Finite Group Databasebeta

← C2×#22622680 #33965729

Subgroups — C2×#22622680 #33965729

Order 18688.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989320C211yesmaximal, characteristic, complemented
2C2×#17989296C211yesmaximal, characteristic, complemented
3#22622680C2116yesmaximal, direct product factor
4C2×#17988950C211yesmaximal, characteristic, complemented
5C2×#17988945C211yesmaximal, characteristic, complemented
6C2×#17988942C211yesmaximal, characteristic, complemented
7C2×#17988893C211yesmaximal, characteristic, complemented
8C2×#17988887C211yesmaximal, characteristic, complemented
9C2×#17988866C211yesmaximal, characteristic, complemented
10C2×#17988802C211yesmaximal, characteristic, complemented
11C2×#17988800C211yesmaximal, characteristic, complemented
12C2×#17988780C211yesmaximal, characteristic
13C2×#17988717C211yesmaximal, characteristic, complemented
14C2×#17988696C211yesmaximal, characteristic, complemented
15C2×#17988684C211yesmaximal, characteristic, complemented
16C2×C4×D8×C73C211yesmaximal, characteristic, complemented
17C22×#11924016C2211yescharacteristic
18C22×#11924013C2211yescharacteristic
19#17989320—24no—
20#17989320C2218yescomplemented
21#17989296—24no—
22#17989296C2218yescomplemented
23C2×#14556590C2211yescharacteristic
24C2×#14556587C2211yescharacteristic
25C2×#14556583C2211yescharacteristic
26C2×#14556582C2211yescharacteristic
27C2×#14556579C2211yescharacteristic
28C2×#14556578C2211yescharacteristic
29C2×#14556577—21no—
30C2×#14556574—21no—
31C2×#14556573—21no—
32C2×#14556570—21no—
33C2×#14556568—21no—
34C2×#14556568—21no—
35C2×C4×Dic146C2211yescharacteristic
36C2×#14556556C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×D4×Dic73C2211yescharacteristic
39C2×#14556553C2211yescharacteristic
40C2×C4×C22⋊D73—21no—
41C22×#11924007—21no—
42#17988950C2218yescomplemented
43#17988945C2218yescomplemented
44#17988942C2218yescomplemented
45#17988893C2218yescomplemented
46#17988887C2218yescomplemented
47#17988866C2218yescomplemented
48#17988802C2218yescomplemented
49#17988800C2218yescomplemented
50#17988780C2218yes—
51#17988717C2218yescomplemented
52#17988696C2218yescomplemented
53#17988684C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×C4⋊#10596831C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C22×D8×C73C2211yescharacteristic
70C2×C4×D4×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72C4×D8×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146D411yescharacteristic
79C22×Dic146C2311yescharacteristic
80C22×D292C2311yescharacteristic
81C22×C22⋊D73—21no—
82C22×C22⋊D73—21no—
83C23×Dic73—21no—
84C23×Dic73—21no—
85C22×C4×D73—21no—
86C2×#11924016—24no—
87C2×#11924016C2314yes—
88C2×#11924013—24no—
89C2×#11924013C2314yes—
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2311yescharacteristic
92#14556590—22no—
93#14556590C2314yes—
94#14556587—22no—
95#14556587C2314yes—
96#14556583—22no—
97#14556583C2314yes—
98#14556582—22no—
99#14556582C2314yes—
100#14556579—22no—
101#14556579C2314yes—
102#14556578—22no—
103#14556578C2314yes—
104#14556577—28no—
105#14556574—28no—
106#14556573—28no—
107#14556570—28no—
108#14556568—28no—
109#14556568—28no—
110C4×Dic146D414yes—
111C4×Dic146C2314yes—
