Finite Group Databasebeta

← C2×#22622657 #33965680

Subgroups — C2×#22622657 #33965680

Order 18688.

2122 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989314C211yesmaximal, characteristic, complemented
2C2×#17989257C211yesmaximal, characteristic
3#22622657C2116yesmaximal, direct product factor
4C2×#17988950C211yesmaximal, characteristic, complemented
5C2×#17988932C211yesmaximal, characteristic, complemented
6C2×#17988885C211yesmaximal, characteristic, complemented
7C2×#17988884C211yesmaximal, characteristic, complemented
8C2×#17988865C211yesmaximal, characteristic, complemented
9C2×#17988786C211yesmaximal, characteristic, complemented
10C2×#17988786C211yesmaximal, characteristic, complemented
11C2×#17988784C211yesmaximal, characteristic, complemented
12C2×#17988715C211yesmaximal, characteristic, complemented
13C2×#17988689C211yesmaximal, characteristic, complemented
14C2×#17988684C211yesmaximal, characteristic, complemented
15C2×#17988678C211yesmaximal, characteristic, complemented
16C2×#490×C73C211yesmaximal, characteristic, complemented
17C22×#11924027—21no—
18C22×#11924017C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924016C2211yescharacteristic
21#17989314—24no—
22#17989314C2218yescomplemented
23#17989257—24no—
24#17989257C2218yes—
25C2×#14556590—21no—
26C2×#14556590C2211yescharacteristic
27C2×#14556587C2211yescharacteristic
28C2×#14556587C2211yescharacteristic
29C2×#14556582C2211yescharacteristic
30C2×#14556581—21no—
31C2×#14556581—21no—
32C2×#14556563—21no—
33C2×#14556563—21no—
34C2×#14556562—21no—
35C2×C4×Dic146C2211yescharacteristic
36C2×C4×Dic146C2211yescharacteristic
37C2×#14556556—21no—
38C2×#14556556C2211yescharacteristic
39C2×#14556556C2211yescharacteristic
40C2×C4×D292C2211yescharacteristic
41C2×D4×Dic73C2211yescharacteristic
42C2×D4×Dic73C2211yescharacteristic
43#17988950C2218yescomplemented
44#17988932C2218yescomplemented
45#17988885C2218yescomplemented
46#17988884C2218yescomplemented
47#17988865C2218yescomplemented
48#17988786C2218yescomplemented
49#17988786C2218yescomplemented
50#17988784C2218yescomplemented
51#17988715C2218yescomplemented
52#17988689C2218yescomplemented
53#17988684C2218yescomplemented
54#17988678C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×C4⋊#10596831C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×#127×C73C2211yescharacteristic
70C2×#125×C73C2211yescharacteristic
71#490×C73C2218yescomplemented
72C2×#102×C73C2211yescharacteristic
73C2×#102×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C2×#11924027—28no—
78C2×#11924027—48no—
79C22×Dic146—21no—
80C22×Dic146D411yescharacteristic
81C22×Dic146C2311yescharacteristic
82C22×D292C2311yescharacteristic
83C22×C22⋊D73—21no—
84C22×C22⋊D73—21no—
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C23×Dic73—21no—
88C23×Dic73—21no—
89C22×C4×D73—21no—
90C2×#11924017—24no—
91C2×#11924017C2314yes—
92C2×#11924016—24no—
93C2×#11924016—24no—
94C2×#11924016C2314yes—
95C2×#11924016C2314yes—
96C22×#10596831C2311yescharacteristic
97C22×#10596831C2311yescharacteristic
98#14556590—28no—
99#14556590—22no—
100#14556590C2314yes—
101#14556587—22no—
102#14556587—22no—
103#14556587C2314yes—
104#14556587C2314yes—
105#14556582—22no—
106#14556582C2314yes—
107#14556581—28no—
108#14556581—28no—
109#14556563—28no—
110#14556563—28no—
111#14556562—28no—
112C4×Dic146—22no—
