Finite Group Databasebeta

← C2×#22622273 #33964391

Subgroups — C2×#22622273 #33964391

Order 18688.

2374 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989238C211yesmaximal, characteristic, complemented
2C2×#17989237C211yesmaximal, characteristic, complemented
3#22622273C2116yesmaximal, direct product factor
4C2×#17988991C211yesmaximal, characteristic, complemented
5C2×#17988902C211yesmaximal, characteristic, complemented
6C2×#17988901C211yesmaximal, characteristic, complemented
7C2×#17988899C211yesmaximal, characteristic, complemented
8C2×#17988866C211yesmaximal, characteristic, complemented
9C2×#17988865C211yesmaximal, characteristic, complemented
10C2×#17988822C211yesmaximal, characteristic, complemented
11C2×#17988821C211yesmaximal, characteristic, complemented
12C2×#17988667C211yesmaximal, characteristic, complemented
13C2×#17988650C211yesmaximal, characteristic, complemented
14C22×#14556524C211yesmaximal, characteristic, complemented
15C2×#107×D73C211yesmaximal, characteristic, complemented
16C2×#480×C73C211yesmaximal, characteristic, complemented
17C22×#11924028—21no—
18C22×#11924027—21no—
19C22×#11924013C2211yescharacteristic
20C23×#10596831C2211yescharacteristic
21C22×C8×D73C2211yescharacteristic
22#17989238—24no—
23#17989238C2218yescomplemented
24#17989237—24no—
25#17989237C2218yescomplemented
26C2×#14556590C2211yescharacteristic
27C2×#14556590C2211yescharacteristic
28C2×#14556576—21no—
29C2×#14556574—21no—
30C2×#14556573—21no—
31C2×#14556572—21no—
32C2×#14556569—21no—
33C2×#14556568—21no—
34C2×#14556566C2211yescharacteristic
35C2×#14556565C2211yescharacteristic
36C2×#14556562C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×#14556553C2211yescharacteristic
39C2×C4×C22⋊D73C2211yescharacteristic
40C22×C4⋊Dic73C2211yescharacteristic
41C2×C4⋊C4×D73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988991C2218yescomplemented
44#17988902C2218yescomplemented
45#17988901C2218yescomplemented
46#17988899C2218yescomplemented
47#17988866C2218yescomplemented
48#17988865C2218yescomplemented
49#17988822C2218yescomplemented
50#17988821C2218yescomplemented
51#17988667C2218yescomplemented
52#17988650C2218yescomplemented
53C2×#14556525C2211yescharacteristic
54C2×#14556525C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556524C2211yescharacteristic
59C2×#14556524C2211yescharacteristic
60C2×#14556524C2218yescomplemented
61#107×D73C2218yescomplemented
62C2×#14556520C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×#121×C73C2211yescharacteristic
70C22×C4⋊C4×C73C2211yescharacteristic
71#480×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#107×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C2×#11924028—28no—
78C2×#11924028—48no—
79C2×#11924027—28no—
80C2×#11924027—48no—
81C22×Dic146—21no—
82C22×Dic146—21no—
83C22×D292—21no—
84C22×D292C2311yescharacteristic
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C22⋊D73D411yescharacteristic