112#14556556—22no—
113#14556556C2314yes—
114D4×Dic73—22no—
115D4×Dic73—22no—
116D4×Dic73C2314yes—
117D4×Dic73C2314yes—
118#14556553—22no—
119#14556553C2314yes—
120C4×C22⋊D73—28no—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73D411yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—28no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007D411yescharacteristic
132C2×#11924007D411yescharacteristic
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73C2311yescharacteristic
142C2×C4×Dic73C2311yescharacteristic
143#14556524C2314yes—
144#14556522C2314yes—
145C4⋊#10596831C2314yes—
146#14556520C2314yes—
147#14556520C2314yes—
148#14556516C2314yes—
149#14556516C2314yes—
150#14556514C2314yes—
151#14556513C2314yes—
152#14556513C2314yes—
153#14556512C2314yes—
154#14556512C2314yes—
155#14556511C2314yes—
156#14556501C2314yes—
157#14556501C2314yes—
158C22×D4×C73C2311yescharacteristic
159C22×D4×C73C2311yescharacteristic
160C23×C4×C73—21no—
161C23×C4×C73—21no—
162C2×D8×C73—24no—
163C2×D8×C73C2314yes—
164C22×C8×C73C2311yescharacteristic
165C22×C8×C73C2311yescharacteristic
166C4×D4×C73—22no—
167C4×D4×C73—22no—
168C4×D4×C73C2314yes—
169C4×D4×C73C2314yes—
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C22⋊C4×C73—21no—
173C2×C22⋊C4×C73—21no—
174C2×C42×C73C2311yescharacteristic
175#107×C73C2314yes—
176#102×C73C2314yes—
177#102×C73C2314yes—
178C4×C8×C73C2314yes—
179C23×D73—21no—
180C2×Dic146—22no—
181C2×Dic146—22no—
182C2×Dic146—21no—
183C2×Dic146—24no—
184C2×Dic146—42no—
185C2×Dic146—82no—
186C2×Dic146C2×D414yes—
187C2×Dic146C2412yes—
188C2×D292—22no—
189C2×D292—22no—
190C2×D292—21no—
191C2×D292C2412yes—
192C2×C22⋊D73—24no—
193C2×C22⋊D73—24no—
194C2×C22⋊D73—44no—
195C2×C22⋊D73—82no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—24no—
200C22×Dic73—24no—
201C22×Dic73—44no—
202C22×Dic73—82no—
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C2×C4×D73—24no—
208C2×C4×D73—82no—
209#11924016—28no—
210#11924013—28no—
211C2×#10596831—22no—
212C2×#10596831—22no—
213C2×#10596831C2412yes—
214C2×#10596831C2412yes—
215C4⋊Dic73—21no—
216C4⋊Dic73—21no—
217C4⋊Dic73—24no—
218C4⋊Dic73C2×D414yes—
219C4⋊Dic73C2412yes—
220C4⋊Dic73C2412yes—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007C2×D414yes—
227#11924007C2×D414yes—
228C22⋊Dic73—24no—
229C22⋊Dic73—24no—
230C22⋊Dic73—24no—
231C22⋊Dic73—24no—
232#11924005—24no—
233#11924005—24no—
234#11924005—24no—
235C4×Dic73—24no—
236C4×Dic73C2×D412yes—
237C4×Dic73C2×D412yes—
238C4×Dic73C2412yes—
239C4×Dic73C2412yes—
240C24×C73—21no—
241C24×C73—21no—
242C2×D4×C73—21no—
243C2×D4×C73—21no—
244C2×D4×C73—22no—
245C2×D4×C73—22no—
246C2×D4×C73—22no—
247C2×D4×C73#4114yes—
248C2×D4×C73C2412yes—
249C2×D4×C73C2412yes—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—24no—
253C22×C4×C73—24no—
254C22×C4×C73—82no—
255C22×C4×C73—82no—
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2411yescharacteristic
259D8×C73—28no—
260C2×C8×C73—22no—
261C2×C8×C73—22no—
262C2×C8×C73C2412yes—
263C2×C8×C73C2412yes—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73C2412yes—
267C4⋊C4×C73C2412yes—
268C22⋊C4×C73—24no—
269C22⋊C4×C73—24no—
270C42×C73C2×D412yes—
271C42×C73C2412yes—
272C23×C73—24no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—42no—
