Finite Group Databasebeta

← C2×#22621839 #33962413

Subgroups — C2×#22621839 #33962413

Order 18688.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989289C211yesmaximal, characteristic, complemented
2C2×#17989243C211yesmaximal, characteristic, complemented
3#22621839C2116yesmaximal, direct product factor
4C2×#17988940C211yesmaximal, characteristic, complemented
5C2×#17988903C211yesmaximal, characteristic, complemented
6C2×#17988930C211yesmaximal, characteristic, complemented
7C2×#17988893C211yesmaximal, characteristic, complemented
8C2×#17988815C211yesmaximal, characteristic, complemented
9C2×#17988800C211yesmaximal, characteristic, complemented
10C2×#17988729C211yesmaximal, characteristic, complemented
11C2×#17988725C211yesmaximal, characteristic, complemented
12C2×#17988678C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D73C211yesmaximal, characteristic, complemented
14C2×#17988580C211yesmaximal, characteristic, complemented
15C22×#14556516C211yesmaximal, characteristic, complemented
16C2×#466×C73C211yesmaximal, characteristic, complemented
17C22×#11924027C2211yescharacteristic
18C23×Dic146C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924016C2211yescharacteristic
21C22×C8×D73C2211yescharacteristic
22#17989289—24no—
23#17989289C2218yescomplemented
24#17989243—24no—
25#17989243C2218yescomplemented
26C2×#14556584—21no—
27C2×#14556582C2211yescharacteristic
28C2×#14556578C2211yescharacteristic
29C2×#14556577—21no—
30C2×#14556575—21no—
31C2×#14556571C2211yescharacteristic
32C2×#14556568—21no—
33C2×#14556563—21no—
34C2×#14556563—21no—
35C2×#14556562C2211yescharacteristic
36C2×#14556556C2211yescharacteristic
37C2×D4×Dic73—21no—
38C2×D4×Dic73—21no—
39C2×D4×Dic73C2211yescharacteristic
40C2×C4×C22⋊D73C2211yescharacteristic
41C2×#14556549C2211yescharacteristic
42C22×C4⋊Dic73C2211yescharacteristic
43#17988940C2218yescomplemented
44#17988930C2218yescomplemented
45#17988903C2218yescomplemented
46#17988893C2218yescomplemented
47#17988815C2218yescomplemented
48#17988800C2218yescomplemented
49#17988729C2218yescomplemented
50#17988725C2218yescomplemented
51#17988678C2218yescomplemented
52C8×C22⋊D73C2218yescomplemented
53C2×#14556522C2211yescharacteristic
54C2×#14556522C2211yescharacteristic
55C2×#14556520C2211yescharacteristic
56#17988580C2218yescomplemented
57C2×#14556516C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2218yescomplemented
62C2×#14556514C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×D8×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×#121×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#466×C73C2218yescomplemented
74C2×#107×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×#11924027—24no—
78C2×#11924027—22no—
79C2×#11924027—42no—
80C2×#11924027C2314yes—
81C22×Dic146—24no—
82C22×Dic146—22no—
83C22×Dic146—21no—
84C22×Dic146—42no—
85C22×Dic146C2311yescharacteristic
86C22×Dic146C2314yes—
87C22×Dic146C2311yescharacteristic
88C22×C22⋊D73—21no—
89C22×C22⋊D73—21no—
90C22×C22⋊D73D411yescharacteristic
91C23×Dic73—21no—