113C4×Dic146D414yes—
114C4×Dic146C2314yes—
115C4×Dic146C2314yes—
116#14556556—28no—
117#14556556—22no—
118#14556556—22no—
119#14556556C2314yes—
120#14556556C2314yes—
121C4×D292—22no—
122C4×D292C2314yes—
123D4×Dic73—22no—
124D4×Dic73—22no—
125D4×Dic73C2314yes—
126D4×Dic73C2314yes—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73D411yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×C4⋊Dic73C2311yescharacteristic
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007D411yescharacteristic
137C2×#11924007D411yescharacteristic
138C2×C22⋊Dic73—21no—
139C2×C22⋊Dic73—21no—
140C2×#11924005—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73C2311yescharacteristic
145C2×C4×Dic73C2311yescharacteristic
146#14556525C2314yes—
147#14556524C2314yes—
148#14556522C2314yes—
149C4⋊#10596831C2314yes—
150#14556520C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556513C2314yes—
154#14556512C2314yes—
155#14556512C2314yes—
156#14556511C2314yes—
157#14556511C2314yes—
158#14556501C2314yes—
159C8×Dic73C2314yes—
160C22×D4×C73—21no—
161C22×D4×C73—21no—
162C22×D4×C73C2311yescharacteristic
163C22×D4×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C22×C8×C73C2311yescharacteristic
166#127×C73—22no—
167#127×C73C2314yes—
168#125×C73—22no—
169#125×C73C2314yes—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C42×C73C2311yescharacteristic
175#102×C73C2314yes—
176#102×C73C2314yes—
177#102×C73C2314yes—
178#102×C73C2314yes—
179#97×C73C2314yes—
180C23×D73—21no—
181#11924027—432no—
182C2×Dic146—21no—
183C2×Dic146—22no—
184C2×Dic146—24no—
185C2×Dic146—24no—
186C2×Dic146—44no—
187C2×Dic146C2×D414yes—
188C2×Dic146#4114yescomplemented
189C2×Dic146C2412yes—
190C2×D292—22no—
191C2×D292—22no—
192C2×D292—21no—
193C2×D292C2412yes—
194C2×C22⋊D73—24no—
195C2×C22⋊D73—24no—
196C2×C22⋊D73—24no—
197C2×C22⋊D73—24no—
198C2×C22⋊D73—44no—
199C2×C22⋊D73—44no—
200C2×C22⋊D73—82no—
201C2×C22⋊D73—82no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—24no—
206C22×Dic73—24no—
207C22×Dic73—44no—
208C22×Dic73—44no—
209C22×Dic73C2×D411yescharacteristic
210C22×Dic73C2×D411yescharacteristic
211C22×Dic73C2×D411yescharacteristic
212C22×Dic73C2×D411yescharacteristic
213C2×C4×D73—24no—
214C2×C4×D73—44no—
215#11924017—28no—
216#11924016—28no—
217#11924016—28no—
218C2×#10596831—22no—
219C2×#10596831—22no—
220C2×#10596831C2412yes—
221C2×#10596831C2412yes—
222C4⋊Dic73—21no—
223C4⋊Dic73—21no—
224C4⋊Dic73—24no—
225C4⋊Dic73C2×D414yes—
226C4⋊Dic73C2412yes—
227C4⋊Dic73C2412yes—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007C2×D414yes—
234#11924007C2×D414yes—
235C22⋊Dic73—24no—
236C22⋊Dic73—24no—
237#11924005—24no—
238C4×Dic73—24no—
239C4×Dic73—24no—
240C4×Dic73—24no—
241C4×Dic73C2×D412yes—
242C4×Dic73C2×D412yes—
243C4×Dic73C2412yes—
244C4×Dic73C2412yes—
245C24×C73—21no—
246C24×C73—21no—
247C2×D4×C73—21no—
248C2×D4×C73—21no—
249C2×D4×C73—24no—
250C2×D4×C73—24no—
251C2×D4×C73—22no—
252C2×D4×C73—22no—
253C2×D4×C73—22no—
254C2×D4×C73—22no—
255C2×D4×C73—44no—
256C2×D4×C73—82no—
257C2×D4×C73C2412yes—
258C2×D4×C73C2412yes—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2×D411yescharacteristic
263C22×C4×C73C2411yescharacteristic
264C2×C8×C73—22no—
265C2×C8×C73—22no—
266C2×C8×C73C2412yes—
267C2×C8×C73C2412yes—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—24no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73C2412yes—
