Finite Group Databasebeta

← C2×#22622655 #33965678

Subgroups — C2×#22622655 #33965678

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×#17989313C211yesmaximal, characteristic, complemented
2C2×#17989257C211yesmaximal, characteristic
3#22622655C2116yesmaximal, direct product factor
4C2×#17988951C211yesmaximal, characteristic, complemented
5C2×#17988950C211yesmaximal, characteristic, complemented
6C2×#17988932C211yesmaximal, characteristic, complemented
7C2×#17988889C211yesmaximal, characteristic, complemented
8C2×#17988888C211yesmaximal, characteristic, complemented
9C2×#17988865C211yesmaximal, characteristic, complemented
10C2×#17988785C211yesmaximal, characteristic, complemented
11C2×#17988785C211yesmaximal, characteristic, complemented
12C2×#17988716C211yesmaximal, characteristic, complemented
13C2×#17988688C211yesmaximal, characteristic, complemented
14C2×#17988685C211yesmaximal, characteristic, complemented
15C2×SD16×Dic73C211yesmaximal, characteristic, complemented
16C2×#460×C73C211yesmaximal, characteristic, complemented
17C22×#11924027—21no—
18C22×#11924015C2211yescharacteristic
19#17989313—24no—
20#17989313C2218yescomplemented
21#17989257—24no—
22#17989257C2218yes—
23C2×#14556590—21no—
24C2×#14556590C2211yescharacteristic
25C2×#14556587C2211yescharacteristic
26C2×#14556587C2211yescharacteristic
27C2×#14556583—21no—
28C2×#14556583C2211yescharacteristic
29C2×#14556582—21no—
30C2×#14556582C2211yescharacteristic
31C2×#14556563—21no—
32C2×#14556563—21no—
33C2×#14556562—21no—
34C2×Q8×Dic73C2211yescharacteristic
35C2×Q8×Dic73C2211yescharacteristic
36C2×C4×Dic146—21no—
37C2×C4×Dic146C2211yescharacteristic
38C2×C4×D292C2211yescharacteristic
39C2×D4×Dic73C2211yescharacteristic
40C2×D4×Dic73C2211yescharacteristic
41#17988951C2218yescomplemented
42#17988950C2218yescomplemented
43#17988932C2218yescomplemented
44#17988889C2218yescomplemented
45#17988888C2218yescomplemented
46#17988865C2218yescomplemented
47#17988785C2218yescomplemented
48#17988785C2218yescomplemented
49#17988716C2218yescomplemented
50#17988688C2218yescomplemented
51#17988685C2218yescomplemented
52SD16×Dic73C2218yescomplemented
53C2×#14556525C2211yescharacteristic
54C2×#14556524C2211yescharacteristic
55C2×#14556523C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556515C2211yescharacteristic
59C2×#14556513C2211yescharacteristic
60C2×#14556513C2211yescharacteristic
61C2×#14556512C2211yescharacteristic
62C2×#14556512C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556502C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C22×SD16×C73C2211yescharacteristic
71C2×#127×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73#460×C73C2218yescomplemented
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×#11924027—28no—
78C2×#11924027—48no—
79C22×Dic146—21no—
80C22×Dic146D411yescharacteristic
81C22×D292C2311yescharacteristic
82C22×C22⋊D73—21no—
83C22×C22⋊D73—21no—
84C22×C22⋊D73—21no—
85C22×C22⋊D73—21no—
86C23×Dic73—21no—
87C23×Dic73—21no—
88C22×C4×D73—21no—
89C2×#11924015—24no—
90C2×#11924015C2314yes—
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93#14556590—28no—
94#14556590—22no—
95#14556590C2314yes—
96#14556587—22no—
97#14556587—22no—
98#14556587C2314yes—
99#14556587C2314yes—
100#14556583—28no—
101#14556583—22no—
102#14556583C2314yes—
103#14556582—28no—
104#14556582—22no—
105#14556582C2314yes—
106#14556563—28no—
107#14556563—28no—
108#14556562—28no—
109Q8×Dic73—22no—
