Finite Group Databasebeta

← C2×#22621926 #33962562

Subgroups — C2×#22621926 #33962562

Order 18688.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989248C211yesmaximal, characteristic, complemented
2C2×#17989237C211yesmaximal, characteristic, complemented
3#22621926C2116yesmaximal, direct product factor
4C2×#17988948C211yesmaximal, characteristic, complemented
5C2×#17988921C211yesmaximal, characteristic, complemented
6C2×#17988901C211yesmaximal, characteristic, complemented
7C2×#17988880C211yesmaximal, characteristic, complemented
8C2×#17988830C211yesmaximal, characteristic, complemented
9C2×#17988821C211yesmaximal, characteristic, complemented
10C2×#17988804C211yesmaximal, characteristic, complemented
11C2×#17988731C211yesmaximal, characteristic, complemented
12C2×#17988688C211yesmaximal, characteristic, complemented
13C2×#17988655C211yesmaximal, characteristic, complemented
14C2×#17988587C211yesmaximal, characteristic, complemented
15C22×#14556515C211yesmaximal, characteristic, complemented
16C2×#448×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924027—21no—
19C22×#11924013C2211yescharacteristic
20C22×#11924011C2211yescharacteristic
21C23×#10596831C2211yescharacteristic
22#17989248—24no—
23#17989248C2218yescomplemented
24#17989237—24no—
25#17989237C2218yescomplemented
26C2×#14556590C2211yescharacteristic
27C2×#14556580—21no—
28C2×#14556580C2211yescharacteristic
29C2×#14556573—21no—
30C2×#14556572—21no—
31C2×#14556568—21no—
32C2×#14556567—21no—
33C2×#14556567C2211yescharacteristic
34C2×#14556565—21no—
35C2×#14556565C2211yescharacteristic
36C2×#14556562C2211yescharacteristic
37C2×Q8×Dic73C2211yescharacteristic
38C2×D4×Dic73C2211yescharacteristic
39C2×C4×C22⋊D73—21no—
40C2×C4×C22⋊D73C2211yescharacteristic
41C22×C4⋊Dic73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988948C2218yescomplemented
44#17988921C2218yescomplemented
45#17988901C2218yescomplemented
46#17988880C2218yescomplemented
47#17988830C2218yescomplemented
48#17988821C2218yescomplemented
49#17988804C2218yescomplemented
50#17988731C2218yescomplemented
51#17988688C2218yescomplemented
52#17988655C2218yescomplemented
53C2×#14556525C2211yescharacteristic
54C2×#14556525C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57#17988587C2218yescomplemented
58C2×#14556515C2211yescharacteristic
59C2×#14556515C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2218yescomplemented
63C2×#14556513C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C23×Q8×C73C2211yescharacteristic
70C22×SD16×C73C2211yescharacteristic
71C22×SD16×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#448×C73C2218yescomplemented
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C2×#11924029—22no—
78C2×#11924029—24no—
79C2×#11924029—42no—
80C2×#11924029C2314yes—
81C2×#11924027—28no—
82C2×#11924027—48no—
83C22×Dic146—21no—
84C22×D292—21no—
85C22×D292C2311yescharacteristic
86C22×C22⋊D73—21no—
87C22×C22⋊D73—21no—
88C22×C22⋊D73D411yescharacteristic
89C23×Dic73—21no—
90C23×Dic73—21no—
91C22×C4×D73—21no—
92C22×C4×D73—21no—
93C22×C4×D73C2311yescharacteristic
94C2×#11924013—42no—
