Finite Group Databasebeta

← C2×#22623015 #33967010

Subgroups — C2×#22623015 #33967010

Order 18688.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989322C211yesmaximal, characteristic, complemented
2#22623015C2116yesmaximal, direct product factor
3C2×#17988977C211yesmaximal, characteristic, complemented
4C2×#17988974C211yesmaximal, characteristic, complemented
5C2×#17988969C211yesmaximal, characteristic, complemented
6C2×#17988809C211yesmaximal, characteristic, complemented
7C2×#17988806C211yesmaximal, characteristic, complemented
8C2×#17988802C211yesmaximal, characteristic, complemented
9C2×#17988799C211yesmaximal, characteristic, complemented
10C2×#17988782C211yesmaximal, characteristic, complemented
11C2×#17988779C211yesmaximal, characteristic, complemented
12C2×#17988718C211yesmaximal, characteristic, complemented
13C2×#17988687C211yesmaximal, characteristic, complemented
14C2×#17988685C211yesmaximal, characteristic, complemented
15C2×C4×#11924013C211yesmaximal, characteristic, complemented
16C2×#559×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924016C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21C22×#11924015C2211yescharacteristic
22C22×#11924013C2211yescharacteristic
23C22×#11924013C2211yescharacteristic
24C22×#11924013C2211yescharacteristic
25C22×#11924013C2211yescharacteristic
26#17989322—24no—
27#17989322C2218yescomplemented
28C2×#14556588C2211yescharacteristic
29C2×#14556580—21no—
30C2×#14556579C2211yescharacteristic
31C2×#14556579C2211yescharacteristic
32C2×#14556576—21no—
33C2×#14556576—21no—
34C2×C4×Dic146C2211yescharacteristic
35C2×C4×D292C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C2×#14556553—21no—
38#17988977C2218yescomplemented
39#17988974C2218yescomplemented
40#17988969C2218yescomplemented
41#17988809C2218yescomplemented
42#17988806C2218yescomplemented
43#17988802C2218yescomplemented
44#17988799C2218yescomplemented
45#17988782C2218yescomplemented
46#17988779C2218yescomplemented
47#17988718C2218yescomplemented
48#17988687C2218yescomplemented
49#17988685C2218yescomplemented
50C4×#11924013C2218yescomplemented
51C2×#14556524C2211yescharacteristic
52C2×C4⋊#10596831C2211yescharacteristic
53C2×C4⋊#10596831C2211yescharacteristic
54C2×C4⋊#10596831C2211yescharacteristic
55C2×#14556515C2211yescharacteristic
56C2×#14556514C2211yescharacteristic
57C2×#14556512C2211yescharacteristic
58C2×#14556512C2211yescharacteristic
59C2×#14556511C2211yescharacteristic
60C2×#14556511C2211yescharacteristic
61C2×#14556502C2211yescharacteristic
62C2×#14556502C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64#559×C73—24no—
65#559×C73C2218yescomplemented
66C2×#127×C73C2211yescharacteristic
67C2×#124×C73—21no—
68C2×#124×C73C2211yescharacteristic
69C2×#124×C73C2211yescharacteristic
70C2×#123×C73—21no—
71C2×#123×C73—21no—
72C2×C4×Q8×C73C2211yescharacteristic
73C2×C4×Q8×C73C2211yescharacteristic
74C2×C4×D4×C73—21no—
75C2×C4×D4×C73C2211yescharacteristic
76C2×C4×D4×C73C2211yescharacteristic
77C22×Dic146C2311yescharacteristic
78C22×D292—21no—
