Finite Group Databasebeta

← C2×#22610450 #33087954

Subgroups — C2×#22610450 #33087954

Order 18688.

1686 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989353C211yesmaximal, characteristic
2C2×#17989161C211yesmaximal, characteristic
3C2×#17988596C211yesmaximal, characteristic, complemented
4C2×#17988560C211yesmaximal, characteristic
5#22610450C218yesmaximal, direct product factor
6C2×#17988344C211yesmaximal, characteristic, complemented
7C2×#17988343C211yesmaximal, characteristic, complemented
8C2×#419×C73C211yesmaximal, characteristic, complemented
9C22×#11924028C2211yescharacteristic
10#17989353—22no—
11#17989353—22no—
12#17989353—22no—
13#17989353C2214yes—
14C2×#14556599—22no—
15C2×#14556597—22no—
16C22×#11924012C2211yescharacteristic
17C2×M16×D73—22no—
18#17989161—22no—
19#17989161—22no—
20#17989161C414yescomplemented
21#17989161C2214yes—
22C2×#14556589C412yescomplemented
23C2×#14556580C412yescomplemented
24C2×#14556574—22no—
25C2×#14556567—22no—
26C2×#14556550C2211yescharacteristic
27C2×#14556550C2211yescharacteristic
28#17988596—22no—
29#17988596C2214yescomplemented
30C2×#14556515—22no—
31#17988560—22no—
32#17988560C2214yes—
33C2×#14556505—22no—
34#17988344C2214yescomplemented
35#17988343C2214yescomplemented
36C23×Q8×C73C2211yescharacteristic
37C22×M16×C73C2211yescharacteristic
38C2×#117×C73C2211yescharacteristic
39#419×C73—22no—
40#419×C73C2214yescomplemented
41C2×#103×C73—22no—
42C2×#11924028—21no—
43C2×#11924028—21no—
44C2×#11924028—21no—
45C2×#11924028—21no—
46C2×#11924028—21no—
47C2×#11924028—21no—
48C2×#11924028—21no—
49C2×#11924028—21no—
50C2×#11924028C2×C412yes—
51C2×#11924028D412yes—
52C2×#11924028D412yes—
53C2×#11924028C2312yes—
54C22×Dic146C2×C411yescharacteristic
55C22×D292C2×C411yescharacteristic
56C22×C22⋊D73D412yes—
57C22×C4×D73D412yes—
58#14556599—28no—
59#14556599—28no—
60#14556597—28no—
61#14556597—28no—
62C2×#11924012—21no—
63C2×#11924012—21no—
64C2×#11924012—21no—
65C2×#11924012—21no—
66C2×#11924012D412yes—
67C2×#11924012C2312yes—
68C2×#11924011—24no—
69M16×D73—28no—
70M16×D73—28no—
71C22×#10596831D412yes—
72C2×C8×D73—24no—
73#14556589—24no—
74#14556589C2×C418yescomplemented
75#14556580—24no—
76#14556580C2×C418yescomplemented
77#14556574—28no—
78#14556574—28no—
79#14556567—28no—
80#14556567—28no—
81#14556550—21no—
82#14556550—21no—
83#14556550—21no—
84#14556550—21no—
85#14556550—21no—
86#14556550C2×C412yes—
87#14556550C2312yes—
88#14556550C2312yes—
89C2×C4⋊Dic73—21no—
90C2×C4⋊Dic73—21no—
91C2×#11924007—24no—
92C2×C22⋊Dic73—21no—
93C2×C22⋊Dic73—21no—
94C2×#11924005—24no—
95C2×C4×Dic73—21no—
96C2×C4×Dic73C2×C412yes—
97#14556515—28no—
98#14556505—28no—
99C22×Q8×C73—21no—
100C22×Q8×C73—21no—
101C22×Q8×C73—21no—
102C22×Q8×C73—21no—
103C22×Q8×C73—21no—
104C22×Q8×C73—21no—
105C22×Q8×C73—21no—
106C22×Q8×C73—21no—
107C22×Q8×C73—21no—
108C22×Q8×C73—21no—
109C22×Q8×C73—21no—