273C4⋊C4×C73C2412yes—
274C42×C73C2×D412yes—
275C42×C73C2412yes—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—42no—
279C23×C73—42no—
280C23×C73—42no—
281C23×C73—42no—
282C23×C73—42no—
283C23×C73—42no—
284C23×C73C22×D411yescharacteristic
285C22×D73—22no—
286C22×D73—42no—
287C22×D73—42no—
288C22×D73—42no—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—22no—
292D4×C73—22no—
293D4×C73—48no—
294D4×C73—42no—
295D4×C73—42no—
296D4×C73—84no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—42no—
302C2×C4×C73—42no—
303C2×C4×C73C22×D412yes—
304C2×C4×C73C22×D412yes—
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C2×#4112yes—
307C2×C4×C732−1+412yes—
308C2×C4×C73C2511yescharacteristic
309C22⋊D73—48no—
310C22⋊D73—48no—
311C22⋊D73—84no—
312C22⋊D73—84no—
313C2×Dic73—24no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—48no—
321C2×Dic73—42no—
322C2×Dic73—42no—
323C2×Dic73—48no—
324C2×Dic73AGL(1,ℤ/8)14yes—
325C2×Dic73C22×D412yes—
326C2×Dic73C22×D412yes—
327C2×Dic73C22×D412yes—
328C2×Dic73C22×D412yes—
329D292—22no—
330D292—22no—
331D292—42no—
332C4×D73—48no—
333Dic146—24no—
334Dic146—22no—
335Dic146—28no—
336Dic146—48no—
337Dic146C2×#4114yescomplemented
338C8×C73—22no—
339C8×C73—22no—
340#10596831—22no—
341#10596831—22no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—42no—
347C22×C73—42no—
348C22×C73—84no—
349C22×C73—84no—
350C22×C73#54812yes—
351C22×C73C2×AGL(1,ℤ/8)12yes—
352C22×C73#57712yes—
353C22×C73C23×D411yescharacteristic
354C2×D73—42no—
355C2×D73—42no—
356C2×D73—42no—
357C2×D73—84no—
358C4×C73—22no—
359C4×C73—22no—
360C4×C73—42no—
361C4×C73—42no—
362C4×C73#54812yes—
363C4×C73C22×#4111yescharacteristic
364C4×C73C2×2−1+411yescharacteristic
365Dic73—24no—
366Dic73—22no—
367Dic73—22no—
368Dic73—22no—
369Dic73—42no—
370Dic73—42no—
371Dic73C2×AGL(1,ℤ/8)14yes—
372C2×#3368—731nomaximal, Sylow
373C2×C73—82no—
374C2×C73—82no—
375C2×C73#336814yescomplemented
376C2×C73C2×#54811yescharacteristic
377C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
378C2×C73C2×#57711yescharacteristic
379D73—82no—
380C2×#557—731no—
381C2×#550—731no—
382#3368—7316no—
383C2×#490—731no—
384C2×#490D7311yescharacteristic, complemented
385C2×#486—731no—
386C2×#478—731no—
387C2×#478—731no—
388C2×#474—731no—
389C2×#460—731no—
390C2×#460—731no—
391C2×#460—731no—
392C2×#446—731no—
393C2×#440—731no—
394C2×#440—731no—
395C2×C4×SD16—731no—
396C73C2×#336811yescharacteristic, complemented, Sylow
397C22×#41—1461no—
398C22×SD16—731no—
399C22×SD16—731no—
400C22×SD16—731no—
401#557—738no—
402#557—1464no—
403#550—738no—
404#550—1464no—
405C2×C4⋊Q8—731no—
406C2×C4⋊Q8—1461no—
407C2×#127—731no—
408C2×#127—731no—
409C2×#127C2×D7311yescharacteristic
410C2×#125—731no—
411C2×#125—1461no—
412C2×#125—1461no—
413C2×#125C2×D7311yescharacteristic
414C2×#121—1461no—
415C2×#121—1461no—
416C2×#121—1461no—
417C2×C4×Q8—731no—
418C2×C4×Q8—731no—
419C2×C4×Q8—731no—
420C2×C4×Q8—731no—
421C2×C4×Q8—1461no—
422C2×C4×D4—731no—
423C2×C4×D4—731no—
424C2×C4×D4—731no—
425#490—738no—
426#490C2×D7318yescomplemented
427#486—738no—
428#478—738no—
429#478—738no—
430#474—738no—
431#460—738no—
432#460—738no—
433#460—738no—
434#446—738no—
435#440—738no—
436#440—738no—
437C4×SD16—738no—
438C2×#107—731no—
439C2×#107—731no—
440C2×#106—731no—
441C2×C4⋊C8—731no—
442C2×C4⋊C8—731no—
443C2×C4⋊C8—731no—
444C2×#103—731no—