88C23×Dic73—21no—
89C23×Dic73—21no—
90C22×C4×D73—21no—
91C22×C4×D73—21no—
92C22×C4×D73—21no—
93C22×C4×D73C2311yescharacteristic
94C2×#11924013—24no—
95C2×#11924013C2314yes—
96C22×#10596831—24no—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2314yes—
99C22×#10596831C2311yescharacteristic
100C2×C8×D73—24no—
101C2×C8×D73C2314yes—
102#14556590—22no—
103#14556590—22no—
104#14556590C2314yes—
105#14556590C2314yes—
106#14556576—28no—
107#14556574—28no—
108#14556573—28no—
109#14556572—28no—
110#14556569—28no—
111#14556568—28no—
112#14556566—22no—
113#14556566C2314yes—
114#14556565—22no—
115#14556565C2314yes—
116#14556562—22no—
117#14556562C2314yes—
118D4×Dic73—22no—
119D4×Dic73C2314yes—
120#14556553—22no—
121#14556553C2314yes—
122C4×C22⋊D73D414yes—
123C4×C22⋊D73C2314yes—
124C2×C4⋊Dic73—22no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2314yes—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007D411yescharacteristic
135C4⋊C4×D73—22no—
136C4⋊C4×D73—22no—
137C4⋊C4×D73C2314yes—
138C4⋊C4×D73C2314yes—
139C2×C22⋊Dic73—21no—
140C2×C22⋊Dic73—21no—
141C2×C22⋊Dic73D411yescharacteristic
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005D411yescharacteristic
146C2×C4×Dic73C2311yescharacteristic
147#14556525C2314yes—
148#14556525C2314yes—
149#14556524C2314yes—
150#14556524C2314yes—
151#14556524C2314yes—
152#14556524C2314yes—
153#14556524C2314yes—
154#14556520C2314yes—
155#14556513C2314yes—
156#14556513C2314yes—
157#14556512C2314yes—
158#14556511C2314yes—
159#14556503C2314yes—
160C8×Dic73C2314yes—
161C22×D4×C73—21no—
162C22×D4×C73C2311yescharacteristic
163C23×C4×C73—21no—
164C23×C4×C73C2311yescharacteristic
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167#121×C73—22no—
168#121×C73C2314yes—
169C2×C4⋊C4×C73—22no—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2314yes—
175C2×C22⋊C4×C73—21no—
176#107×C73C2314yes—
177#107×C73C2314yes—
178#102×C73C2314yes—
179#102×C73C2314yes—
180C22⋊C8×C73C2314yes—
181C23×D73—21no—
182C23×D73C2×D411yescharacteristic
183#11924028—432no—
184#11924027—432no—
185C2×Dic146—24no—
186C2×Dic146—24no—
187C2×Dic146—44no—
188C2×Dic146—44no—
189C2×D292—22no—
190C2×D292—22no—
191C2×D292—24no—
192C2×D292—21no—
193C2×D292—44no—
194C2×D292C2412yes—
195C2×C22⋊D73—24no—
196C2×C22⋊D73—24no—
197C2×C22⋊D73—44no—
198C2×C22⋊D73—44no—
199C2×C22⋊D73D818yescomplemented
200C2×C22⋊D73C2×D414yes—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—24no—
205C22×Dic73—24no—
206C22×Dic73—44no—
207C22×Dic73—44no—
208C22×Dic73C2×D411yescharacteristic
209C22×Dic73C2×D411yescharacteristic
210C22×Dic73C2×D411yescharacteristic
211C2×C4×D73—22no—
212C2×C4×D73—22no—
213C2×C4×D73—24no—
214C2×C4×D73—24no—
215C2×C4×D73—24no—
216C2×C4×D73—44no—
217C2×C4×D73—44no—
218C2×C4×D73—44no—
219C2×C4×D73C2×D412yes—
220C2×C4×D73C2412yes—
221#11924013—28no—
222C2×#10596831—22no—
223C2×#10596831—28no—
224C2×#10596831#4114yescomplemented
225C2×#10596831C2412yes—
226C2×#10596831C2412yes—