110C22×Q8×C73C2×C412yes—
111C22×Q8×C73C2×C412yes—
112C22×Q8×C73C2312yes—
113C23×C4×C73—21no—
114C23×C4×C73C2311yescharacteristic
115C2×M16×C73—21no—
116C2×M16×C73—21no—
117C2×M16×C73—21no—
118C2×M16×C73—21no—
119C2×M16×C73D412yes—
120C2×M16×C73C2312yes—
121C22×C8×C73D412yes—
122#117×C73—21no—
123#117×C73—21no—
124#117×C73—21no—
125#117×C73C2312yes—
126C2×C4⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C42×C73—21no—
129#103×C73—28no—
130C23×D73C22⋊C412yes—
131#11924028—22no—
132#11924028—22no—
133#11924028—22no—
134#11924028—22no—
135#11924028—22no—
136#11924028—22no—
137#11924028—22no—
138#11924028—22no—
139#11924028—22no—
140#11924028—22no—
141#11924028—22no—
142#11924028—22no—
143#11924028—22no—
144#11924028—22no—
145#11924028—22no—
146#11924028—22no—
147C2×Dic146—21no—
148C2×Dic146—21no—
149C2×Dic146—21no—
150C2×Dic146—21no—
151C2×Dic146C22⋊C412yes—
152C2×Dic146C22×C412yes—
153C2×D292—21no—
154C2×D292—21no—
155C2×D292—21no—
156C2×D292—21no—
157C2×D292C22⋊C412yes—
158C2×D292C22×C412yes—
159C2×C22⋊D73—22no—
160C2×C22⋊D73—22no—
161C2×C22⋊D73—22no—
162C2×C22⋊D73—22no—
163C2×C22⋊D73C22⋊C414yes—
164C2×C22⋊D73C2×D414yes—
165C22×Dic73—22no—
166C22×Dic73—41no—
167C22×Dic73C22⋊C412yes—
168C2×C4×D73—22no—
169C2×C4×D73—22no—
170C2×C4×D73—22no—
171C2×C4×D73—22no—
172C2×C4×D73C22⋊C414yes—
173C2×C4×D73C2×D414yes—
174#11924012—22no—
175#11924012—22no—
176#11924012—22no—
177#11924012—22no—
178#11924011—216no—
179C2×#10596831—22no—
180C2×#10596831—22no—
181C2×#10596831C2×D414yes—
182C8×D73—216no—
183C4⋊Dic73—22no—
184C4⋊Dic73—22no—
185C4⋊Dic73—22no—
186C4⋊Dic73—41no—
187#11924007—216no—
188C22⋊Dic73—22no—
189C22⋊Dic73—22no—
190C22⋊Dic73—22no—
191C22⋊Dic73—41no—
192#11924005—216no—
193C4×Dic73—22no—
194C4×Dic73—22no—
195C4×Dic73—41no—
196C4×Dic73C22×C414yes—
197C24×C73C2×D411yescharacteristic
198C2×Q8×C73—22no—
199C2×Q8×C73—22no—
200C2×Q8×C73—22no—
201C2×Q8×C73—22no—
202C2×Q8×C73—22no—
203C2×Q8×C73—22no—
204C2×Q8×C73—22no—
205C2×Q8×C73—22no—
206C2×Q8×C73—22no—
207C2×Q8×C73—22no—
208C2×Q8×C73—22no—
209C2×Q8×C73—22no—
210C2×Q8×C73—22no—
211C2×Q8×C73—22no—
212C2×Q8×C73—22no—
213C2×Q8×C73—41no—
214C2×Q8×C73—41no—
215C2×Q8×C73—41no—
216C2×Q8×C73—41no—
217C2×Q8×C73—41no—
218C2×Q8×C73—41no—
219C2×Q8×C73—41no—
220C2×Q8×C73—41no—
221C2×Q8×C73—41no—
222C2×Q8×C73—41no—
223C2×Q8×C73—41no—
224C2×Q8×C73—41no—
225C2×Q8×C73C22×C414yes—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73—41no—
230C22×C4×C73—41no—
231C22×C4×C73—41no—
232C22×C4×C73—41no—
233C22×C4×C73—41no—
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C22×C411yescharacteristic
236C22×C4×C73C2×D411yescharacteristic
237C22×C4×C73C2×D411yescharacteristic
238C22×C4×C73C2×D411yescharacteristic
239C22×C4×C73C2×D411yescharacteristic
240C22×C4×C73C2×D411yescharacteristic
241C22×C4×C73C2×D411yescharacteristic
242C22×C4×C73C2×D411yescharacteristic
243C22×C4×C73#4111yescharacteristic