276C23×C73—42no—
277C23×C73—42no—
278C23×C73—42no—
279C23×C73—42no—
280C23×C73C22×D411yescharacteristic
281C22×D73—22no—
282C22×D73—42no—
283C22×D73—42no—
284C22×D73—42no—
285D4×C73—24no—
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—22no—
289D4×C73—42no—
290D4×C73C2×#4114yes—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—42no—
296C2×C4×C73—42no—
297C2×C4×C73—84no—
298C2×C4×C73—84no—
299C2×C4×C73C22×D412yes—
300C2×C4×C73C22×D412yes—
301C2×C4×C73C22×D411yescharacteristic
302C2×C4×C73C2×#4112yes—
303C2×C4×C732−1+412yes—
304C2×C4×C73C2511yescharacteristic
305C22⋊D73—48no—
306C22⋊D73—84no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—48no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73—42no—
318C2×Dic73—84no—
319C2×Dic73C22×D412yes—
320C2×Dic73C22×D412yes—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323D292—22no—
324D292—22no—
325D292—42no—
326C4×D73—84no—
327Dic146—22no—
328Dic146—22no—
329Dic146—44no—
330Dic146—42no—
331Dic146—84no—
332C8×C73—22no—
333C8×C73—22no—
334#10596831—22no—
335#10596831—22no—
336C22×C73—24no—
337C22×C73—48no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73—42no—
343C22×C73—84no—
344C22×C73#54812yes—
345C22×C73#57512yes—
346C22×C73#57612yes—
347C22×C73C23×D411yescharacteristic
348C2×D73—42no—
349C2×D73—42no—
350C2×D73—42no—
351C2×D73—84no—
352C4×C73—22no—
353C4×C73—22no—
354C4×C73—42no—
355C4×C73—42no—
356C4×C73#54812yes—
357C4×C73C22×#4111yescharacteristic
358C4×C73C2×2−1+411yescharacteristic
359Dic73—22no—
360Dic73—22no—
361Dic73—22no—
362Dic73—22no—
363Dic73—42no—
364Dic73—42no—
365Dic73—42no—
366C2×#3370—731nomaximal, Sylow
367C2×C73—44no—
368C2×C73—82no—
369C2×C73#337014yescomplemented
370C2×C73C2×#54811yescharacteristic
371C2×C73C2×#57511yescharacteristic
372C2×C73C2×#57611yescharacteristic
373D73—82no—
374C2×#559—731no—
375C2×#554—731no—
376#3370—7316no—
377C2×#490—731no—
378C2×#489—731no—
379C2×#488—731no—
380C2×#479—731no—
381C2×#478—731no—
382C2×#474—731no—
383C2×#463—731no—
384C2×#463—731no—
385C2×#459—731no—
386C2×#446—731no—
387C2×#442—731no—
388C2×#440—731no—
389C2×C4×D8D7311yescharacteristic, complemented
390C73C2×#337011yescharacteristic, complemented, Sylow
391C22×SD16—731no—
392C22×D8—731no—
393C22×D8C2×D7311yescharacteristic
394#559—738no—
395#559—1464no—
396#554—738no—
397#554—1464no—
398C2×C4⋊Q8—731no—
399C2×#127—731no—
400C2×#125—731no—
401C2×#125—731no—
402C2×#124—731no—
403C2×#124—731no—
404C2×#124—1461no—
405C2×#123—1461no—
406C2×#123—1461no—
407C2×C22⋊Q8—1461no—
408C2×C22⋊Q8—1461no—
409C2×C22⋊Q8—1461no—
410C2×C4×Q8—731no—
411C2×C4×Q8—731no—
412C2×C4×D4—731no—
413C2×C4×D4—731no—
414C2×C4×D4—731no—
415C2×C4×D4—1461no—
416C2×C4×D4C2×D7311yescharacteristic
417C2×C4×D4C2×D7311yescharacteristic
418C22×C4⋊C4—1461no—
419#490—738no—
420#489—738no—
421#488—738no—
422#479—738no—
423#478—738no—
424#474—738no—
425#463—738no—
426#463—738no—
427#459—738no—
428#446—738no—
429#442—738no—
430#440—738no—
431C4×D8C2×D7318yescomplemented
432C2×#107—731no—
433C2×#107C2×D7311yescharacteristic
434C2×#106—731no—
435C2×C4⋊C8—731no—
436C2×C4⋊C8—731no—
437C2×C4⋊C8—731no—
438C2×#103—731no—
439C2×#103—731no—
440C2×#103—731no—
441C2×#102—731no—