227C8×D73—28no—
228C4⋊Dic73—21no—
229C4⋊Dic73—21no—
230C4⋊Dic73—21no—
231C4⋊Dic73—24no—
232C4⋊Dic73C2412yes—
233C4⋊Dic73C2412yes—
234C4⋊Dic73C2412yes—
235#11924007—24no—
236#11924007—24no—
237#11924007—24no—
238#11924007—24no—
239#11924007C2×D414yes—
240C22⋊Dic73—24no—
241C22⋊Dic73—24no—
242C22⋊Dic73C2×D414yes—
243#11924005—24no—
244#11924005—24no—
245#11924005—24no—
246#11924005C2×D414yes—
247C4×Dic73C2×D412yes—
248C4×Dic73C2412yes—
249C24×C73—21no—
250C24×C73C2×D411yescharacteristic
251C2×D4×C73—24no—
252C2×D4×C73—21no—
253C2×D4×C73—22no—
254C2×D4×C73—22no—
255C2×D4×C73—44no—
256C2×D4×C73C2412yes—
257C22×C4×C73—22no—
258C22×C4×C73—22no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—24no—
263C22×C4×C73—44no—
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2×D412yes—
266C22×C4×C73C2412yes—
267C22×C4×C73C2411yescharacteristic
268C2×C8×C73—22no—
269C2×C8×C73—22no—
270C2×C8×C73C2412yes—
271C2×C8×C73C2412yes—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73—24no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73C2412yes—
277C4⋊C4×C73C2412yes—
278C4⋊C4×C73C2412yes—
279C22⋊C4×C73—24no—
280C23×C73—22no—
281C23×C73—22no—
282C23×C73—22no—
283C23×C73—42no—
284C23×C73—42no—
285C23×C73—42no—
286C23×C73C2×D814yes—
287C23×C73C22×D412yes—
288C23×C73C22×D411yescharacteristic
289C22×D73—22no—
290C22×D73—22no—
291C22×D73—22no—
292C22×D73—42no—
293C22×D73—42no—
294C22×D73—42no—
295C22×D73C2×D814yes—
296C22×D73C22×D412yes—
297D4×C73—22no—
298D4×C73—22no—
299D4×C73—48no—
300D4×C73—42no—
301C2×C4×C73—22no—
302C2×C4×C73—24no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—42no—
309C2×C4×C73—42no—
310C2×C4×C73—48no—
311C2×C4×C73—42no—
312C2×C4×C73C22×D412yes—
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C2×#4112yes—
315C2×C4×C732−1+412yes—
316C2×C4×C73C2511yescharacteristic
317C22⋊D73—48no—
318C22⋊D73—48no—
319C22⋊D73C2×D8116yescomplemented
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—48no—
329C2×Dic73—48no—
330C2×Dic73C2×D814yes—
331C2×Dic73C22×D412yes—
332C2×Dic73C22×D412yes—
333C2×Dic73C22×D412yes—
334D292—22no—
335D292—22no—
336D292—48no—
337D292—42no—
338C4×D73—24no—
339C4×D73—22no—
340C4×D73—22no—
341C4×D73—48no—
342C4×D73—48no—
343C4×D73—48no—
344Dic146—48no—
345Dic146—48no—
346C8×C73—22no—
347C8×C73—22no—
348#10596831—22no—
349#10596831C2×#4114yescomplemented
350C22×C73—28no—
351C22×C73—22no—
352C22×C73—22no—
353C22×C73—42no—
354C22×C73—42no—
355C22×C73—42no—
356C22×C73—84no—
357C22×C73#54712yes—
358C22×C73C22×D814yes—
359C22×C73C22×D812yes—
360C22×C73#57812yes—
361C22×C73C23×D411yescharacteristic
362C2×D73—28no—
363C2×D73—22no—
364C2×D73—22no—
365C2×D73—42no—
366C2×D73—42no—
367C2×D73—42no—
368C2×D73—84no—
369C2×D73C22×D814yes—
370C4×C73—22no—
371C4×C73—42no—
372C4×C73—42no—
373C4×C73—42no—
374C4×C73#54712yes—
375C4×C73C22×#4111yescharacteristic
376C4×C73C2×2−1+411yescharacteristic
377Dic73—22no—
378Dic73—22no—
379Dic73—42no—
380Dic73—42no—