244C22×C4×C73#4111yescharacteristic
245C22×C4×C73#4111yescharacteristic
246C22×C4×C73#4111yescharacteristic
247C22×C4×C73C2411yescharacteristic
248M16×C73—22no—
249M16×C73—22no—
250M16×C73—22no—
251M16×C73—22no—
252C2×C8×C73—22no—
253C2×C8×C73—22no—
254C2×C8×C73C2×D414yes—
255C4⋊C4×C73—22no—
256C4⋊C4×C73—41no—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—41no—
259C42×C73—22no—
260C42×C73—41no—
261C23×C73—42no—
262C23×C73C2×C22⋊C411yescharacteristic
263C23×C73C2×C22⋊C411yescharacteristic
264C23×C73#12111yescharacteristic
265C23×C73#12111yescharacteristic
266C23×C73#12111yescharacteristic
267C23×C73#12111yescharacteristic
268C23×C73C22×D411yescharacteristic
269C22×D73—22no—
270C22×D73—22no—
271C22×D73—44no—
272C22×D73C2×C22⋊C414yes—
273Q8×C73—24no—
274Q8×C73—24no—
275Q8×C73—42no—
276Q8×C73—42no—
277Q8×C73—42no—
278Q8×C73—42no—
279Q8×C73—42no—
280Q8×C73—42no—
281C2×C4×C73—24no—
282C2×C4×C73—42no—
283C2×C4×C73—42no—
284C2×C4×C73—42no—
285C2×C4×C73—42no—
286C2×C4×C73—42no—
287C2×C4×C73—42no—
288C2×C4×C73—42no—
289C2×C4×C73—82no—
290C2×C4×C73C2×C22⋊C411yescharacteristic
291C2×C4×C73C2×C22⋊C411yescharacteristic
292C2×C4×C73C4×D411yescharacteristic
293C2×C4×C73C4×D411yescharacteristic
294C2×C4×C73C4×D411yescharacteristic
295C2×C4×C73C4×D411yescharacteristic
296C2×C4×C73C4×D411yescharacteristic
297C2×C4×C73C4×D411yescharacteristic
298C2×C4×C73C4×D411yescharacteristic
299C2×C4×C73C4×D411yescharacteristic
300C2×C4×C73#12011yescharacteristic
301C2×C4×C73#12011yescharacteristic
302C2×C4×C73#12011yescharacteristic
303C2×C4×C73#12011yescharacteristic
304C2×C4×C73#12111yescharacteristic
305C2×C4×C73#12111yescharacteristic
306C2×C4×C73#12111yescharacteristic
307C2×C4×C73#12111yescharacteristic
308C2×C4×C73#12311yescharacteristic
309C2×C4×C73#12311yescharacteristic
310C2×C4×C73#12311yescharacteristic
311C2×C4×C73#12311yescharacteristic
312C2×C4×C73C23×C411yescharacteristic
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C22×D411yescharacteristic
315C2×C4×C73C22×D411yescharacteristic
316C2×C4×C73C2×#4111yescharacteristic
317C2×C4×C73C2×#4111yescharacteristic
318C22⋊D73—24no—
319C22⋊D73—24no—
320C22⋊D73—24no—
321C22⋊D73—24no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—24no—
325C2×Dic73—44no—
326C2×Dic73—42no—
327C2×Dic73—82no—
328C2×Dic73C2×C22⋊C414yes—
329D292—22no—
330D292—22no—
331D292—22no—
332D292—22no—
333C4×D73—24no—
334C4×D73—24no—
335C4×D73—24no—
336C4×D73—24no—
337Dic146—22no—
338Dic146—22no—
339Dic146—22no—
340Dic146—22no—
341C8×C73—24no—
342#10596831—24no—
343C22×C73—22no—
344C22×C73—22no—
345C22×C73—22no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73#38611yescharacteristic
351C22×C73#38611yescharacteristic
352C22×C73#38611yescharacteristic
353C22×C73#38611yescharacteristic
354C22×C73C22×C22⋊C411yescharacteristic
355C22×C73C2×#12111yescharacteristic