445C2×#102—731no—
446C2×#102—731no—
447C2×#102—731no—
448C2×#102—731no—
449C2×#102—731no—
450C2×#102C2×D7311yescharacteristic
451C2×#102C2×D7311yescharacteristic
452C2×#102C2×D7311yescharacteristic
453C2×#102C2×D7311yescharacteristic
454C2×#97—731no—
455C2×#97C2×D7311yescharacteristic
456C2×C4×C8—731no—
457C2×#41—2928no—
458C2×#41—1468no—
459C22×Q8—731no—
460C22×Q8—731no—
461C22×Q8—1461no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—731no—
465C22×D4—1461no—
466C22×D4—1461no—
467C22×D4—1461no—
468C22×D4—1461no—
469C22×D4C22×D7311yescharacteristic
470C22×D4C22×D7311yescharacteristic
471C23×C4—1461no—
472C23×C4—1461no—
473C23×C4—1461no—
474C2×SD16—734no—
475C2×SD16—734no—
476C2×SD16—734no—
477C2×SD16—1464no—
478C2×SD16—1464no—
479C2×SD16—1464no—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8C22×D7311yescharacteristic
483C22×C8C22×D7311yescharacteristic
484C4⋊Q8—734no—
485C4⋊Q8—1462no—
486C4⋊Q8—1468no—
487#127—22no—
488#127—734no—
489#127—734no—
490#127—1462no—
491#127—1462no—
492#127C22×D7314yes—
493#125—22no—
494#125—734no—
495#125—1462no—
496#125—1468no—
497#125—1468no—
498#125C22×D7314yes—
499#121—1468no—
500#121—1468no—
501#121—1468no—
502C4×Q8—734no—
503C4×Q8—734no—
504C4×Q8—734no—
505C4×Q8—734no—
506C4×Q8—734no—
507C4×Q8—1462no—
508C4×Q8—1462no—
509C4×Q8—1468no—
510C4×Q8—1462no—
511C4×D4—734no—
512C4×D4—734no—
513C4×D4—734no—
514C4×D4—1462no—
515C4×D4—1462no—
516C4×D4—1462no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4—1461no—
530C2×C4⋊C4C22×D7311yescharacteristic
531C2×C4⋊C4C22×D7311yescharacteristic
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C42—731no—
536C2×C42—731no—
537C2×C42—1461no—
538C2×C42—1461no—
539C2×C42—1461no—
540C2×C42C22×D7311yescharacteristic
541#107—734no—
542#107—734no—
543#106—734no—
544C4⋊C8—734no—
545C4⋊C8—734no—
546C4⋊C8—734no—
547#103—734no—
548#102—734no—
549#102—734no—
550#102—734no—
551#102—734no—
552#102—734no—
553#102C22×D7314yes—
554#102C22×D7314yes—
555#102C22×D7314yes—
556#102C22×D7314yes—
557#97—734no—
558#97C22×D7314yes—
559C4×C8—734no—
560C24—21no—
561C24—21no—
562C24—1461no—
563#41—29232no—
564C2×Q8—2924no—
565C2×Q8—734no—
566C2×Q8—734no—
567C2×Q8—732no—
568C2×Q8—1464no—
569C2×Q8—1464no—
570C2×Q8—1461no—
571C2×Q8—1462no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—44no—
581C2×D4—82no—
582C2×D4—2924no—
583C2×D4—2924no—
584C2×D4—5842no—
585C2×D4—5842no—
586C2×D4—732no—
587C2×D4—1464no—
588C2×D4—1464no—
589C2×D4—1464no—
590C2×D4—1464no—
591C2×D4—1461no—
592C2×D4—1462no—
593C2×D4—1462no—
594C2×D4C23×D7312yes—
595C2×D4C23×D7312yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—2924no—
599C22×C4—2924no—
600C22×C4—2924no—
601C22×C4—731no—
602C22×C4—731no—
603C22×C4—731no—
604C22×C4—731no—
605C22×C4—1464no—
606C22×C4—1464no—
607C22×C4—1461no—
608C22×C4—1461no—
609C22×C4—1464no—
610C22×C4—1461no—
611C22×C4D4×D7311yescharacteristic
612C22×C4D4×D7311yescharacteristic
613C22×C4C23×D7311yescharacteristic
614SD16—1468no—
615SD16—1468no—
616SD16—1468no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—732no—
620C2×C8—732no—
621C2×C8—1462no—
622C2×C8—1462no—
623C2×C8C23×D7312yes—
624C2×C8C23×D7312yes—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—734no—
630C4⋊C4—734no—
631C4⋊C4—734no—
632C4⋊C4—732no—
633C4⋊C4—732no—
634C4⋊C4—1464no—
635C4⋊C4—1464no—
636C4⋊C4—1464no—
637C4⋊C4—1464no—
638C4⋊C4—1464no—