381Dic73—42no—
382Dic73C22×D814yes—
383C2×#3334—731nomaximal, Sylow
384C2×C73—24no—
385C2×C73—82no—
386C2×C73#333414yescomplemented
387C2×C73C2×#54711yescharacteristic
388C2×C73C23×D811yescharacteristic
389C2×C73C2×#57811yescharacteristic
390D73—24no—
391D73—82no—
392C2×#547—731no—
393C2×#547—731no—
394#3334—7316no—
395C2×#500—731no—
396C2×#480—731no—
397C2×#480—731no—
398C2×#480—731no—
399C2×#480D7311yescharacteristic, complemented
400C2×#474—731no—
401C2×#474—731no—
402C2×#466—731no—
403C2×#466—731no—
404C2×C4×D8—731no—
405C2×C8×D4—731no—
406C22×#107—731no—
407C22×#107—731no—
408C73C2×#333411yescharacteristic, complemented, Sylow
409C22×#41—1461no—
410C22×#41—1461no—
411C22×D8—731no—
412C23×C8—731no—
413C23×C8—731no—
414#547—738no—
415#547—738no—
416#547—1464no—
417#547—1464no—
418C2×C4⋊Q8—731no—
419C2×C4⋊Q8—731no—
420C2×#123—1461no—
421C2×#123—1461no—
422C2×#123—1461no—
423C2×#123—1461no—
424C2×C22⋊Q8—1461no—
425C2×C22⋊Q8—1461no—
426C2×#121—731no—
427C2×#121—731no—
428C2×#121—731no—
429C2×#121C2×D7311yescharacteristic
430C2×C4×D4—731no—
431C2×C4×D4—731no—
432C2×C4×D4—731no—
433C22×C4⋊C4—731no—
434C22×C4⋊C4—731no—
435C22×C4⋊C4—731no—
436C22×C4⋊C4C2×D7311yescharacteristic
437#500—738no—
438#480—738no—
439#480—738no—
440#480—738no—
441#480C2×D7318yescomplemented
442#474—738no—
443#474—738no—
444#466—738no—
445#466—738no—
446C4×D8—738no—
447C8×D4—738no—
448C2×#107—731no—
449C2×#107—731no—
450C2×#107—738no—
451C2×#107—731no—
452C2×#107—731no—
453C2×#107—731no—
454C2×#107—731no—
455C2×#107—731no—
456C2×#107—738no—
457C2×#107C2×D7311yescharacteristic
458C2×#107C2×D7311yescharacteristic
459C2×C4⋊C8—731no—
460C2×#102—731no—
461C2×#102—731no—
462C2×#102—731no—
463C2×#102—731no—
464C2×#102C2×D7311yescharacteristic
465C2×#102C2×D7311yescharacteristic
466C2×C22⋊C8—731no—
467C2×C22⋊C8C2×D7311yescharacteristic
468C2×C4×C8—731no—
469C2×#41—2928no—
470C2×#41—2928no—
471C2×#41—1468no—
472C2×#41—1468no—
473C22×Q8—1461no—
474C22×Q8—1461no—
475C22×D4—21no—
476C22×D4—731no—
477C22×D4—731no—
478C22×D4—1461no—
479C22×D4—1461no—
480C22×D4—1461no—
481C22×D4C22×D7311yescharacteristic
482C23×C4—21no—
483C23×C4—731no—
484C23×C4—1461no—
485C23×C4—1461no—
486C23×C4—1461no—
487C23×C4—1461no—
488C23×C4—1461no—
489C23×C4C22×D7311yescharacteristic
490C2×D8—734no—
491C2×D8—1464no—
492C22×C8—731no—
493C22×C8—731no—
494C22×C8—734no—
495C22×C8—734no—
496C22×C8—1464no—
497C22×C8—1464no—
498C22×C8C22×D7311yescharacteristic
499C22×C8C22×D7311yescharacteristic
500C4⋊Q8—734no—
501C4⋊Q8—734no—
502C4⋊Q8—1462no—
503C4⋊Q8—1462no—
504#123—1468no—
505#123—1468no—
506#123—1468no—
507#123—1468no—
508C22⋊Q8—1468no—
509C22⋊Q8—1468no—
510#121—22no—
511#121—734no—
512#121—734no—
513#121—734no—
514#121—1462no—
515#121—1462no—
516#121—1462no—
517#121C22×D7314yes—
518C4×D4—734no—
519C4×D4—734no—
520C4×D4—734no—
521C4×D4—734no—
522C4×D4—1462no—
523C4×D4—1462no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—731no—