95C2×#11924013C2314yes—
96C2×#11924011—42no—
97C2×#11924011C2314yes—
98C22×#10596831—42no—
99C22×#10596831C2311yescharacteristic
100C22×#10596831C2311yescharacteristic
101C22×#10596831C2314yes—
102#14556590—22no—
103#14556590C2314yes—
104#14556580—28no—
105#14556580—22no—
106#14556580C2314yes—
107#14556573—28no—
108#14556572—28no—
109#14556568—28no—
110#14556567—22no—
111#14556567—28no—
112#14556567C2314yes—
113#14556565—28no—
114#14556565—22no—
115#14556565C2314yes—
116#14556562—22no—
117#14556562C2314yes—
118Q8×Dic73—22no—
119Q8×Dic73C2314yes—
120D4×Dic73—22no—
121D4×Dic73C2314yes—
122C4×C22⋊D73—28no—
123C4×C22⋊D73D414yes—
124C4×C22⋊D73C2314yes—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73—22no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2314yes—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007D411yescharacteristic
136C4⋊C4×D73—22no—
137C4⋊C4×D73C2314yes—
138C2×C22⋊Dic73—21no—
139C2×C22⋊Dic73—21no—
140C2×C22⋊Dic73D411yescharacteristic
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005D411yescharacteristic
146C2×C4×Dic73—21no—
147C2×C4×Dic73C2311yescharacteristic
148#14556525C2314yes—
149#14556525C2314yes—
150#14556524C2314yes—
151#14556520C2314yes—
152#14556515C2314yes—
153#14556515C2314yes—
154#14556515C2314yes—
155#14556515C2314yes—
156#14556513C2314yes—
157#14556513C2314yes—
158#14556512C2314yes—
159#14556511C2314yes—
160#14556503C2314yes—
161#14556501C2314yes—
162C22×Q8×C73—22no—
163C22×Q8×C73—21no—
164C22×Q8×C73—24no—
165C22×Q8×C73—42no—
166C22×Q8×C73C2311yescharacteristic
167C22×Q8×C73C2314yes—
168C22×Q8×C73C2311yescharacteristic
169C22×D4×C73—21no—
170C22×D4×C73C2311yescharacteristic
171C23×C4×C73—21no—
172C23×C4×C73C2311yescharacteristic
173C2×SD16×C73—24no—
174C2×SD16×C73—42no—
175C2×SD16×C73C2314yes—
176C2×SD16×C73C2314yes—
177C22×C8×C73C2311yescharacteristic
178C22×C8×C73C2311yescharacteristic
179#121×C73—22no—
180#121×C73C2314yes—
181C2×C4⋊C4×C73C2311yescharacteristic
182C2×C22⋊C4×C73—21no—
183#103×C73C2314yes—
184#103×C73C2314yes—
185C22⋊C8×C73C2314yes—
186C23×D73—21no—
187C23×D73C2×D411yescharacteristic
188#11924029—28no—
189#11924029—44no—
190#11924029—48no—
191#11924027—432no—
192C2×Dic146—24no—
193C2×Dic146—44no—
194C2×D292—22no—
195C2×D292—22no—
196C2×D292—24no—
197C2×D292—21no—
198C2×D292—44no—
199C2×D292C2412yes—
200C2×C22⋊D73—24no—
201C2×C22⋊D73—24no—
202C2×C22⋊D73—24no—
203C2×C22⋊D73—44no—
204C2×C22⋊D73—44no—
205C2×C22⋊D73C2×D414yes—
206C22×Dic73—21no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73—24no—
210C22×Dic73—24no—
211C22×Dic73—44no—
212C22×Dic73—44no—
213C22×Dic73C2×D411yescharacteristic
214C22×Dic73C2×D411yescharacteristic
215C22×Dic73C2×D411yescharacteristic
216C2×C4×D73—22no—
217C2×C4×D73—22no—
218C2×C4×D73—24no—
219C2×C4×D73—24no—
220C2×C4×D73—44no—
221C2×C4×D73—44no—
222C2×C4×D73C2×D412yes—
223C2×C4×D73C2412yes—
224#11924013—44no—
225#11924011—44no—
226C2×#10596831—22no—
227C2×#10596831—22no—
228C2×#10596831—44no—
229C2×#10596831C2412yes—
230C2×#10596831C2412yes—
231C4⋊Dic73—21no—
232C4⋊Dic73—21no—
233C4⋊Dic73—24no—
234C4⋊Dic73—21no—
235C4⋊Dic73—24no—