639C4⋊C4—1464no—
640C4⋊C4—1461no—
641C4⋊C4—1461no—
642C4⋊C4C23×D7312yes—
643C4⋊C4C23×D7312yes—
644C22⋊C4—1464no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C42—732no—
648C42—732no—
649C42—732no—
650C42—732no—
651C42—1464no—
652C42—1464no—
653C42—1464no—
654C42D4×D7312yes—
655C42C23×D7312yes—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—2922no—
665C23—2922no—
666C23—2922no—
667C23—1462no—
668C23C2×D4×D7311yescharacteristic
669Q8—2928no—
670Q8—734no—
671Q8—1468no—
672Q8—1462no—
673Q8—1464no—
674D4—22no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—48no—
679D4—42no—
680D4—42no—
681D4—84no—
682D4—2928no—
683D4—2928no—
684D4—2922no—
685D4—5844no—
686D4—5844no—
687D4—1462no—
688D4—1462no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—2928no—
696C2×C4—2922no—
697C2×C4—2922no—
698C2×C4—2928no—
699C2×C4—2928no—
700C2×C4—732no—
701C2×C4—734no—
702C2×C4—732no—
703C2×C4—732no—
704C2×C4—732no—
705C2×C4—1462no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4—1462no—
710C2×C4—1464no—
711C2×C4—1462no—
712C2×C4C2×D4×D7312yes—
713C2×C4C2×D4×D7312yes—
714C2×C4C2×D4×D7311yescharacteristic
715C2×C4#41×D7312yes—
716C2×C4#1455663812yes—
717C2×C4C24×D7311yescharacteristic
718C8—22no—
719C8—22no—
720C8—1462no—
721C8—1462no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—2922no—
731C22—2922no—
732C22—2922no—
733C22—5844no—
734C22#1798924512yes—
735C22AGL(1,ℤ/8)×D7312yes—
736C22#1798939712yes—
737C22C22×D4×D7311yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—2922no—
743C4—2922no—
744C4—734no—
745C4—1462no—
746C4—1464no—
747C4—1462no—
748C4—1462no—
749C4#1798924512yes—
750C4C2×#41×D7311yescharacteristic
751C4C2×#1455663811yescharacteristic
752C2—82no—
753C2—82no—
754C2—5842no—
755C2#2262265714yesdirect product factor
756C2C2×#1798924511yescharacteristic
757C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
758C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#490×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989257C2
hypercenterC2×#490D73
hypocenterC73C2×#3368
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#17989314C2semidirect
3. #22622657C2direct (N × H)
4. C2×#17988950C2semidirect
5. C2×#17988932C2semidirect
6. C2×#17988885C2semidirect
7. C2×#17988884C2semidirect
8. C2×#17988865C2semidirect
9. C2×#17988786C2semidirect
10. C2×#17988786C2semidirect
11. C2×#17988784C2semidirect
12. C2×#17988715C2semidirect
13. C2×#17988689C2semidirect
14. C2×#17988684C2semidirect
15. C2×#17988678C2semidirect
16. C2×#490×C73C2semidirect
22. #17989314C22semidirect
43. #17988950C22semidirect
44. #17988932C22semidirect
45. #17988885C22semidirect
46. #17988884C22semidirect
47. #17988865C22semidirect
48. #17988786C22semidirect
49. #17988786C22semidirect
50. #17988784C22semidirect
51. #17988715C22semidirect
52. #17988689C22semidirect
53. #17988684C22semidirect
54. #17988678C22semidirect
71. #490×C73C22semidirect
188. C2×Dic146#41semidirect
337. Dic146C2×#41semidirect
375. C2×C73#3368semidirect
384. C2×#490D73semidirect
396. C73C2×#3368semidirect
426. #490C2×D73semidirect
755. C2#22622657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893142
C2×#179892572
#226226572
C2×#179889502
C2×#179889322
C2×#179888852
C2×#179888842
C2×#179888652
C2×#179887862
C2×#179887842
C2×#179887152
C2×#179886892
C2×#179886842
C2×#179886782
C2×#490×C732
C2×#336873