527C2×C4⋊C4—731no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C4⋊C4—734no—
531C2×C4⋊C4—734no—
532C2×C4⋊C4—734no—
533C2×C4⋊C4—1462no—
534C2×C4⋊C4—1462no—
535C2×C4⋊C4—1461no—
536C2×C4⋊C4—1461no—
537C2×C4⋊C4—1461no—
538C2×C4⋊C4—1461no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4—1462no—
541C2×C4⋊C4C22×D7311yescharacteristic
542C2×C4⋊C4C22×D7311yescharacteristic
543C2×C4⋊C4C22×D7311yescharacteristic
544C2×C4⋊C4C22×D7314yes—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—731no—
547C2×C22⋊C4—731no—
548C2×C22⋊C4—1461no—
549C2×C22⋊C4—1461no—
550C2×C22⋊C4—1461no—
551C2×C22⋊C4—1461no—
552C2×C22⋊C4—1461no—
553C2×C42—731no—
554#107—734no—
555#107—734no—
556#107—734no—
557#107—734no—
558#107—734no—
559#107—734no—
560#107—734no—
561#107C22×D7314yes—
562#107C22×D7314yes—
563C4⋊C8—734no—
564#102—734no—
565#102—734no—
566#102—734no—
567#102—734no—
568#102C22×D7314yes—
569#102C22×D7314yes—
570C22⋊C8—734no—
571C22⋊C8C22×D7314yes—
572C4×C8—734no—
573C24—21no—
574C24—731no—
575C24—1461no—
576C24D4×D7311yescharacteristic
577#41—29232no—
578#41—29232no—
579C2×Q8—2924no—
580C2×Q8—2924no—
581C2×Q8—1464no—
582C2×Q8—1464no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—44no—
588C2×D4—2924no—
589C2×D4—2924no—
590C2×D4—2924no—
591C2×D4—738no—
592C2×D4—734no—
593C2×D4—732no—
594C2×D4—1464no—
595C2×D4—1464no—
596C2×D4—1464no—
597C2×D4—1461no—
598C2×D4—1462no—
599C2×D4—1462no—
600C2×D4C23×D7312yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—44no—
608C22×C4—2924no—
609C22×C4—2924no—
610C22×C4—2924no—
611C22×C4—2924no—
612C22×C4—2924no—
613C22×C4—731no—
614C22×C4—731no—
615C22×C4—731no—
616C22×C4—732no—
617C22×C4—732no—
618C22×C4—1464no—
619C22×C4—1464no—
620C22×C4—1464no—
621C22×C4—1464no—
622C22×C4—1464no—
623C22×C4—1461no—
624C22×C4—1461no—
625C22×C4—1461no—
626C22×C4—1462no—
627C22×C4—1462no—
628C22×C4D4×D7312yes—
629C22×C4D4×D7311yescharacteristic
630C22×C4C23×D7312yes—
631C22×C4C23×D7311yescharacteristic
632D8—1468no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—734no—
636C2×C8—732no—
637C2×C8—732no—
638C2×C8—1468no—
639C2×C8—1468no—
640C2×C8—1462no—
641C2×C8C23×D7312yes—
642C2×C8C23×D7312yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—734no—
648C4⋊C4—732no—
649C4⋊C4—732no—
650C4⋊C4—732no—
651C4⋊C4—1464no—
652C4⋊C4—1464no—
653C4⋊C4—1464no—
654C4⋊C4—1464no—
655C4⋊C4—1461no—
656C4⋊C4—1461no—
657C4⋊C4—1461no—
658C4⋊C4—1464no—
659C4⋊C4C23×D7312yes—
660C4⋊C4C23×D7312yes—
661C4⋊C4C23×D7312yes—
662C22⋊C4—24no—
663C22⋊C4—734no—
664C22⋊C4—734no—
665C22⋊C4—1464no—
666C22⋊C4—1464no—
667C22⋊C4—1464no—
668C22⋊C4—1464no—
669C22⋊C4—1464no—
670C42—732no—
671C42—732no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—2922no—
679C23—2922no—
680C23—2922no—
681C23—732no—
682C23—734no—
683C23—1462no—
684C23—1462no—
685C23—1462no—
686C23D8×D7314yes—
687C23C2×D4×D7312yes—
688C23C2×D4×D7311yescharacteristic
689Q8—2928no—
690Q8—2928no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—42no—