92C23×Dic73—21no—
93C23×Dic73—21no—
94C23×Dic73—21no—
95C22×C4×D73C2311yescharacteristic
96C2×#11924016—24no—
97C2×#11924016—42no—
98C2×#11924016C2314yes—
99C2×#11924016C2314yes—
100C22×#10596831C2311yescharacteristic
101C22×#10596831C2311yescharacteristic
102C2×C8×D73—42no—
103C2×C8×D73C2314yes—
104#14556584—28no—
105#14556582—22no—
106#14556582C2314yes—
107#14556578—22no—
108#14556578C2314yes—
109#14556577—28no—
110#14556575—28no—
111#14556571—22no—
112#14556571C2314yes—
113#14556568—28no—
114#14556563—28no—
115#14556563—28no—
116#14556562—22no—
117#14556562C2314yes—
118#14556556—22no—
119#14556556C2314yes—
120D4×Dic73—28no—
121D4×Dic73—28no—
122D4×Dic73—22no—
123D4×Dic73C2314yes—
124C4×C22⋊D73D414yes—
125C4×C22⋊D73C2314yes—
126#14556549—22no—
127#14556549C2314yes—
128C2×C4⋊Dic73—21no—
129C2×C4⋊Dic73—21no—
130C2×C4⋊Dic73—22no—
131C2×C4⋊Dic73—21no—
132C2×C4⋊Dic73C2311yescharacteristic
133C2×C4⋊Dic73C2311yescharacteristic
134C2×C4⋊Dic73C2314yes—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007D411yescharacteristic
138C2×C22⋊Dic73—21no—
139C2×C22⋊Dic73—21no—
140C2×C22⋊Dic73—21no—
141C2×C22⋊Dic73—21no—
142C2×C22⋊Dic73D411yescharacteristic
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005D411yescharacteristic
146C2×C4×Dic73—21no—
147C2×C4×Dic73—21no—
148C2×C4×Dic73C2311yescharacteristic
149#14556522C2314yes—
150#14556522C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556516C2314yes—
156#14556514C2314yes—
157#14556514C2314yes—
158#14556512C2314yes—
159#14556512C2314yes—
160C22⋊#10596831C2314yes—
161#14556503C2314yes—
162C8×Dic73C2314yes—
163C22×D4×C73—21no—
164C22×D4×C73—21no—
165C22×D4×C73C2311yescharacteristic
166C22×D4×C73C2311yescharacteristic
167C23×C4×C73C2311yescharacteristic
168C2×D8×C73—42no—
169C2×D8×C73C2314yes—
170C22×C8×C73—42no—
171C22×C8×C73C2311yescharacteristic
172C22×C8×C73C2311yescharacteristic
173C22×C8×C73C2314yes—
174#121×C73—22no—
175#121×C73—22no—
176#121×C73C2314yes—
177#121×C73C2314yes—
178C2×C4⋊C4×C73C2311yescharacteristic
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C22⋊C4×C73—21no—
181C2×C22⋊C4×C73—21no—
182#107×C73C2314yes—
183#102×C73C2314yes—
184#102×C73C2314yes—
185C23×D73C2×D411yescharacteristic
186#11924027—28no—
187#11924027—44no—
188#11924027—48no—
189C2×Dic146—21no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—22no—
193C2×Dic146—28no—
194C2×Dic146—24no—
195C2×Dic146—21no—
196C2×Dic146—44no—
197C2×Dic146—48no—
198C2×Dic146—44no—
199C2×Dic146#4114yes—
200C2×Dic146C2412yes—
201C2×Dic146C2412yes—
202C2×C22⋊D73—24no—
203C2×C22⋊D73—24no—
204C2×C22⋊D73—24no—
205C2×C22⋊D73—44no—
206C2×C22⋊D73—82no—
207C2×C22⋊D73C2×D414yes—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C22×Dic73—21no—
211C22×Dic73—21no—
212C22×Dic73—24no—
213C22×Dic73—24no—
214C22×Dic73—24no—
215C22×Dic73—24no—
216C22×Dic73—44no—
217C22×Dic73—44no—
218C22×Dic73—82no—
219C22×Dic73—82no—
220C22×Dic73C2×D411yescharacteristic
221C22×Dic73C2×D411yescharacteristic
222C22×Dic73C2×D411yescharacteristic
223C2×C4×D73—22no—
224C2×C4×D73—22no—