79C22×D292—21no—
80C22×D292C2311yescharacteristic
81C22×D292C2311yescharacteristic
82C22×C4×D73—21no—
83C22×C4×D73—21no—
84C2×#11924018—42no—
85C2×#11924018C2314yes—
86C2×#11924016—24no—
87C2×#11924016—42no—
88C2×#11924016C2314yes—
89C2×#11924016C2314yes—
90C2×#11924015—24no—
91C2×#11924015—42no—
92C2×#11924015C2314yes—
93C2×#11924015C2314yes—
94C2×#11924013—24no—
95C2×#11924013—42no—
96C2×#11924013—42no—
97C2×#11924013—42no—
98C2×#11924013C2314yes—
99C2×#11924013C2314yes—
100C2×#11924013C2314yes—
101C2×#11924013C2314yes—
102C22×#10596831C2311yescharacteristic
103C22×#10596831C2311yescharacteristic
104C22×#10596831C2311yescharacteristic
105C22×#10596831C2311yescharacteristic
106#14556588—22no—
107#14556588C2314yes—
108#14556580—28no—
109#14556579—22no—
110#14556579—22no—
111#14556579C2314yes—
112#14556579C2314yes—
113#14556576—28no—
114#14556576—28no—
115C4×Dic146—22no—
116C4×Dic146C2314yes—
117C4×D292—22no—
118C4×D292—22no—
119C4×D292C2314yes—
120C4×D292C2314yes—
121#14556553—28no—
122C2×C4⋊Dic73C2311yescharacteristic
123C2×#11924007—21no—
124C2×#11924005—21no—
125C2×#11924005—21no—
126C2×#11924005—21no—
127C2×#11924005—21no—
128C2×#11924005—21no—
129C2×#11924005—21no—
130C2×C4×Dic73—21no—
131#14556524C2314yes—
132C4⋊#10596831C2314yes—
133C4⋊#10596831C2314yes—
134C4⋊#10596831C2314yes—
135#14556515C2314yes—
136#14556514C2314yes—
137#14556512C2314yes—
138#14556512C2314yes—
139#14556511C2314yes—
140#14556511C2314yes—
141#14556502C2314yes—
142#14556502C2314yes—
143C4×#10596831C2314yes—
144C22×Q8×C73D411yescharacteristic
145C22×Q8×C73C2311yescharacteristic
146C22×D4×C73—21no—
147C22×D4×C73—21no—
148C22×D4×C73C2311yescharacteristic
149C22×D4×C73C2311yescharacteristic
150C23×C4×C73—21no—
151C23×C4×C73—21no—
152#127×C73—22no—
153#127×C73C2314yes—
154#124×C73—28no—
155#124×C73—22no—
156#124×C73—22no—
157#124×C73C2314yes—
158#124×C73C2314yes—
159#123×C73—28no—
160#123×C73—28no—
161C4×Q8×C73—22no—
162C4×Q8×C73D414yes—
163C4×Q8×C73C2314yes—
164C4×Q8×C73C2314yes—
165C4×D4×C73—28no—
166C4×D4×C73—22no—
167C4×D4×C73—22no—
168C4×D4×C73C2314yes—
169C4×D4×C73C2314yes—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73D411yescharacteristic
172C2×C4⋊C4×C73D411yescharacteristic
173C2×C4⋊C4×C73D411yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73—21no—
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180C2×C22⋊C4×C73—21no—
181C2×C42×C73—21no—
182C2×C42×C73C2311yescharacteristic
183C2×C42×C73C2311yescharacteristic
184C2×C42×C73C2311yescharacteristic
185C23×D73—21no—
186C23×D73—21no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—21no—
190C2×Dic146C2412yes—
191C2×D292—22no—
192C2×D292—22no—
193C2×D292—22no—
194C2×D292—22no—
195C2×D292—24no—
196C2×D292—21no—
197C2×D292—21no—
198C2×D292—24no—
199C2×D292—44no—
200C2×D292—82no—
201C2×D292C2412yes—
202C2×D292C2412yes—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C2×C4×D73—24no—
206C2×C4×D73—24no—
207C2×C4×D73—82no—
208C2×C4×D73—82no—
209#11924018—44no—
210#11924016—28no—
211#11924016—44no—
212#11924015—28no—