236C4⋊Dic73C2412yes—
237C4⋊Dic73C2412yes—
238C4⋊Dic73C2412yes—
239#11924007—24no—
240#11924007—24no—
241#11924007—24no—
242#11924007C2×D414yes—
243C22⋊Dic73—24no—
244C22⋊Dic73—24no—
245C22⋊Dic73C2×D414yes—
246#11924005—24no—
247#11924005—24no—
248#11924005—24no—
249#11924005—24no—
250#11924005C2×D414yes—
251C4×Dic73—24no—
252C4×Dic73C2×D412yes—
253C4×Dic73C2412yes—
254C24×C73—21no—
255C24×C73C2×D411yescharacteristic
256C2×Q8×C73—21no—
257C2×Q8×C73—24no—
258C2×Q8×C73—21no—
259C2×Q8×C73—22no—
260C2×Q8×C73—28no—
261C2×Q8×C73—22no—
262C2×Q8×C73—22no—
263C2×Q8×C73—44no—
264C2×Q8×C73—44no—
265C2×Q8×C73—48no—
266C2×Q8×C73#4114yescomplemented
267C2×Q8×C73C2412yes—
268C2×Q8×C73C2412yes—
269C2×D4×C73—24no—
270C2×D4×C73—21no—
271C2×D4×C73—22no—
272C2×D4×C73—22no—
273C2×D4×C73—44no—
274C2×D4×C73C2412yes—
275C22×C4×C73—21no—
276C22×C4×C73—22no—
277C22×C4×C73—22no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73—24no—
281C22×C4×C73—44no—
282C22×C4×C73C2×D411yescharacteristic
283C22×C4×C73C2×D412yes—
284C22×C4×C73C2412yes—
285C22×C4×C73C2411yescharacteristic
286SD16×C73—28no—
287SD16×C73—44no—
288C2×C8×C73—22no—
289C2×C8×C73—22no—
290C2×C8×C73C2412yes—
291C2×C8×C73C2412yes—
292C4⋊C4×C73—21no—
293C4⋊C4×C73C2412yes—
294C22⋊C4×C73—24no—
295C23×C73—22no—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—42no—
299C23×C73—42no—
300C23×C73—42no—
301C23×C73AGL(1,ℤ/8)14yes—
302C23×C73C22×D412yes—
303C23×C73C22×D411yescharacteristic
304C22×D73—22no—
305C22×D73—22no—
306C22×D73—22no—
307C22×D73—22no—
308C22×D73—42no—
309C22×D73—42no—
310C22×D73—42no—
311C22×D73C22×D412yes—
312Q8×C73—24no—
313Q8×C73—22no—
314Q8×C73—22no—
315Q8×C73—22no—
316Q8×C73—48no—
317Q8×C73—42no—
318Q8×C73C2×#4114yescomplemented
319D4×C73—22no—
320D4×C73—22no—
321D4×C73—48no—
322D4×C73—42no—
323C2×C4×C73—22no—
324C2×C4×C73—24no—
325C2×C4×C73—22no—
326C2×C4×C73—24no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—48no—
332C2×C4×C73—42no—
333C2×C4×C73—42no—
334C2×C4×C73C22×D412yes—
335C2×C4×C73C22×D411yescharacteristic
336C2×C4×C73C2×#4112yes—
337C2×C4×C73H(5,𝔽2)12yes—
338C2×C4×C73C2511yescharacteristic
339C22⋊D73—28no—
340C22⋊D73—48no—
341C22⋊D73—48no—
342C2×Dic73—22no—
343C2×Dic73—22no—
344C2×Dic73—22no—
345C2×Dic73—22no—
346C2×Dic73—22no—
347C2×Dic73—22no—
348C2×Dic73—48no—
349C2×Dic73—42no—
350C2×Dic73—42no—
351C2×Dic73—48no—
352C2×Dic73—42no—
353C2×Dic73C22×D412yes—
354C2×Dic73C22×D412yes—
355C2×Dic73C22×D412yes—
356D292—22no—
357D292—22no—
358D292—48no—
359D292—42no—
360C4×D73—24no—
361C4×D73—22no—
362C4×D73—22no—
363C4×D73—48no—
364C4×D73—48no—
365Dic146—48no—
366C8×C73—22no—
367C8×C73—22no—
368#10596831—22no—
369#10596831—22no—
370C22×C73—22no—
371C22×C73—28no—
372C22×C73—22no—
373C22×C73—42no—
374C22×C73—42no—
375C22×C73—42no—
376C22×C73—84no—
377C22×C73#54612yes—
378C22×C73C2×AGL(1,ℤ/8)14yes—
379C22×C73C2×AGL(1,ℤ/8)12yes—
380C22×C73#57812yes—
381C22×C73C23×D411yescharacteristic
382C2×D73—22no—
383C2×D73—22no—
384C2×D73—22no—
385C2×D73—44no—
386C2×D73—42no—
387C2×D73—42no—
388C2×D73—42no—
389C2×D73—84no—
390C4×C73—24no—
391C4×C73—22no—
392C4×C73—42no—
393C4×C73—42no—