225C2×C4×D73C2×D412yes—
226C2×C4×D73C2412yes—
227#11924016—28no—
228#11924016—44no—
229C2×#10596831—22no—
230C2×#10596831—22no—
231C2×#10596831C2412yes—
232C2×#10596831C2412yes—
233C8×D73—44no—
234C4⋊Dic73—21no—
235C4⋊Dic73—21no—
236C4⋊Dic73—24no—
237C4⋊Dic73—24no—
238C4⋊Dic73—24no—
239C4⋊Dic73C2412yes—
240C4⋊Dic73C2412yes—
241#11924007—24no—
242#11924007—24no—
243#11924007C2×D414yes—
244C22⋊Dic73—24no—
245C22⋊Dic73—24no—
246C22⋊Dic73—24no—
247C22⋊Dic73—24no—
248C22⋊Dic73C2×D414yes—
249#11924005—24no—
250#11924005—24no—
251#11924005C2×D414yes—
252C4×Dic73—24no—
253C4×Dic73—24no—
254C4×Dic73C2×D412yes—
255C4×Dic73C2412yes—
256C24×C73—21no—
257C24×C73—21no—
258C24×C73C2×D411yescharacteristic
259C2×D4×C73—24no—
260C2×D4×C73—24no—
261C2×D4×C73—21no—
262C2×D4×C73—21no—
263C2×D4×C73—22no—
264C2×D4×C73—22no—
265C2×D4×C73—22no—
266C2×D4×C73—22no—
267C2×D4×C73—44no—
268C2×D4×C73—44no—
269C2×D4×C73C2412yes—
270C2×D4×C73C2412yes—
271C22×C4×C73—22no—
272C22×C4×C73—22no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73C2×D411yescharacteristic
276C22×C4×C73C2×D412yes—
277C22×C4×C73C2412yes—
278C22×C4×C73C2411yescharacteristic
279D8×C73—44no—
280C2×C8×C73—22no—
281C2×C8×C73—22no—
282C2×C8×C73—44no—
283C2×C8×C73C2412yes—
284C2×C8×C73C2412yes—
285C4⋊C4×C73—21no—
286C4⋊C4×C73—21no—
287C4⋊C4×C73C2412yes—
288C4⋊C4×C73C2412yes—
289C22⋊C4×C73—24no—
290C22⋊C4×C73—24no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—22no—
294C23×C73—22no—
295C23×C73—42no—
296C23×C73—42no—
297C23×C73—42no—
298C23×C73—42no—
299C23×C73—42no—
300C23×C73—42no—
301C23×C73#13514yes—
302C23×C73C22×D412yes—
303C23×C73C22×D411yescharacteristic
304C22×D73—22no—
305C22×D73—22no—
306C22×D73—22no—
307C22×D73C22×D412yes—
308D4×C73—22no—
309D4×C73—22no—
310D4×C73—22no—
311D4×C73—22no—
312D4×C73—48no—
313D4×C73—48no—
314D4×C73—42no—
315D4×C73—42no—
316C2×C4×C73—22no—
317C2×C4×C73—24no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—42no—
323C2×C4×C73—42no—
324C2×C4×C73C22×D412yes—
325C2×C4×C73C22×D411yescharacteristic
326C2×C4×C73C2×#4112yes—
327C2×C4×C73H(5,𝔽2)12yes—
328C2×C4×C73C2511yescharacteristic
329C22⋊D73—28no—
330C22⋊D73—48no—
331C22⋊D73—84no—
332C2×Dic73—22no—
333C2×Dic73—24no—
334C2×Dic73—22no—
335C2×Dic73—22no—
336C2×Dic73—22no—
337C2×Dic73—22no—
338C2×Dic73—22no—
339C2×Dic73—22no—
340C2×Dic73—48no—
341C2×Dic73—48no—
342C2×Dic73—42no—
343C2×Dic73—42no—
344C2×Dic73—42no—
345C2×Dic73—84no—
346C2×Dic73—84no—
347C2×Dic73C22×D412yes—
348C2×Dic73C22×D412yes—
349C2×Dic73C22×D412yes—
350C4×D73—24no—
351C4×D73—22no—
352C4×D73—22no—
353Dic146—24no—
354Dic146—22no—
355Dic146—22no—
356Dic146—22no—
357Dic146—48no—
358Dic146—42no—
359Dic146C2×#4114yes—
360C8×C73—22no—
361C8×C73—22no—
362#10596831—22no—
363#10596831—22no—
364C22×C73—22no—
365C22×C73—28no—
366C22×C73—22no—
367C22×C73—42no—
368C22×C73—42no—
369C22×C73—42no—
370C22×C73—42no—
371C22×C73—42no—
372C22×C73—42no—
373C22×C73—84no—
374C22×C73—84no—
375C22×C73#54612yes—
376C22×C73C2×#13514yes—
377C22×C73C2×#13512yes—
378C22×C73#57712yes—