442C2×#102—731no—
443C2×#102—731no—
444C2×#102—731no—
445C2×#102—731no—
446C2×#102C2×D7311yescharacteristic
447C2×#102C2×D7311yescharacteristic
448C2×#97—731no—
449C2×#97—731no—
450C2×C4×C8C2×D7311yescharacteristic
451C22×Q8—731no—
452C22×Q8—731no—
453C22×Q8—1461no—
454C22×D4—731no—
455C22×D4—1461no—
456C22×D4—1461no—
457C22×D4C22×D7311yescharacteristic
458C22×D4C22×D7311yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—1461no—
462C23×C4—1461no—
463C23×C4—1461no—
464C2×SD16—734no—
465C2×SD16—1464no—
466C2×D8—24no—
467C2×D8—734no—
468C2×D8—1464no—
469C2×D8C22×D7314yes—
470C22×C8—731no—
471C22×C8—731no—
472C22×C8C22×D7311yescharacteristic
473C22×C8C22×D7311yescharacteristic
474C4⋊Q8—734no—
475C4⋊Q8—1462no—
476#127—734no—
477#127—1462no—
478#125—734no—
479#125—734no—
480#125—1462no—
481#125—1462no—
482#124—734no—
483#124—734no—
484#124—1462no—
485#124—1468no—
486#124—1462no—
487#123—1468no—
488#123—1468no—
489C22⋊Q8—1468no—
490C22⋊Q8—1468no—
491C22⋊Q8—1468no—
492C4×Q8—734no—
493C4×Q8—734no—
494C4×Q8—734no—
495C4×Q8—1462no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—734no—
499C4×D4—734no—
500C4×D4—734no—
501C4×D4—1462no—
502C4×D4—1462no—
503C4×D4—1462no—
504C4×D4—1468no—
505C4×D4C22×D7314yes—
506C4×D4C22×D7314yes—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—731no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—1468no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4C22×D7311yescharacteristic
520C2×C4⋊C4C22×D7311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C22⋊C4—1461no—
529C2×C22⋊C4—1461no—
530C2×C42—731no—
531C2×C42—731no—
532C2×C42—1461no—
533C2×C42C22×D7311yescharacteristic
534#107—734no—
535#107C22×D7314yes—
536#106—734no—
537C4⋊C8—734no—
538C4⋊C8—734no—
539C4⋊C8—734no—
540#103—734no—
541#103—734no—
542#103—734no—
543#102—734no—
544#102—734no—
545#102—734no—
546#102—734no—
547#102—734no—
548#102C22×D7314yes—
549#102C22×D7314yes—
550#97—734no—
551#97—734no—
552C4×C8C22×D7314yes—
553C24—21no—
554C24—21no—
555C24—1461no—
556C2×Q8—2922no—
557C2×Q8—5842no—
558C2×Q8—734no—
559C2×Q8—732no—
560C2×Q8—1464no—
561C2×Q8—1462no—
562C2×Q8—1462no—
563C2×Q8—1461no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—2924no—
570C2×D4—5842no—
571C2×D4—732no—
572C2×D4—1464no—
573C2×D4—1464no—
574C2×D4—1461no—
575C2×D4—1462no—
576C2×D4—1462no—
577C2×D4#1192402814yes—
578C2×D4C23×D7312yes—
579C2×D4C23×D7312yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—2924no—
587C22×C4—5842no—
588C22×C4—5842no—
589C22×C4—731no—
590C22×C4—731no—
591C22×C4—731no—
592C22×C4—731no—
593C22×C4—1464no—
594C22×C4—1464no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4—1461no—
598C22×C4—1464no—
599C22×C4D4×D7311yescharacteristic
600C22×C4D4×D7311yescharacteristic
601C22×C4C23×D7311yescharacteristic
602SD16—1468no—
603D8—28no—
604D8—1468no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—732no—
608C2×C8—732no—
609C2×C8—1462no—
610C2×C8—1462no—
611C2×C8C23×D7312yes—
612C2×C8C23×D7312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—734no—
616C4⋊C4—734no—
617C4⋊C4—734no—
618C4⋊C4—732no—
619C4⋊C4—732no—
620C4⋊C4—1464no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1461no—
627C4⋊C4—1461no—
628C4⋊C4C23×D7312yes—