356C22×C73C2×#12111yescharacteristic
357C2×D73—24no—
358C2×D73—44no—
359C2×D73—44no—
360C2×D73—82no—
361C4×C73—44no—
362C4×C73—82no—
363C4×C73#38611yescharacteristic
364C4×C73#38611yescharacteristic
365C4×C73#38611yescharacteristic
366C4×C73#38611yescharacteristic
367C4×C73C2×C4×D411yescharacteristic
368C4×C73C2×C4×D411yescharacteristic
369C4×C73C2×#12011yescharacteristic
370C4×C73C2×#12311yescharacteristic
371Dic73—24no—
372Dic73—44no—
373Dic73—82no—
374C2×#1909—731nomaximal, Sylow
375C2×C73—21no—
376C2×C73—21no—
377C2×C73—21no—
378C2×C73—21no—
379C2×C73—21no—
380C2×C73—21no—
381C2×C73#190912yescomplemented
382C2×C73C2×#38611yescharacteristic
383D73—44no—
384C2×#568—731no—
385C2×#536—731no—
386C2×#419—731no—
387C2×#419D7311yescharacteristic, complemented
388C2×#410—731no—
389#1909—738no—
390C2×H(3,ℤ/4)—731no—
391C2×H(3,ℤ/4)—731no—
392C73C2×#190911yescharacteristic, complemented, Sylow
393C22×#41—731no—
394C23×Q8C2×D7311yescharacteristic
395#568—734no—
396#568—1462no—
397#568—1462no—
398#568—1462no—
399C2×#131—1462no—
400C2×#131—1462no—
401C22×M16—731no—
402C22×M16—1462no—
403C22×M16C2×D7311yescharacteristic
404#536—734no—
405#536—734no—
406#536—1462no—
407#536—1462no—
408C2×C4⋊Q8—732no—
409C2×#124—732no—
410C2×#123—1462no—
411C2×C22⋊Q8—1462no—
412C2×#117—731no—
413C2×#117—731no—
414C2×#117C2×D7311yescharacteristic
415#419—22no—
416#419—734no—
417#419—1462no—
418#419C2×D7314yescomplemented
419C2×#103—22no—
420C2×#103—1462no—
421#410—734no—
422#410—1462no—
423C2×#99—1462no—
424H(3,ℤ/4)—734no—
425H(3,ℤ/4)—734no—
426C2×#41—732no—
427C2×#41—732no—
428C2×#41—732no—
429C2×#41—732no—
430C2×#41—1461no—
431C2×#41—1461no—
432C2×#41—1461no—
433C2×#41—1461no—
434C2×#41—1461no—
435C2×#41—1461no—
436C2×#41—1461no—
437C2×#41—1461no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—731no—
450C22×Q8C4×D7312yes—
451C22×Q8C4×D7312yes—
452C22×Q8C22×D7312yes—
453C22×D4—732no—
454C22×D4—731no—
455C23×C4—21no—
456C23×C4—732no—
457C23×C4C22×D7311yescharacteristic
458#131—1468no—
459#131—1468no—
460#131—1468no—
461#131—1468no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—732no—
467C2×M16—732no—
468C2×M16—1464no—
469C2×M16—1468no—
470C2×M16—1468no—
471C2×M16—1461no—
472C2×M16—1461no—
473C2×M16—1461no—
474C2×M16—1461no—
475C2×M16C22⋊D7312yes—
476C2×M16C22×D7312yes—
477C22×C8—732no—
478C22×C8—1464no—
479C22×C8C22⋊D7312yes—
480C4⋊Q8—738no—
481C4⋊Q8—1464no—
482#124—738no—
483#124—1464no—
484#123—1468no—
485#123—1468no—
486C22⋊Q8—1468no—
487C22⋊Q8—1468no—
488#117—21no—
489#117—21no—
490#117—21no—
491#117—732no—
492#117—732no—
493#117—732no—
494#117—1461no—
495#117—1461no—
496#117—1461no—
497#117—1461no—
498#117—1461no—
499#117C22×D7312yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1464no—
503C2×C4⋊C4—1461no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—1461no—
506C2×C22⋊C4—1464no—
507C2×C22⋊C4—1461no—
508C2×C42—21no—
509C2×C42—732no—