213#11924015—44no—
214#11924013—28no—
215#11924013—44no—
216#11924013—44no—
217#11924013—44no—
218C2×#10596831—22no—
219C2×#10596831—22no—
220C2×#10596831—22no—
221C2×#10596831#4114yes—
222C2×#10596831C2412yes—
223C2×#10596831C2412yes—
224C2×#10596831C2412yes—
225C2×#10596831C2412yes—
226C4⋊Dic73—21no—
227C4⋊Dic73C2412yes—
228#11924007—24no—
229#11924005—24no—
230#11924005—24no—
231#11924005—24no—
232#11924005—24no—
233#11924005—24no—
234#11924005—24no—
235C4×Dic73—24no—
236C24×C73—21no—
237C24×C73—21no—
238C2×Q8×C73—21no—
239C2×Q8×C73—22no—
240C2×Q8×C73—22no—
241C2×Q8×C73—42no—
242C2×Q8×C73C2×D414yes—
243C2×Q8×C73C2412yes—
244C2×D4×C73—21no—
245C2×D4×C73—21no—
246C2×D4×C73—24no—
247C2×D4×C73—24no—
248C2×D4×C73—22no—
249C2×D4×C73—22no—
250C2×D4×C73—22no—
251C2×D4×C73—22no—
252C2×D4×C73—44no—
253C2×D4×C73—82no—
254C2×D4×C73C2412yes—
255C2×D4×C73C2412yes—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—24no—
259C22×C4×C73—24no—
260C22×C4×C73—82no—
261C22×C4×C73—82no—
262C22×C4×C73C2×D411yescharacteristic
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2×D411yescharacteristic
266C22×C4×C73C2×D411yescharacteristic
267C22×C4×C73C2×D411yescharacteristic
268C22×C4×C73C2411yescharacteristic
269C4⋊C4×C73—24no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73C2×D414yes—
272C4⋊C4×C73C2×D414yes—
273C4⋊C4×C73C2×D414yes—
274C4⋊C4×C73C2412yes—
275C22⋊C4×C73—24no—
276C22⋊C4×C73—24no—
277C22⋊C4×C73—24no—
278C22⋊C4×C73—24no—
279C22⋊C4×C73—24no—
280C22⋊C4×C73—24no—
281C42×C73—24no—
282C42×C73C2×D412yes—
283C42×C73C2×D412yes—
284C42×C73C2×D412yes—
285C42×C73C2412yes—
286C42×C73C2412yes—
287C42×C73C2412yes—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73—42no—
291C23×C73—42no—
292C23×C73—42no—
293C23×C73—42no—
294C23×C73—42no—
295C23×C73—42no—
296C23×C73C22×D411yescharacteristic
297C22×D73—22no—
298C22×D73—22no—
299C22×D73—42no—
300C22×D73—42no—
301C22×D73—42no—
302C22×D73—42no—
303C22×D73—42no—
304C22×D73—42no—
305Q8×C73—22no—
306Q8×C73—22no—
307Q8×C73—44no—
308Q8×C73—42no—
309D4×C73—22no—
310D4×C73—22no—
311D4×C73—22no—
312D4×C73—22no—
313D4×C73—48no—
314D4×C73—42no—
315D4×C73—42no—
316D4×C73—84no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—42no—
326C2×C4×C73—42no—
327C2×C4×C73—84no—
328C2×C4×C73—84no—
329C2×C4×C73C22×D412yes—
330C2×C4×C73C22×D412yes—
331C2×C4×C73C22×D412yes—
332C2×C4×C73C22×D412yes—
333C2×C4×C73C22×D412yes—
334C2×C4×C73C22×D412yes—
335C2×C4×C73C22×D411yescharacteristic
336C2×C4×C73C2×#4112yes—
337C2×C4×C73H(5,𝔽2)12yes—
338C2×C4×C73C2511yescharacteristic
339C2×Dic73—22no—
340C2×Dic73—22no—
341C2×Dic73—42no—
342C2×Dic73—42no—
343D292—22no—
344D292—22no—
345D292—22no—
346D292—22no—
347D292—48no—
348D292—42no—
349D292—42no—
350D292—84no—
351C4×D73—84no—
352C4×D73—84no—
353Dic146—22no—
354Dic146—22no—
355Dic146—42no—
356#10596831—22no—
357#10596831—22no—
358#10596831—22no—
359#10596831C2×#4114yes—
360C22×C73—42no—
361C22×C73—42no—
362C22×C73—42no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73—42no—
366C22×C73—84no—