629C4⋊C4C23×D7312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—1464no—
633C22⋊C4—1464no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C42—732no—
640C42—732no—
641C42—732no—
642C42—732no—
643C42—1464no—
644C42D4×D7312yes—
645C42C23×D7312yes—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—2922no—
655C23—2922no—
656C23—2922no—
657C23—1462no—
658C23C2×D4×D7311yescharacteristic
659Q8—2924no—
660Q8—2922no—
661Q8—5844no—
662Q8—1462no—
663Q8—1462no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—24no—
668D4—42no—
669D4—2928no—
670D4—2922no—
671D4—5844no—
672D4—1462no—
673D4—1462no—
674D4C2×#1192402814yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—84no—
682C2×C4—84no—
683C2×C4—2922no—
684C2×C4—2922no—
685C2×C4—2922no—
686C2×C4—2928no—
687C2×C4—5844no—
688C2×C4—5844no—
689C2×C4—732no—
690C2×C4—732no—
691C2×C4—732no—
692C2×C4—732no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1462no—
700C2×C4C2×D4×D7312yes—
701C2×C4C2×D4×D7312yes—
702C2×C4C2×D4×D7311yescharacteristic
703C2×C4C2×#1192402812yes—
704C2×C4#1455663812yes—
705C2×C4C24×D7311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1462no—
709C8—1462no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—2922no—
719C22—2922no—
720C22—2922no—
721C22—5844no—
722C22#1798924612yes—
723C22#1798938412yes—
724C22#1798938812yes—
725C22C22×D4×D7311yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—2922no—
731C4—2922no—
732C4—2922no—
733C4—1462no—
734C4—1462no—
735C4—1462no—
736C4—1462no—
737C4#1798924612yes—
738C4C22×#1192402811yescharacteristic
739C4C2×#1455663811yescharacteristic
740C2—44no—
741C2—82no—
742C2—5842no—
743C2#2262268014yesdirect product factor
744C2C2×#1798924611yescharacteristic
745C2C2×#1798938411yescharacteristic
746C2C2×#1798938811yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×C4×D8×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988780C2
hypercenterC2×C4×D8D73
hypocenterC73C2×#3370
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#17989320C2semidirect
2. C2×#17989296C2semidirect
3. #22622680C2direct (N × H)
4. C2×#17988950C2semidirect
5. C2×#17988945C2semidirect
6. C2×#17988942C2semidirect
7. C2×#17988893C2semidirect
8. C2×#17988887C2semidirect
9. C2×#17988866C2semidirect
10. C2×#17988802C2semidirect
11. C2×#17988800C2semidirect
13. C2×#17988717C2semidirect
14. C2×#17988696C2semidirect
15. C2×#17988684C2semidirect
16. C2×C4×D8×C73C2semidirect
20. #17989320C22semidirect
22. #17989296C22semidirect
42. #17988950C22semidirect
43. #17988945C22semidirect
44. #17988942C22semidirect
45. #17988893C22semidirect
46. #17988887C22semidirect
47. #17988866C22semidirect
48. #17988802C22semidirect
49. #17988800C22semidirect
51. #17988717C22semidirect
52. #17988696C22semidirect
53. #17988684C22semidirect
72. C4×D8×C73C22semidirect
369. C2×C73#3370semidirect
389. C2×C4×D8D73semidirect
390. C73C2×#3370semidirect
431. C4×D8C2×D73semidirect
743. C2#22622680direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893202
C2×#179892962
#226226802
C2×#179889502
C2×#179889452
C2×#179889422
C2×#179888932
C2×#179888872
C2×#179888662
C2×#179888022
C2×#179888002
C2×#179887802
C2×#179887172
C2×#179886962
C2×#179886842
C2×C4×D8×C732
C2×#337073