510C2×C42—1461no—
511#103—28no—
512#103—1468no—
513#99—1468no—
514C24—732no—
515C24D4×D7311yescharacteristic
516#41—1462no—
517#41—1462no—
518#41—1462no—
519#41—1462no—
520#41—1462no—
521#41—1462no—
522#41—1462no—
523#41—1462no—
524#41—1462no—
525#41—1462no—
526#41—1462no—
527#41—1462no—
528#41—1462no—
529#41—1462no—
530#41—1462no—
531#41—1462no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—732no—
560C2×Q8—732no—
561C2×Q8—1461no—
562C2×Q8—1461no—
563C2×Q8—1461no—
564C2×Q8—1461no—
565C2×Q8C2×C4×D7314yes—
566C2×D4—734no—
567C2×D4—734no—
568C2×D4—732no—
569C2×D4—732no—
570C2×D4—1462no—
571C2×D4—1462no—
572C2×D4—1462no—
573C2×D4—1462no—
574C2×D4—1461no—
575C2×D4—1461no—
576C2×D4—1461no—
577C2×D4—1461no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—2921no—
587C22×C4—732no—
588C22×C4—734no—
589C22×C4—734no—
590C22×C4—1462no—
591C22×C4—1462no—
592C22×C4—1462no—
593C22×C4—1462no—
594C22×C4—1462no—
595C22×C4C2×C4×D7311yescharacteristic
596C22×C4C2×C4×D7311yescharacteristic
597C22×C4D4×D7311yescharacteristic
598C22×C4D4×D7311yescharacteristic
599C22×C4D4×D7311yescharacteristic
600C22×C4D4×D7311yescharacteristic
601C22×C4D4×D7311yescharacteristic
602C22×C4C2×C22⋊D7311yescharacteristic
603C22×C4C2×C22⋊D7311yescharacteristic
604C22×C4#1192402711yescharacteristic
605C22×C4#1192402711yescharacteristic
606C22×C4#1192402811yescharacteristic
607C22×C4#1192402811yescharacteristic
608C22×C4C23×D7311yescharacteristic
609M16—22no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—14616no—
614M16—1462no—
615M16—1462no—
616M16—1462no—
617M16—1462no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—734no—
621C2×C8—14616no—
622C2×C8—1462no—
623C2×C8—1462no—
624C2×C8C2×C22⋊D7314yes—
625C4⋊C4—22no—
626C4⋊C4—41no—
627C4⋊C4—2921no—
628C4⋊C4—14616no—
629C4⋊C4—1462no—
630C4⋊C4—1462no—
631C4⋊C4—1462no—
632C22⋊C4—22no—
633C22⋊C4—41no—
634C22⋊C4—2921no—
635C22⋊C4—14616no—
636C22⋊C4—1462no—
637C22⋊C4—1462no—
638C22⋊C4—1462no—
639C42—22no—
640C42—41no—
641C42—2921no—
642C42—734no—
643C42—1462no—
644C42—1462no—
645C23—42no—
646C23—2924no—
647C23—734no—
648C23—1462no—
649C23—1462no—
650C23C22⋊C4×D7311yescharacteristic
651C23C22⋊C4×D7311yescharacteristic
652C23#1455656211yescharacteristic
653C23#1455656211yescharacteristic
654C23#1455656411yescharacteristic
655C23#1455656411yescharacteristic
656C23C2×D4×D7311yescharacteristic
657Q8—24no—
658Q8—24no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—1462no—
666Q8—1462no—
667Q8—1462no—
668Q8—1462no—
669D4—1464no—
670D4—1464no—
671D4—1464no—
672D4—1464no—
673D4—1462no—
674D4—1462no—
675D4—1462no—
676D4—1462no—
677C2×C4—24no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—82no—
686C2×C4—2924no—
687C2×C4—2922no—
688C2×C4—5842no—
689C2×C4—734no—
690C2×C4—1464no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1464no—
694C2×C4—1464no—
695C2×C4—1464no—
696C2×C4—1464no—