394C4×C73#54612yes—
395C4×C73C22×#4111yescharacteristic
396C4×C73C2×H(5,𝔽2)11yescharacteristic
397Dic73—22no—
398Dic73—22no—
399Dic73—22no—
400Dic73—42no—
401Dic73—42no—
402Dic73—42no—
403C2×#3308—731nomaximal, Sylow
404C2×C73—24no—
405C2×C73—82no—
406C2×C73#330814yescomplemented
407C2×C73C2×#54611yescharacteristic
408C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
409C2×C73C2×#57811yescharacteristic
410D73—42no—
411D73—82no—
412C2×#548—731no—
413C2×#547—731no—
414#3308—7316no—
415C2×#489—731no—
416C2×#484—731no—
417C2×#480—731no—
418C2×#477—731no—
419C2×#468—731no—
420C2×#466—731no—
421C2×#463—731no—
422C2×#449—731no—
423C2×#448D7311yescharacteristic, complemented
424C2×#440—731no—
425C2×#435—731no—
426C2×#417—731no—
427C22×#103—731no—
428C73C2×#330811yescharacteristic, complemented, Sylow
429C22×#41—731no—
430C22×#41—1461no—
431C23×Q8C2×D7311yescharacteristic
432C22×SD16C2×D7311yescharacteristic
433C22×SD16C2×D7311yescharacteristic
434C22×D8—731no—
435C22×M16—731no—
436C23×C8—731no—
437#548—738no—
438#548—1464no—
439#547—738no—
440#547—1464no—
441C2×C4⋊Q8—731no—
442C2×#124—731no—
443C2×#124—1461no—
444C2×#123—1461no—
445C2×#123—1461no—
446C2×C22⋊Q8—731no—
447C2×C22⋊Q8—1461no—
448C2×C22⋊Q8—1461no—
449C2×#121—731no—
450C2×#121—731no—
451C2×#121—1461no—
452C2×#121C2×D7311yescharacteristic
453C2×C4×Q8—731no—
454C2×C4×D4—731no—
455C2×C4×D4—731no—
456C2×C4×D4—1461no—
457C22×C4⋊C4—731no—
458C22×C4⋊C4—731no—
459#489—738no—
460#484—738no—
461#480—738no—
462#477—738no—
463#468—738no—
464#466—738no—
465#463—738no—
466#449—738no—
467#448C2×D7318yescomplemented
468#440—738no—
469#435—738no—
470C2×#107—731no—
471C2×#107—731no—
472C2×#107—731no—
473C2×C4⋊C8—731no—
474#417—738no—
475C2×#103—731no—
476C2×#103—731no—
477C2×#103—731no—
478C2×#103—731no—
479C2×#103—738no—
480C2×#103C2×D7311yescharacteristic
481C2×#103C2×D7311yescharacteristic
482C2×#102—731no—
483C2×#102—731no—
484C2×#102—731no—
485C2×#102—731no—
486C2×C22⋊C8—731no—
487C2×C22⋊C8C2×D7311yescharacteristic
488C2×#97—731no—
489C2×#41—2928no—
490C2×#41—2922no—
491C2×#41—734no—
492C2×#41—1464no—
493C2×#41—1462no—
494C2×#41—1468no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—24no—
498C22×Q8—42no—
499C22×Q8—1461no—
500C22×Q8C22×D7311yescharacteristic
501C22×Q8C22×D7314yes—
502C22×Q8C22×D7311yescharacteristic
503C22×D4—21no—
504C22×D4—731no—
505C22×D4—731no—
506C22×D4—1461no—
507C22×D4—1461no—
508C22×D4—1461no—
509C22×D4C22×D7311yescharacteristic
510C23×C4—21no—
511C23×C4—731no—
512C23×C4—1461no—
513C23×C4—1461no—
514C23×C4—1461no—
515C23×C4—1461no—
516C23×C4C22×D7311yescharacteristic
517C2×SD16—24no—
518C2×SD16—42no—
519C2×SD16C22×D7314yes—
520C2×SD16C22×D7314yes—
521C2×D8—2922no—
522C2×D8—734no—
523C2×M16—2922no—
524C2×M16—734no—
525C22×C8—2922no—
526C22×C8—734no—
527C22×C8—731no—
528C22×C8—731no—
529C22×C8C22×D7311yescharacteristic
530C22×C8C22×D7311yescharacteristic
531C4⋊Q8—734no—
532C4⋊Q8—1462no—
533#124—734no—
534#124—1462no—
535#124—1468no—
536#123—1468no—
537#123—1468no—
538C22⋊Q8—734no—
539C22⋊Q8—1468no—
540C22⋊Q8—1468no—
541C22⋊Q8—1462no—
542#121—22no—