379C22×C73C23×D411yescharacteristic
380C2×D73—22no—
381C2×D73—22no—
382C2×D73—22no—
383C2×D73—44no—
384C4×C73—22no—
385C4×C73—42no—
386C4×C73—42no—
387C4×C73#54612yes—
388C4×C73C22×#4111yescharacteristic
389C4×C73C2×H(5,𝔽2)11yescharacteristic
390Dic73—24no—
391Dic73—22no—
392Dic73—22no—
393Dic73—22no—
394Dic73—42no—
395Dic73—42no—
396Dic73—42no—
397C2×#3301—731nomaximal, Sylow
398C2×C73—24no—
399C2×C73—82no—
400C2×C73—82no—
401C2×C73#330114yescomplemented
402C2×C73C2×#54611yescharacteristic
403C2×C73C22×#13511yescharacteristic
404C2×C73C2×#57711yescharacteristic
405D73—42no—
406C2×#553—731no—
407C2×#548—731no—
408#3301—7316no—
409C2×#488—731no—
410C2×#481—731no—
411C2×#485—731no—
412C2×#479—731no—
413C2×#466D7311yescharacteristic, complemented
414C2×#465—731no—
415C2×#463—731no—
416C2×#449—731no—
417C2×#448—731no—
418C2×C4×SD16—731no—
419C2×C8×D4—731no—
420C2×#416—731no—
421C22×#103—731no—
422C73C2×#330111yescharacteristic, complemented, Sylow
423C22×#41—731no—
424C23×Q8—731no—
425C22×SD16—731no—
426C22×SD16—731no—
427C22×D8C2×D7311yescharacteristic
428C23×C8—731no—
429C23×C8C2×D7311yescharacteristic
430#553—738no—
431#553—1464no—
432#548—738no—
433#548—1464no—
434C2×#126—1461no—
435C2×#125—731no—
436C2×#124—731no—
437C2×#124—1461no—
438C2×#123—1461no—
439C2×C22⋊Q8—731no—
440C2×C22⋊Q8—1461no—
441C2×#121—731no—
442C2×#121—1461no—
443C2×#121—1461no—
444C2×#121C2×D7311yescharacteristic
445C2×#121C2×D7311yescharacteristic
446C2×C4×Q8—731no—
447C2×C4×D4—731no—
448C2×C4×D4—731no—
449C2×C4×D4—1461no—
450C2×C4×D4—1461no—
451C2×#117—731no—
452C22×C4⋊C4—731no—
453#488—738no—
454#485—738no—
455#481—738no—
456#479—738no—
457#466C2×D7318yescomplemented
458#465—738no—
459#463—738no—
460#449—738no—
461#448—738no—
462C4×SD16—738no—
463C8×D4—738no—
464C2×#107C2×D7311yescharacteristic
465C2×#106—731no—
466C2×#106—731no—
467C2×C4⋊C8—731no—
468#416—738no—
469C2×#103—731no—
470C2×#103—731no—
471C2×#103—731no—
472C2×#103—731no—
473C2×#103—738no—
474C2×#103—731no—
475C2×#103—731no—
476C2×#102—731no—
477C2×#102—731no—
478C2×#102C2×D7311yescharacteristic
479C2×#102C2×D7311yescharacteristic
480C2×C22⋊C8—731no—
481C2×C22⋊C8—731no—
482C2×C4×C8—731no—
483C2×#41—2922no—
484C2×#41—734no—
485C2×#41—1464no—
486C2×#41—1462no—
487C22×Q8—2922no—
488C22×Q8—734no—
489C22×Q8—731no—
490C22×Q8—731no—
491C22×Q8—1464no—
492C22×Q8—1461no—
493C22×Q8—1462no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—731no—
497C22×D4—1461no—
498C22×D4—1461no—
499C22×D4C22×D7311yescharacteristic
500C22×D4C22×D7311yescharacteristic
501C23×C4—731no—
502C23×C4—1461no—
503C23×C4—1461no—
504C23×C4—1461no—
505C23×C4—1461no—
506C23×C4C22×D7311yescharacteristic
507C2×SD16—2922no—
508C2×SD16—734no—
509C2×SD16—734no—
510C2×SD16—1464no—
511C2×D8—42no—
512C2×D8C22×D7314yes—
513C22×C8—42no—
514C22×C8—2922no—
515C22×C8—734no—
516C22×C8—731no—
517C22×C8—731no—
518C22×C8C22×D7311yescharacteristic
519C22×C8C22×D7311yescharacteristic
520C22×C8C22×D7314yes—
521#126—1468no—
522#125—734no—
523#125—1462no—
524#124—734no—
525#124—1462no—
