no—
711C2×C4—2924no—
712C2×C4—731no—
713C2×C4—731no—
714C2×C4—731no—
715C2×C4—731no—
716C2×C4—731no—
717C2×C4—731no—
718C2×C4—731no—
719C2×C4—731no—
720C2×C4—731no—
721C2×C4—731no—
722C2×C4—731no—
723C2×C4—731no—
724C2×C4—731no—
725C2×C4—731no—
726C2×C4—731no—
727C2×C4—731no—
728C2×C4—731no—
729C2×C4—731no—
730C2×C4—731no—
731C2×C4—731no—
732C2×C4—731no—
733C2×C4—731no—
734C2×C4—734no—
735C2×C4—734no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1464no—
741C2×C4—1464no—
742C2×C4—1462no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1464no—
746C2×C4—1464no—
747C2×C4—1461no—
748C2×C4—1462no—
749C2×C4—1462no—
750C2×C4C2×C4×#6440811yescharacteristic
751C2×C4C2×C4×#6440811yescharacteristic
752C2×C4D4×#6440811yescharacteristic
753C2×C4D4×#6440811yescharacteristic
754C2×C4D4×#6440811yescharacteristic
755C2×C4C23×#6440811yescharacteristic
756C8—22no—
757C8—1464no—
758C8—1462no—
759C22—22no—
760C22—22no—
761C22—42no—
762C22—2924no—
763C22—2924no—
764C22—2922no—
765C22—731no—
766C22—731no—
767C22—734no—
768C22—731no—
769C22—731no—
770C22—1462no—
771C22—1462no—
772C22—1462no—
773C22—1462no—
774C22—1462no—
775C22—1462no—
776C22C22⋊C4×#6440811yescharacteristic
777C22C22⋊C4×#6440811yescharacteristic
778C22C2×D4×#6440811yescharacteristic
779C4—22no—
780C4—42no—
781C4—2922no—
782C4—2924no—
783C4—2924no—
784C4—731no—
785C4—731no—
786C4—731no—
787C4—731no—
788C4—1464no—
789C4—1464no—
790C4—1462no—
791C4C22⋊C4×#6440811yescharacteristic
792C4C22⋊C4×#6440811yescharacteristic
793C4C22×C4×#6440811yescharacteristic
794C4C2×D4×#6440811yescharacteristic
795C2—21no—
796C2—21no—
797C2—42no—
798C2—2922no—
799C2—732no—
800C2—732no—
801C2—1461no—
802C2—1461no—
803C2#2262569612yesdirect product factor
804C2C2×C22⋊C4×#6440811yescharacteristic
subgroupG/H
centerC2×C4D4×#64408
commutatorC4×C73C22×C42
FrattiniC2×C4C23×#64408
FittingC2×#104×C73C4
socleC22×C73C4×C22⋊C4
prime radicalC2×#41×D73C22
cosocleC2×C4×D73C24
hypercenterC2×#104#64408
hypocenterC73C2×#1759
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
3. C2×M16×#64408C2semidirect
4. C2×#17989523C2semidirect
5. #22625696C2direct (N × H)
6. C2×#17989459C2semidirect
7. C2×#17989458C2semidirect
12. #41×#64408C4semidirect
14. C2×Q8×#64408C4semidirect
16. C2×D4×#64408C4semidirect
22. C2×#14556656C4semidirect
23. D73⋊#104C4semidirect
25. C2×#14556655C4semidirect
27. M16×#64408C22semidirect
31. #17989523C22semidirect
33. #17989459C22semidirect
34. #17989458C22semidirect
38. C2×#14556519C4semidirect
39. C2×#14556518C4semidirect
40. C2×#14556517C4semidirect
41. #104×D73C4semidirect
43. C2×#104×C73C4semidirect
47. C2×#11924038C2×C4semidirect
50. D73⋊M16C2×C4semidirect
55. Q8×#64408C2×C4semidirect
59. D4×#64408C2×C4semidirect
79. C2×C4×#64408C2×C4semidirect
80. C2×C4×#64408C2×C4semidirect
87. #14556656C2×C4semidirect
88. #14556655C2×C4semidirect
111. C2×#11924012C2×C4semidirect
115. M16×D73C2×C4semidirect
119. C2×C4×Dic73C2×C4semidirect
122. C42×D73C2×C4semidirect
124. #14556519C2×C4semidirect
125. #14556518C2×C4semidirect
126. #14556517C2×C4semidirect
128. C2×M16×C73C2×C4semidirect
129. C2×C42×C73C2×C4semidirect
130. #104×C73C2×C4semidirect
144. #11924038C22×C4semidirect
166. C4×#64408C22×C4semidirect
236. #11924012C22×C4semidirect
245. C4×Dic73C22×C4semidirect
257. M16×C73C22×C4semidirect
260. C42×C73C22×C4semidirect
396. C2×C73#1759semidirect
401. D73#1759semidirect
411. C73C2×#1759semidirect
437. C2×#104#64408semidirect
482. C2×M16C2×#64408semidirect
524. C2×C42C2×#64408semidirect
530. #104C2×#64408semidirect
631. M16C22×#64408semidirect
663. C42C22×#64408semidirect
803. C2#22625696direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×#644082
C2×D73⋊#1042
C2×M16×#644082
C2×#179895232
#226256962
C2×#179894592
C2×#179894582
C2×#104×D732
C2×#175973