543#121—734no—
544#121—734no—
545#121—1468no—
546#121—1462no—
547#121—1462no—
548#121C22×D7314yes—
549C4×Q8—734no—
550C4×Q8—1462no—
551C4×D4—734no—
552C4×D4—734no—
553C4×D4—734no—
554C4×D4—1462no—
555C4×D4—1468no—
556C2×C4⋊C4—731no—
557C2×C4⋊C4—731no—
558C2×C4⋊C4—731no—
559C2×C4⋊C4—734no—
560C2×C4⋊C4—731no—
561C2×C4⋊C4—734no—
562C2×C4⋊C4—1462no—
563C2×C4⋊C4—1461no—
564C2×C4⋊C4—1461no—
565C2×C4⋊C4—1461no—
566C2×C4⋊C4—1461no—
567C2×C4⋊C4—1461no—
568C2×C4⋊C4—1462no—
569C2×C4⋊C4C22×D7311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—731no—
572C2×C22⋊C4—731no—
573C2×C22⋊C4—1461no—
574C2×C22⋊C4—1461no—
575C2×C22⋊C4—1461no—
576C2×C22⋊C4—1461no—
577C2×C22⋊C4—1461no—
578C2×C22⋊C4—1461no—
579C2×C42—731no—
580C2×C42—1461no—
581#107—734no—
582#107—734no—
583#107—734no—
584C4⋊C8—734no—
585#103—734no—
586#103—734no—
587#103—734no—
588#103—734no—
589#103C22×D7314yes—
590#103C22×D7314yes—
591#102—734no—
592#102—734no—
593#102—734no—
594#102—734no—
595C22⋊C8—734no—
596C22⋊C8C22×D7314yes—
597#97—734no—
598C24—21no—
599C24—731no—
600C24—1461no—
601C24D4×D7311yescharacteristic
602#41—29232no—
603#41—2928no—
604#41—2924no—
605#41—1468no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—28no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—48no—
616C2×Q8—2924no—
617C2×Q8—1464no—
618C2×Q8#1192402714yescomplemented
619C2×Q8C23×D7312yes—
620C2×Q8C23×D7312yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—44no—
626C2×D4—2924no—
627C2×D4—2924no—
628C2×D4—2924no—
629C2×D4—734no—
630C2×D4—732no—
631C2×D4—1464no—
632C2×D4—1464no—
633C2×D4—1464no—
634C2×D4—1464no—
635C2×D4—1461no—
636C2×D4—1462no—
637C2×D4—1462no—
638C2×D4C23×D7312yes—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—44no—
646C22×C4—2924no—
647C22×C4—2924no—
648C22×C4—2924no—
649C22×C4—2924no—
650C22×C4—731no—
651C22×C4—731no—
652C22×C4—731no—
653C22×C4—732no—
654C22×C4—732no—
655C22×C4—1464no—
656C22×C4—1464no—
657C22×C4—1464no—
658C22×C4—1464no—
659C22×C4—1461no—
660C22×C4—1461no—
661C22×C4—1461no—
662C22×C4—1462no—
663C22×C4—1462no—
664C22×C4D4×D7312yes—
665C22×C4D4×D7311yescharacteristic
666C22×C4C23×D7312yes—
667C22×C4C23×D7311yescharacteristic
668SD16—28no—
669SD16—44no—
670D8—2924no—
671M16—2924no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—2924no—
675C2×C8—732no—
676C2×C8—732no—
677C2×C8—1462no—
678C2×C8—1462no—
679C2×C8C23×D7312yes—
680C2×C8C23×D7312yes—
681C4⋊C4—21no—
682C4⋊C4—734no—
683C4⋊C4—732no—
684C4⋊C4—732no—
685C4⋊C4—732no—
686C4⋊C4—1464no—
687C4⋊C4—1464no—
688C4⋊C4—1464no—
689C4⋊C4—1464no—
690C4⋊C4—1461no—
691C4⋊C4—1461no—
692C4⋊C4—1464no—
693C4⋊C4—1461no—
694C4⋊C4C23×D7312yes—
695C22⋊C4—24no—
696C22⋊C4—734no—
697C22⋊C4—734no—
698C22⋊C4—1464no—
699C22⋊C4—1464no—
700C22⋊C4—1464no—
701C22⋊C4—1464no—
702C22⋊C4—1464no—
703C22⋊C4—1464no—
704C42—732no—
705C42—732no—
706C42—1464no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—2922no—
714C23—2922no—
715C23—2922no—
716C23—732no—
717C23—1462no—
718C23—1462no—
719C23—1462no—
720C23—1462no—
721C23#1455661814yes—
722C23C2×D4×D7312yes—
723C23C2×D4×D7311yescharacteristic
724Q8—22no—