367C22×C73—84no—
368C22×C73#55012yes—
369C22×C73#57512yes—
370C22×C73#57612yes—
371C22×C73C23×D411yescharacteristic
372C2×D73—42no—
373C2×D73—42no—
374C2×D73—42no—
375C2×D73—42no—
376C2×D73—42no—
377C2×D73—42no—
378C2×D73—84no—
379C2×D73—84no—
380C4×C73—22no—
381C4×C73—22no—
382C4×C73—22no—
383C4×C73—22no—
384C4×C73—22no—
385C4×C73—22no—
386C4×C73—42no—
387C4×C73—42no—
388C4×C73#55012yes—
389C4×C73C22×#4111yescharacteristic
390C4×C73C2×H(5,𝔽2)11yescharacteristic
391Dic73—42no—
392Dic73—42no—
393C2×#3403—731nomaximal, Sylow
394C2×C73—82no—
395C2×C73—82no—
396C2×C73#340314yescomplemented
397C2×C73C2×#55011yescharacteristic
398C2×C73C2×#57511yescharacteristic
399C2×C73C2×#57611yescharacteristic
400D73—82no—
401D73—82no—
402C2×#559—731no—
403C2×#559D7311yescharacteristic, complemented
404#3403—7316no—
405C2×#496—731no—
406C2×#496—731no—
407C2×#495—731no—
408C2×#464—731no—
409C2×#464—731no—
410C2×#463—731no—
411C2×#463—731no—
412C2×#459—731no—
413C2×#459—731no—
414C2×#446—731no—
415C2×#440—731no—
416C2×#440—731no—
417C2×C4×D8—731no—
418C73C2×#340311yescharacteristic, complemented, Sylow
419C22×Q16—731no—
420C22×SD16—731no—
421C22×SD16—731no—
422C22×SD16—731no—
423C22×SD16—731no—
424C22×D8—731no—
425C22×D8—731no—
426C22×D8—731no—
427C22×D8—731no—
428#559—24no—
429#559—738no—
430#559—1464no—
431#559C2×D7318yescomplemented
432C2×#127—731no—
433C2×#127C2×D7311yescharacteristic
434C2×#124—21no—
435C2×#124—731no—
436C2×#124—731no—
437C2×#124—1461no—
438C2×#124C2×D7311yescharacteristic
439C2×#124C2×D7311yescharacteristic
440C2×#123—21no—
441C2×#123—21no—
442C2×#123—1461no—
443C2×#123—1461no—
444C2×C4×Q8—731no—
445C2×C4×Q8C2×D7311yescharacteristic
446C2×C4×Q8C2×D7311yescharacteristic
447C2×C4×D4—21no—
448C2×C4×D4—731no—
449C2×C4×D4—731no—
450C2×C4×D4—1461no—
451C2×C4×D4C2×D7311yescharacteristic
452C2×C4×D4C2×D7311yescharacteristic
453#496—738no—
454#496—738no—
455#495—738no—
456#464—738no—
457#464—738no—
458#463—738no—
459#463—738no—
460#459—738no—
461#459—738no—
462#446—738no—
463#440—738no—
464#440—738no—
465C4×D8—738no—
466C2×#107—731no—
467C2×C4⋊C8—731no—
468C2×C4⋊C8—731no—
469C2×C4⋊C8—731no—
470C2×#103—731no—
471C2×#103—731no—
472C2×#102—731no—
473C2×#102—731no—
474C2×#102—731no—
475C2×#102—731no—
476C2×#97—731no—
477C2×#97—731no—
478C2×C4×C8—731no—
479C22×Q8—731no—
480C22×Q8C22⋊D7311yescharacteristic
481C22×Q8C22×D7311yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—731no—
485C22×D4—731no—
486C22×D4—1461no—
487C22×D4—1461no—
488C22×D4C22×D7311yescharacteristic
489C22×D4C22×D7311yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—1461no—
493C23×C4—1461no—
494C2×Q16—2922no—
495C2×Q16—734no—
496C2×SD16—2922no—
497C2×SD16—2922no—
498C2×SD16—734no—
499C2×SD16—734no—
500C2×SD16—734no—
501C2×SD16—734no—
502C2×SD16—1464no—
503C2×SD16—1464no—
504C2×D8—2922no—
505C2×D8—2922no—
506C2×D8—2922no—
507C2×D8—734no—
508C2×D8—734no—
509C2×D8—734no—
510C2×D8—734no—
511C2×D8—1464no—
512C22×C8—731no—
513C22×C8—731no—
514C22×C8—731no—
515C22×C8—731no—
516#127—22no—
517#127—734no—