110Q8×Dic73—22no—
111Q8×Dic73C2314yes—
112Q8×Dic73C2314yes—
113C4×Dic146—28no—
114C4×Dic146D414yes—
115C4×Dic146C2314yes—
116C4×D292—22no—
117C4×D292C2314yes—
118D4×Dic73—22no—
119D4×Dic73—22no—
120D4×Dic73C2314yes—
121D4×Dic73C2314yes—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73D411yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007D411yescharacteristic
134C2×#11924007D411yescharacteristic
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×#11924005—21no—
138C2×C4×Dic73—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73C2311yescharacteristic
141C2×C4×Dic73C2311yescharacteristic
142#14556525C2314yes—
143#14556524C2314yes—
144#14556523C2314yes—
145#14556520C2314yes—
146#14556520C2314yes—
147#14556515C2314yes—
148#14556513C2314yes—
149#14556513C2314yes—
150#14556512C2314yes—
151#14556512C2314yes—
152#14556512C2314yes—
153#14556512C2314yes—
154#14556511C2314yes—
155#14556502C2314yes—
156#14556501C2314yes—
157C8×Dic73C2314yes—
158C22×Q8×C73C2311yescharacteristic
159C22×D4×C73—21no—
160C22×D4×C73—21no—
161C22×D4×C73C2311yescharacteristic
162C22×D4×C73C2311yescharacteristic
163C2×SD16×C73—24no—
164C2×SD16×C73—24no—
165C2×SD16×C73C2314yes—
166C2×SD16×C73C2314yes—
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169#127×C73—22no—
170#127×C73C2314yes—
171C4×Q8×C73—22no—
172C4×Q8×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C42×C73—21no—
176C2×C42×C73C2311yescharacteristic
177C4⋊C8×C73C2314yes—
178#102×C73C2314yes—
179#102×C73C2314yes—
180C23×D73—21no—
181#11924027—432no—
182C2×Dic146—24no—
183C2×Dic146—24no—
184C2×Dic146—44no—
185C2×Dic146C2×D414yes—
186C2×D292—22no—
187C2×D292—22no—
188C2×D292—21no—
189C2×D292C2412yes—
190C2×C22⋊D73—24no—
191C2×C22⋊D73—24no—
192C2×C22⋊D73—24no—
193C2×C22⋊D73—24no—
194C2×C22⋊D73—44no—
195C2×C22⋊D73—44no—
196C2×C22⋊D73—82no—
197C2×C22⋊D73—82no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73—24no—
202C22×Dic73—24no—
203C22×Dic73—44no—
204C22×Dic73—44no—
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C22×Dic73C2×D411yescharacteristic
208C22×Dic73C2×D411yescharacteristic
209C2×C4×D73—24no—
210C2×C4×D73—44no—
211#11924015—28no—
212C2×#10596831—22no—
213C2×#10596831—22no—
214C2×#10596831C2412yes—
215C2×#10596831C2412yes—
216C4⋊Dic73—21no—
217C4⋊Dic73—21no—
218C4⋊Dic73—21no—
219C4⋊Dic73—24no—
220C4⋊Dic73—24no—
221C4⋊Dic73—24no—
222C4⋊Dic73C2×D414yes—
223C4⋊Dic73C2412yes—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007C2×D414yes—
231#11924007C2×D414yes—
232C22⋊Dic73—24no—
233C22⋊Dic73—24no—
234#11924005—24no—
235C4×Dic73—24no—
236C4×Dic73—24no—
237C4×Dic73C2×D412yes—
238C4×Dic73C2×D412yes—
239C4×Dic73C2412yes—
240C4×Dic73C2412yes—
241C24×C73—21no—
242C24×C73—21no—
243C2×Q8×C73—21no—
244C2×Q8×C73—22no—
245C2×Q8×C73#4114yescomplemented
246C2×Q8×C73C2412yes—
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
264SD16×C73—28no—
265SD16×C73—28no—
266C2×C8×C73—22no—
267C2×C8×C73—22no—
268C2×C8×C73C2412yes—
269C2×C8×C73C2412yes—
270C4⋊C4×C73—24no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73C2412yes—
273C42×C73—24no—
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—
289Q8×C73—24no—
290Q8×C73—22no—
291Q8×C73C2×#4114yescomplemented
292D4×C73—22no—
293D4×C73—22no—
294D4×C73—22no—
295D4×C73—22no—
296D4×C73—48no—
297D4×C73—42no—
298D4×C73—42no—
299D4×C73—84no—
300C2×C4×C73—24no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—42no—
306C2×C4×C73C22×D412yes—
307C2×C4×C73C22×D412yes—