526#124—1468no—
527#123—1468no—
528C22⋊Q8—734no—
529C22⋊Q8—1468no—
530C22⋊Q8—1462no—
531#121—22no—
532#121—22no—
533#121—734no—
534#121—1462no—
535#121—1468no—
536#121—1468no—
537#121C22×D7314yes—
538#121C22×D7314yes—
539C4×Q8—734no—
540C4×Q8—1462no—
541C4×D4—734no—
542C4×D4—734no—
543C4×D4—734no—
544C4×D4—1462no—
545C4×D4—1468no—
546C4×D4—1468no—
547#117—734no—
548#117—1462no—
549C2×C4⋊C4—731no—
550C2×C4⋊C4—731no—
551C2×C4⋊C4—731no—
552C2×C4⋊C4—734no—
553C2×C4⋊C4—1461no—
554C2×C4⋊C4—1461no—
555C2×C4⋊C4—1461no—
556C2×C4⋊C4—1461no—
557C2×C4⋊C4—1461no—
558C2×C4⋊C4—1462no—
559C2×C4⋊C4C22×D7311yescharacteristic
560C2×C4⋊C4C22×D7311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—731no—
564C2×C22⋊C4—731no—
565C2×C22⋊C4—1461no—
566C2×C22⋊C4—1461no—
567C2×C22⋊C4—1461no—
568C2×C22⋊C4—1461no—
569C2×C22⋊C4—1461no—
570C2×C22⋊C4—1461no—
571C2×C42—731no—
572C2×C42—1461no—
573C2×C42—1461no—
574#107C22×D7314yes—
575#106—734no—
576#106—734no—
577C4⋊C8—734no—
578#103—734no—
579#103—734no—
580#103—734no—
581#103—734no—
582#103—734no—
583#103—734no—
584#102—734no—
585#102—734no—
586#102C22×D7314yes—
587#102C22×D7314yes—
588C22⋊C8—734no—
589C22⋊C8—734no—
590C4×C8—734no—
591C24—21no—
592C24—21no—
593C24—731no—
594C24D4×D7311yescharacteristic
595#41—2924no—
596#41—2928no—
597#41—1468no—
598C2×Q8—2928no—
599C2×Q8—2924no—
600C2×Q8—2924no—
601C2×Q8—734no—
602C2×Q8—732no—
603C2×Q8—732no—
604C2×Q8—1468no—
605C2×Q8—1462no—
606C2×Q8—1462no—
607C2×Q8—1461no—
608C2×Q8—1464no—
609C2×Q8—1461no—
610C2×Q8—1462no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—2924no—
622C2×D4—5842no—
623C2×D4—734no—
624C2×D4—1464no—
625C2×D4—1464no—
626C2×D4—1464no—
627C2×D4C23×D7312yes—
628C2×D4C23×D7312yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—2924no—
634C22×C4—2924no—
635C22×C4—5842no—
636C22×C4—5842no—
637C22×C4—731no—
638C22×C4—731no—
639C22×C4—731no—
640C22×C4—732no—
641C22×C4—732no—
642C22×C4—1464no—
643C22×C4—1464no—
644C22×C4—1461no—
645C22×C4—1461no—
646C22×C4—1461no—
647C22×C4—1464no—
648C22×C4—1464no—
649C22×C4—1461no—
650C22×C4—1462no—
651C22×C4—1462no—
652C22×C4D4×D7312yes—
653C22×C4D4×D7311yescharacteristic
654C22×C4C23×D7312yes—
655C22×C4C23×D7311yescharacteristic
656SD16—2924no—
657SD16—1468no—
658D8—44no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—44no—
662C2×C8—2924no—
663C2×C8—732no—
664C2×C8—732no—
665C2×C8—1462no—
666C2×C8—1462no—
667C2×C8C23×D7312yes—
668C2×C8C23×D7312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—734no—
672C4⋊C4—732no—
673C4⋊C4—732no—
674C4⋊C4—1464no—
675C4⋊C4—1464no—
676C4⋊C4—1464no—
677C4⋊C4—1464no—
678C4⋊C4—1461no—
679C4⋊C4—1461no—
680C4⋊C4—1464no—
681C4⋊C4C23×D7312yes—
682C4⋊C4C23×D7312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—734no—
686C22⋊C4—734no—
687C22⋊C4—1464no—
688C22⋊C4—1464no—
689C22⋊C4—1464no—
690C22⋊C4—1464no—
691C22⋊C4—1464no—
692C22⋊C4—1464no—
693C42—732no—
694C42—732no—
695C42—1464no—
696C42—1464no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—732no—
708C23—1462no—
709C23—1462no—
710C23—1462no—