518#127—1462no—
519#127C22×D7314yes—
520#124—28no—
521#124—22no—
522#124—22no—
523#124—734no—
524#124—734no—
525#124—1468no—
526#124—1462no—
527#124—1462no—
528#124C22×D7314yes—
529#124C22×D7314yes—
530#123—28no—
531#123—28no—
532#123—1468no—
533#123—1468no—
534C4×Q8—22no—
535C4×Q8—734no—
536C4×Q8—1462no—
537C4×Q8C22⋊D7314yes—
538C4×Q8C22×D7314yes—
539C4×Q8C22×D7314yes—
540C4×D4—28no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—734no—
544C4×D4—734no—
545C4×D4—1468no—
546C4×D4—1462no—
547C4×D4—1462no—
548C4×D4C22×D7314yes—
549C4×D4C22×D7314yes—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—731no—
552C2×C4⋊C4—1461no—
553C2×C4⋊C4C22⋊D7311yescharacteristic
554C2×C4⋊C4C22⋊D7311yescharacteristic
555C2×C4⋊C4C22⋊D7311yescharacteristic
556C2×C4⋊C4C22×D7311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—1461no—
564C2×C22⋊C4—1461no—
565C2×C22⋊C4—1461no—
566C2×C22⋊C4—1461no—
567C2×C22⋊C4—1461no—
568C2×C22⋊C4—1461no—
569C2×C42—21no—
570C2×C42—1461no—
571C2×C42C22×D7311yescharacteristic
572C2×C42C22×D7311yescharacteristic
573C2×C42C22×D7311yescharacteristic
574#107—734no—
575C4⋊C8—734no—
576C4⋊C8—734no—
577C4⋊C8—734no—
578#103—734no—
579#103—734no—
580#102—734no—
581#102—734no—
582#102—734no—
583#102—734no—
584#97—734no—
585#97—734no—
586C4×C8—734no—
587C24—21no—
588C24—21no—
589C24—1461no—
590C24—1461no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—42no—
595C2×Q8—732no—
596C2×Q8—1462no—
597C2×Q8—1462no—
598C2×Q8—1461no—
599C2×Q8C2×C22⋊D7314yes—
600C2×Q8C23×D7312yes—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—44no—
610C2×D4—82no—
611C2×D4—2924no—
612C2×D4—5842no—
613C2×D4—732no—
614C2×D4—732no—
615C2×D4—1464no—
616C2×D4—1461no—
617C2×D4—1461no—
618C2×D4—1464no—
619C2×D4—1462no—
620C2×D4—1462no—
621C2×D4—1462no—
622C2×D4—1462no—
623C2×D4C23×D7312yes—
624C2×D4C23×D7312yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—82no—
630C22×C4—82no—
631C22×C4—5842no—
632C22×C4—5842no—
633C22×C4—1461no—
634C22×C4—1461no—
635C22×C4—1464no—
636C22×C4—1464no—
637C22×C4C2×C22⋊D7311yescharacteristic
638C22×C4C2×C22⋊D7311yescharacteristic
639C22×C4C2×C22⋊D7311yescharacteristic
640C22×C4C2×C22⋊D7311yescharacteristic
641C22×C4C2×C22⋊D7311yescharacteristic
642C22×C4C2×C22⋊D7311yescharacteristic
643C22×C4C23×D7311yescharacteristic
644Q16—2924no—
645SD16—2924no—
646SD16—2924no—
647SD16—1468no—
648SD16—1468no—
649D8—2924no—
650D8—2924no—
651D8—2924no—
652D8—1468no—
653C2×C8—734no—
654C2×C8—732no—
655C2×C8—732no—
656C2×C8—732no—
657C2×C8—732no—
658C2×C8—1462no—
659C2×C8—1462no—
660C2×C8—1462no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—732no—
664C4⋊C4—1464no—
665C4⋊C4—1461no—
666C4⋊C4C2×C22⋊D7314yes—
667C4⋊C4C2×C22⋊D7314yes—
668C4⋊C4C2×C22⋊D7314yes—
669C4⋊C4C23×D7312yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—1464no—
677C22⋊C4—1464no—
678C22⋊C4—1464no—
679C22⋊C4—1464no—
680C22⋊C4—1464no—
681C22⋊C4—1464no—
682C42—24no—
683C42—1464no—
684C42C2×C22⋊D7312yes—
685C42C2×C22⋊D7312yes—
686C42C2×C22⋊D7312yes—
687C42C23×D7312yes—
688C42C23×D7312yes—