697C2×C4C22⋊C4×D7311yescharacteristic
698C2×C4C22⋊C4×D7311yescharacteristic
699C2×C4#1455655111yescharacteristic
700C2×C4#1455655111yescharacteristic
701C2×C4#1455655111yescharacteristic
702C2×C4#1455655111yescharacteristic
703C2×C4C4×C22⋊D7311yescharacteristic
704C2×C4C4×C22⋊D7311yescharacteristic
705C2×C4C4×C22⋊D7311yescharacteristic
706C2×C4C4×C22⋊D7311yescharacteristic
707C2×C4#1455655911yescharacteristic
708C2×C4#1455655911yescharacteristic
709C2×C4#1455655911yescharacteristic
710C2×C4#1455655911yescharacteristic
711C2×C4#1455656211yescharacteristic
712C2×C4#1455656211yescharacteristic
713C2×C4#1455656411yescharacteristic
714C2×C4#1455656411yescharacteristic
715C2×C4#1455657311yescharacteristic
716C2×C4#1455657311yescharacteristic
717C2×C4#1455657311yescharacteristic
718C2×C4#1455657311yescharacteristic
719C2×C4C22×C4×D7311yescharacteristic
720C2×C4C2×D4×D7311yescharacteristic
721C2×C4C2×D4×D7311yescharacteristic
722C2×C4C22×C22⋊D7311yescharacteristic
723C2×C4C2×#1192402711yescharacteristic
724C2×C4C2×#1192402811yescharacteristic
725C8—24no—
726C8—1464no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—2924no—
735C22—2924no—
736C22—5842no—
737C22—1464no—
738C22#1798846311yescharacteristic
739C22#1798846311yescharacteristic
740C22#1798846311yescharacteristic
741C22#1798846311yescharacteristic
742C22C2×C22⋊C4×D7311yescharacteristic
743C22C2×#1455656211yescharacteristic
744C22C2×#1455656411yescharacteristic
745C4—44no—
746C4—82no—
747C4—2924no—
748C4—5842no—
749C4—1464no—
750C4#1798846311yescharacteristic
751C4#1798846311yescharacteristic
752C4#1798846311yescharacteristic
753C4#1798846311yescharacteristic
754C4C2×#1455655111yescharacteristic
755C4C2×C4×C22⋊D7311yescharacteristic
756C4C2×#1455655911yescharacteristic
757C4C2×#1455657311yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—2924no—
765C2#2261045012yesdirect product factor
766C2C2×#1798846311yescharacteristic
subgroupG/H
centerC22#17988463
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#419×C73C2
socleC22×C73#386
prime radicalC22×#11924028C22
cosocleC22×C4×C73C24
hypercenterC2×#419D73
hypocenterC73C2×#1909
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. C2×#17988596C2semidirect
5. #22610450C2direct (N × H)
6. C2×#17988344C2semidirect
7. C2×#17988343C2semidirect
8. C2×#419×C73C2semidirect
20. #17989161C4semidirect
22. C2×#14556589C4semidirect
23. C2×#14556580C4semidirect
29. #17988596C22semidirect
34. #17988344C22semidirect
35. #17988343C22semidirect
40. #419×C73C22semidirect
74. #14556589C2×C4semidirect
76. #14556580C2×C4semidirect
381. C2×C73#1909semidirect
387. C2×#419D73semidirect
392. C73C2×#1909semidirect
418. #419C2×D73semidirect
765. C2#22610450direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893532
C2×#179891612
C2×#179885962
C2×#179885602
#226104502
C2×#179883442
C2×#179883432
C2×#419×C732
C2×#190973