711C23#1455661014yes—
712C23C2×D4×D7312yes—
713C23C2×D4×D7311yescharacteristic
714Q8—2928no—
715Q8—2922no—
716Q8—734no—
717Q8—1462no—
718Q8—1462no—
719Q8—1462no—
720Q8—1464no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—48no—
726D4—48no—
727D4—42no—
728D4—42no—
729D4—2928no—
730D4—5844no—
731D4—1468no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—2922no—
741C2×C4—2922no—
742C2×C4—2922no—
743C2×C4—2928no—
744C2×C4—2928no—
745C2×C4—5844no—
746C2×C4—5844no—
747C2×C4—732no—
748C2×C4—732no—
749C2×C4—732no—
750C2×C4—1462no—
751C2×C4—1462no—
752C2×C4—1462no—
753C2×C4—1462no—
754C2×C4—1462no—
755C2×C4—1462no—
756C2×C4—1464no—
757C2×C4—1462no—
758C2×C4—1462no—
759C2×C4—1462no—
760C2×C4—1464no—
761C2×C4C2×D4×D7312yes—
762C2×C4C2×D4×D7311yescharacteristic
763C2×C4#41×D7312yes—
764C2×C4#1455663612yes—
765C2×C4C24×D7311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1462no—
769C8—1462no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—84no—
781C22—2924no—
782C22—1462no—
783C22—1462no—
784C22—1462no—
785C22#1798922612yes—
786C22C2×#1455661014yes—
787C22C2×#1455661012yes—
788C22#1798939412yes—
789C22C22×D4×D7311yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—2922no—
794C4—2922no—
795C4—2922no—
796C4—1462no—
797C4—1464no—
798C4—1462no—
799C4—1462no—
800C4#1798922612yes—
801C4C2×#41×D7311yescharacteristic
802C4C2×#1455663611yescharacteristic
803C2—24no—
804C2—82no—
805C2—82no—
806C2—2922no—
807C2#2262183914yesdirect product factor
808C2C2×#1798922611yescharacteristic
809C2C22×#1455661011yescharacteristic
810C2C2×#1798939411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#466×C73C2
socleC23×C73C22×D4
hypercenterC2×#466D73
hypocenterC73C2×#3301
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#17989289C2semidirect
2. C2×#17989243C2semidirect
3. #22621839C2direct (N × H)
4. C2×#17988940C2semidirect
5. C2×#17988903C2semidirect
6. C2×#17988930C2semidirect
7. C2×#17988893C2semidirect
8. C2×#17988815C2semidirect
9. C2×#17988800C2semidirect
10. C2×#17988729C2semidirect
11. C2×#17988725C2semidirect
12. C2×#17988678C2semidirect
13. C2×C8×C22⋊D73C2semidirect
14. C2×#17988580C2semidirect
15. C22×#14556516C2semidirect
16. C2×#466×C73C2semidirect
23. #17989289C22semidirect
25. #17989243C22semidirect
43. #17988940C22semidirect
44. #17988930C22semidirect
45. #17988903C22semidirect
46. #17988893C22semidirect
47. #17988815C22semidirect
48. #17988800C22semidirect
49. #17988729C22semidirect
50. #17988725C22semidirect
51. #17988678C22semidirect
52. C8×C22⋊D73C22semidirect
56. #17988580C22semidirect
61. C2×#14556516C22semidirect
73. #466×C73C22semidirect
401. C2×C73#3301semidirect
413. C2×#466D73semidirect
422. C73C2×#3301semidirect
457. #466C2×D73semidirect
807. C2#22621839direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892892
C2×#179892432
#226218392
C2×#179889402
C2×#179889032
C2×#179889302
C2×#179888932
C2×#179888152
C2×#179888002
C2×#179887292
C2×#179887252
C2×#179886782
C2×C8×C22⋊D732
C2×#179885802
C22×#145565162
C2×#466×C732
C2×#330173