695D4—2928no—
696D4—2928no—
697D4—2928no—
698D4—2922no—
699D4—7316no—
700D4—1462no—
701D4—1462no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—2928no—
714C2×C4—2928no—
715C2×C4—2928no—
716C2×C4—2922no—
717C2×C4—2922no—
718C2×C4—2922no—
719C2×C4—2928no—
720C2×C4—2928no—
721C2×C4—732no—
722C2×C4—734no—
723C2×C4—732no—
724C2×C4—732no—
725C2×C4—1462no—
726C2×C4—1462no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1464no—
733C2×C4C2×D4×D7312yes—
734C2×C4C2×D4×D7311yescharacteristic
735C2×C4#41×D7312yes—
736C2×C4#1455663812yes—
737C2×C4C24×D7311yescharacteristic
738C8—22no—
739C8—22no—
740C8—734no—
741C8—1462no—
742C22—28no—
743C22—22no—
744C22—22no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—2922no—
750C22—2922no—
751C22—2922no—
752C22—5844no—
753C22—734no—
754C22—1468no—
755C22—1462no—
756C22—1462no—
757C22#1798923512yes—
758C22C2×D8×D7314yes—
759C22C2×D8×D7312yes—
760C22#1798940312yes—
761C22C22×D4×D7311yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—2922no—
767C4—2922no—
768C4—2922no—
769C4—734no—
770C4—1462no—
771C4—1462no—
772C4#1798923512yes—
773C4C2×#41×D7311yescharacteristic
774C4C2×#1455663811yescharacteristic
775C2—24no—
776C2—82no—
777C2—5842no—
778C2—1464no—
779C2#2262227314yesdirect product factor
780C2C2×#1798923511yescharacteristic
781C2C22×D8×D7311yescharacteristic
782C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#480×C73C2
socleC23×C73C22×D4
hypercenterC2×#480D73
hypocenterC73C2×#3334
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#17989238C2semidirect
2. C2×#17989237C2semidirect
3. #22622273C2direct (N × H)
4. C2×#17988991C2semidirect
5. C2×#17988902C2semidirect
6. C2×#17988901C2semidirect
7. C2×#17988899C2semidirect
8. C2×#17988866C2semidirect
9. C2×#17988865C2semidirect
10. C2×#17988822C2semidirect
11. C2×#17988821C2semidirect
12. C2×#17988667C2semidirect
13. C2×#17988650C2semidirect
14. C22×#14556524C2semidirect
15. C2×#107×D73C2semidirect
16. C2×#480×C73C2semidirect
23. #17989238C22semidirect
25. #17989237C22semidirect
43. #17988991C22semidirect
44. #17988902C22semidirect
45. #17988901C22semidirect
46. #17988899C22semidirect
47. #17988866C22semidirect
48. #17988865C22semidirect
49. #17988822C22semidirect
50. #17988821C22semidirect
51. #17988667C22semidirect
52. #17988650C22semidirect
60. C2×#14556524C22semidirect
61. #107×D73C22semidirect
71. #480×C73C22semidirect
199. C2×C22⋊D73D8semidirect
224. C2×#10596831#41semidirect
319. C22⋊D73C2×D8semidirect
349. #10596831C2×#41semidirect
386. C2×C73#3334semidirect
399. C2×#480D73semidirect
408. C73C2×#3334semidirect
441. #480C2×D73semidirect
779. C2#22622273direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892382
C2×#179892372
#226222732
C2×#179889912
C2×#179889022
C2×#179889012
C2×#179888992
C2×#179888662
C2×#179888652
C2×#179888222
C2×#179888212
C2×#179886672
C2×#179886502
C22×#145565242
C2×#107×D732
C2×#480×C732
C2×#333473