308C2×C4×C73C22×D411yescharacteristic
309C2×C4×C73C2×#4112yes—
310C2×C4×C732−1+412yes—
311C2×C4×C73C2511yescharacteristic
312C22⋊D73—48no—
313C22⋊D73—48no—
314C22⋊D73—84no—
315C22⋊D73—84no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—48no—
323C2×Dic73—42no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326C2×Dic73—48no—
327C2×Dic73AGL(1,ℤ/8)14yes—
328C2×Dic73C22×D412yes—
329C2×Dic73C22×D412yes—
330C2×Dic73C22×D412yes—
331C2×Dic73C22×D412yes—
332D292—22no—
333D292—22no—
334D292—42no—
335C4×D73—48no—
336Dic146—28no—
337Dic146—48no—
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—24no—
359C4×C73—22no—
360C4×C73—22no—
361C4×C73—42no—
362C4×C73#54812yes—
363C4×C73C22×#4111yescharacteristic
364C4×C73C2×2−1+411yescharacteristic
365Dic73—22no—
366Dic73—22no—
367Dic73—22no—
368Dic73—42no—
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×#490—731no—
385C2×#486—731no—
386C2×#478—731no—
387C2×#478—731no—
388C2×#474—731no—
389C2×#460—731no—
390C2×#460—731no—
391C2×#460D7311yescharacteristic, complemented
392C2×#446—731no—
393C2×#440—731no—
394C2×#440—731no—
395C2×C4×SD16—731no—
396C73C2×#336811yescharacteristic, complemented, Sylow
397C22×#41—1461no—
398C22×SD16—731no—
399C22×SD16C2×D7311yescharacteristic
400C22×SD16C2×D7311yescharacteristic
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—731no—
412C2×#125—1461no—
413C2×#125—1461no—
414C2×#121—1461no—
415C2×#121—1461no—
416C2×#121—1461no—
417C2×C4×Q8—731no—
418C2×C4×Q8—731no—
419C2×C4×Q8—731no—
420C2×C4×Q8—1461no—
421C2×C4×Q8C2×D7311yescharacteristic
422C2×C4×D4—731no—
423C2×C4×D4—731no—
424C2×C4×D4—731no—
425#490—738no—
426#490—738no—
427#486—738no—
428#478—738no—
429#478—738no—
430#474—738no—
431#460—738no—
432#460—738no—
433#460C2×D7318yescomplemented
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⋊C8C2×D7311yescharacteristic
444C2×#103—731no—
445C2×#102—731no—
446C2×#102—731no—
447C2×#102—731no—
448C2×#102—731no—
449C2×#102—731no—
450C2×#102—731no—
451C2×#102—731no—
452C2×#102C2×D7311yescharacteristic
453C2×#102C2×D7311yescharacteristic
454C2×#97—731no—
455C2×#97—731no—
456C2×C4×C8—731no—
457C2×#41—2928no—
458C2×#41—1468no—
459C22×Q8—731no—
460C22×Q8—1461no—
461C22×Q8C22×D7311yescharacteristic
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—24no—
475C2×SD16—24no—
476C2×SD16—734no—
477C2×SD16—1464no—
478C2×SD16C22×D7314yes—
479C2×SD16C22×D7314yes—
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—734no—
494#125—734no—
495#125—1468no—
496#125—1462no—
497#125—1468no—
498#125—1462no—
499#121—1468no—
500#121—1468no—
501#121—1468no—
502C4×Q8—22no—
503C4×Q8—734no—
504C4×Q8—734no—
505C4×Q8—734no—
506C4×Q8—734no—
507C4×Q8—1468no—
508C4×Q8—1462no—
509C4×Q8—1462no—
510C4×Q8C22×D7314yes—
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—731no—
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⋊C4—1461no—
531C2×C4⋊C4C22×D7311yescharacteristic
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C42—21no—
536C2×C42—731no—
537C2×C42—731no—
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⋊C8C22×D7314yes—
547#103—734no—
548#102—734no—
549#102—734no—
550#102—734no—
551#102—734no—
552#102—734no—
553#102—734no—
554#102—734no—
555#102C22×D7314yes—
556#102C22×D7314yes—
557#97—734no—
558#97—734no—
559C4×C8—734no—
560C24—21no—
561C24—21no—
562C24—1461no—
563#41—29232no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—2924no—
567C2×Q8—734no—
568C2×Q8—1464no—