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—2928no—
731Q8C2×#1192402714yescomplemented
732D4—22no—
733D4—22no—
734D4—48no—
735D4—42no—
736D4—2928no—
737D4—2928no—
738D4—2928no—
739D4—2922no—
740D4—1468no—
741D4—1462no—
742D4—1462no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—48no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—2928no—
755C2×C4—2928no—
756C2×C4—2922no—
757C2×C4—2922no—
758C2×C4—2928no—
759C2×C4—2922no—
760C2×C4—2928no—
761C2×C4—732no—
762C2×C4—732no—
763C2×C4—732no—
764C2×C4—1462no—
765C2×C4—1462no—
766C2×C4—1462no—
767C2×C4—1462no—
768C2×C4—1462no—
769C2×C4—1462no—
770C2×C4—1462no—
771C2×C4—1462no—
772C2×C4—1464no—
773C2×C4C2×D4×D7312yes—
774C2×C4C2×D4×D7311yescharacteristic
775C2×C4C2×#1192402712yes—
776C2×C4#1455663612yes—
777C2×C4C24×D7311yescharacteristic
778C8—22no—
779C8—22no—
780C8—1462no—
781C8—1462no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22—2924no—
790C22—2922no—
791C22—2922no—
792C22—2922no—
793C22—5844no—
794C22—1462no—
795C22—1462no—
796C22—1462no—
797C22#1798922412yes—
798C22C2×#1455661814yes—
799C22C2×#1455661812yes—
800C22#1798940312yes—
801C22C22×D4×D7311yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—2922no—
807C4—2922no—
808C4—2922no—
809C4—1462no—
810C4—1462no—
811C4—1462no—
812C4#1798922412yes—
813C4C22×#1192402711yescharacteristic
814C4C2×#1455663611yescharacteristic
815C2—24no—
816C2—82no—
817C2—2922no—
818C2—5842no—
819C2#2262192614yesdirect product factor
820C2C2×#1798922411yescharacteristic
821C2C22×#1455661811yescharacteristic
822C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#448×C73C2
socleC23×C73C22×D4
hypercenterC2×#448D73
hypocenterC73C2×#3308
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#17989248C2semidirect
2. C2×#17989237C2semidirect
3. #22621926C2direct (N × H)
4. C2×#17988948C2semidirect
5. C2×#17988921C2semidirect
6. C2×#17988901C2semidirect
7. C2×#17988880C2semidirect
8. C2×#17988830C2semidirect
9. C2×#17988821C2semidirect
10. C2×#17988804C2semidirect
11. C2×#17988731C2semidirect
12. C2×#17988688C2semidirect
13. C2×#17988655C2semidirect
14. C2×#17988587C2semidirect
15. C22×#14556515C2semidirect
16. C2×#448×C73C2semidirect
23. #17989248C22semidirect
25. #17989237C22semidirect
43. #17988948C22semidirect
44. #17988921C22semidirect
45. #17988901C22semidirect
46. #17988880C22semidirect
47. #17988830C22semidirect
48. #17988821C22semidirect
49. #17988804C22semidirect
50. #17988731C22semidirect
51. #17988688C22semidirect
52. #17988655C22semidirect
57. #17988587C22semidirect
62. C2×#14556515C22semidirect
73. #448×C73C22semidirect
266. C2×Q8×C73#41semidirect
318. Q8×C73C2×#41semidirect
406. C2×C73#3308semidirect
423. C2×#448D73semidirect
428. C73C2×#3308semidirect
467. #448C2×D73semidirect
618. C2×Q8#11924027semidirect
731. Q8C2×#11924027semidirect
819. C2#22621926direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892482
C2×#179892372
#226219262
C2×#179889482
C2×#179889212
C2×#179889012
C2×#179888802
C2×#179888302
C2×#179888212
C2×#179888042
C2×#179887312
C2×#179886882
C2×#179886552
C2×#179885872
C22×#145565152
C2×#448×C732
C2×#330873