689C42C23×D7312yes—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—2922no—
699C23—2922no—
700C23—2922no—
701C23—2922no—
702C23—2922no—
703C23—2922no—
704C23—1462no—
705C23—1462no—
706C23C22×C22⋊D7311yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—44no—
710Q8—42no—
711Q8—2922no—
712Q8—1462no—
713Q8—1462no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—2928no—
723D4—2922no—
724D4—2922no—
725D4—5844no—
726D4—1462no—
727D4—1462no—
728D4—1462no—
729D4—1462no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—2922no—
743C2×C4—2922no—
744C2×C4—5844no—
745C2×C4—5844no—
746C2×C4—1462no—
747C2×C4—1462no—
748C2×C4C22×C22⋊D7312yes—
749C2×C4C22×C22⋊D7312yes—
750C2×C4C22×C22⋊D7312yes—
751C2×C4C22×C22⋊D7312yes—
752C2×C4C22×C22⋊D7312yes—
753C2×C4C22×C22⋊D7312yes—
754C2×C4C22×C22⋊D7311yescharacteristic
755C2×C4#41×D7312yes—
756C2×C4#1455663712yes—
757C2×C4C24×D7311yescharacteristic
758C8—734no—
759C8—1462no—
760C8—1462no—
761C8—1462no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—2922no—
771C22—2922no—
772C22—2922no—
773C22—2922no—
774C22—2922no—
775C22—2922no—
776C22—5844no—
777C22—5844no—
778C22#1798925612yes—
779C22#1798938512yes—
780C22#1798939012yes—
781C22C23×C22⋊D7311yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—2922no—
791C4—2922no—
792C4#1798925612yes—
793C4C2×#41×D7311yescharacteristic
794C4C2×#1455663711yescharacteristic
795C2—82no—
796C2—82no—
797C2—5842no—
798C2—5842no—
799C2#2262301514yesdirect product factor
800C2C2×#1798925611yescharacteristic
801C2C2×#1798938511yescharacteristic
802C2C2×#1798939011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#559×C73C2
socleC23×C73C22×D4
hypercenterC2×#559D73
hypocenterC73C2×#3403
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#17989322C2semidirect
2. #22623015C2direct (N × H)
3. C2×#17988977C2semidirect
4. C2×#17988974C2semidirect
5. C2×#17988969C2semidirect
6. C2×#17988809C2semidirect
7. C2×#17988806C2semidirect
8. C2×#17988802C2semidirect
9. C2×#17988799C2semidirect
10. C2×#17988782C2semidirect
11. C2×#17988779C2semidirect
12. C2×#17988718C2semidirect
13. C2×#17988687C2semidirect
14. C2×#17988685C2semidirect
15. C2×C4×#11924013C2semidirect
16. C2×#559×C73C2semidirect
27. #17989322C22semidirect
38. #17988977C22semidirect
39. #17988974C22semidirect
40. #17988969C22semidirect
41. #17988809C22semidirect
42. #17988806C22semidirect
43. #17988802C22semidirect
44. #17988799C22semidirect
45. #17988782C22semidirect
46. #17988779C22semidirect
47. #17988718C22semidirect
48. #17988687C22semidirect
49. #17988685C22semidirect
50. C4×#11924013C22semidirect
65. #559×C73C22semidirect
396. C2×C73#3403semidirect
403. C2×#559D73semidirect
418. C73C2×#3403semidirect
431. #559C2×D73semidirect
799. C2#22623015direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893222
#226230152
C2×#179889772
C2×#179889742
C2×#179889692
C2×#179888092
C2×#179888062
C2×#179888022
C2×#179887992
C2×#179887822
C2×#179887792
C2×#179887182
C2×#179886872
C2×#179886852
C2×C4×#119240132
C2×#559×C732
C2×#340373