569C2×Q8—1464no—
570C2×Q8#1192402714yescomplemented
571C2×Q8C23×D7312yes—
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—1461no—
610C22×C4—1464no—
611C22×C4D4×D7311yescharacteristic
612C22×C4D4×D7311yescharacteristic
613C22×C4C23×D7311yescharacteristic
614SD16—28no—
615SD16—28no—
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—21no—
627C4⋊C4—734no—
628C4⋊C4—734no—
629C4⋊C4—734no—
630C4⋊C4—732no—
631C4⋊C4—732no—
632C4⋊C4—732no—
633C4⋊C4—1464no—
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⋊C4—1461no—
643C4⋊C4C23×D7312yes—
644C22⋊C4—1464no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C42—24no—
648C42—732no—
649C42—732no—
650C42—732no—
651C42—732no—
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—22no—
670Q8—24no—
671Q8—2928no—
672Q8—1468no—
673Q8C2×#1192402714yescomplemented
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—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—2928no—
696C2×C4—2922no—
697C2×C4—2922no—
698C2×C4—2922no—
699C2×C4—2928no—
700C2×C4—2928no—
701C2×C4—732no—
702C2×C4—734no—
703C2×C4—732no—
704C2×C4—732no—
705C2×C4—732no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4—1462no—
710C2×C4—1462no—
711C2×C4—1462no—
712C2×C4C2×D4×D7312yes—
713C2×C4C2×D4×D7312yes—
714C2×C4C2×D4×D7311yescharacteristic
715C2×C4C2×#1192402712yes—
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#1798924312yes—
735C22AGL(1,ℤ/8)×D7312yes—
736C22#1798939312yes—
737C22C22×D4×D7311yescharacteristic
738C4—22no—
739C4—24no—
740C4—22no—
741C4—42no—
742C4—2922no—
743C4—2922no—
744C4—2922no—
745C4—734no—
746C4—1462no—
747C4—1462no—
748C4—1462no—
749C4#1798924312yes—
750C4C22×#1192402711yescharacteristic
751C4C2×#1455663811yescharacteristic
752C2—82no—
753C2—82no—
754C2—5842no—
755C2#2262265514yesdirect product factor
756C2C2×#1798924311yescharacteristic
757C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
758C2C2×#1798939311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#460×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989257C2
hypercenterC2×#460D73
hypocenterC73C2×#3368
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#17989313C2semidirect
3. #22622655C2direct (N × H)
4. C2×#17988951C2semidirect
5. C2×#17988950C2semidirect
6. C2×#17988932C2semidirect
7. C2×#17988889C2semidirect
8. C2×#17988888C2semidirect
9. C2×#17988865C2semidirect
10. C2×#17988785C2semidirect
11. C2×#17988785C2semidirect
12. C2×#17988716C2semidirect
13. C2×#17988688C2semidirect
14. C2×#17988685C2semidirect
15. C2×SD16×Dic73C2semidirect
16. C2×#460×C73C2semidirect
20. #17989313C22semidirect
41. #17988951C22semidirect
42. #17988950C22semidirect
43. #17988932C22semidirect
44. #17988889C22semidirect
45. #17988888C22semidirect
46. #17988865C22semidirect
47. #17988785C22semidirect
48. #17988785C22semidirect
49. #17988716C22semidirect
50. #17988688C22semidirect
51. #17988685C22semidirect
52. SD16×Dic73C22semidirect
73. #460×C73C22semidirect
245. C2×Q8×C73#41semidirect
291. Q8×C73C2×#41semidirect
375. C2×C73#3368semidirect
391. C2×#460D73semidirect
396. C73C2×#3368semidirect
433. #460C2×D73semidirect
570. C2×Q8#11924027semidirect
673. Q8C2×#11924027semidirect
755. C2#22622655direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893132
C2×#179892572
#226226552
C2×#179889512
C2×#179889502
C2×#179889322
C2×#179888892
C2×#179888882
C2×#179888652
C2×#179887852
C2×#179887162
C2×#179886882
C2×#179886852
C2×SD16×Dic732
C2×#460×C732
C2×#336873