Finite Group Databasebeta

← C2×#22622979 #33966971

Subgroups — C2×#22622979 #33966971

Order 18688.

1970 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989320C211yesmaximal, characteristic
2C2×#17989312C211yesmaximal, characteristic, complemented
3#22622979C2116yesmaximal, direct product factor
4C2×#17988979C211yesmaximal, characteristic, complemented
5C2×#17988978C211yesmaximal, characteristic, complemented
6C2×#17988958C211yesmaximal, characteristic
7C2×#17988810C211yesmaximal, characteristic, complemented
8C2×#17988807C211yesmaximal, characteristic, complemented
9C2×#17988796C211yesmaximal, characteristic, complemented
10C2×#17988785C211yesmaximal, characteristic
11C2×#17988791C211yesmaximal, characteristic, complemented
12C2×#17988716C211yesmaximal, characteristic, complemented
13C2×#17988690C211yesmaximal, characteristic, complemented
14C2×#17988687C211yesmaximal, characteristic, complemented
15C2×#17988679C211yesmaximal, characteristic, complemented
16C2×#461×C73C211yesmaximal, characteristic, complemented
17C22×Dic292C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924017C2211yescharacteristic
21C22×#11924016C2211yescharacteristic
22C22×#11924015C2211yescharacteristic
23C22×#11924015C2211yescharacteristic
24#17989320—24no—
25#17989320C2218yes—
26#17989312—24no—
27#17989312C2218yescomplemented
28C2×#14556589C2211yescharacteristic
29C2×#14556589C2211yescharacteristic
30C2×#14556587C2211yescharacteristic
31C2×#14556582—21no—
32C2×#14556581—21no—
33C2×#14556581—21no—
34C2×#14556579C2211yescharacteristic
35C2×#14556578C2211yescharacteristic
36C2×#14556577—21no—
37C2×#14556574—21no—
38C2×#14556573—21no—
39C2×Q8×Dic73C2211yescharacteristic
40C2×Q8×Dic73C2211yescharacteristic
41C2×C4×Dic146C2211yescharacteristic
42C2×C4×Dic146C2211yescharacteristic
43C2×#14556556—21no—
44C2×#14556556C2211yescharacteristic
45C2×#14556553C2211yescharacteristic
46C2×C4×C22⋊D73—21no—
47#17988979C2218yescomplemented
48#17988978C2218yescomplemented
49#17988958C2218yes—
50#17988810C2218yescomplemented
51#17988807C2218yescomplemented
52#17988796C2218yescomplemented
53#17988791C2218yescomplemented
54#17988785C2218yes—
55#17988716C2218yescomplemented
56#17988690C2218yescomplemented
57#17988687C2218yescomplemented
58#17988679C2218yescomplemented
59C2×#14556524C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556502C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C22×SD16×C73C2211yescharacteristic
71C2×C4⋊Q8×C73C2211yescharacteristic
72C2×C4×D4×C73C2211yescharacteristic
73#461×C73C2218yescomplemented
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C22×Dic146D411yescharacteristic
78C22×Dic146C2311yescharacteristic
79C22×Dic146C2311yescharacteristic
80C22×D292C2311yescharacteristic
81C22×C22⋊D73—21no—
82C22×C22⋊D73—21no—
83C22×C4×D73—21no—
84C2×Dic292—42no—
85C2×Dic292C2314yes—
86C2×#11924018—24no—
87C2×#11924018—42no—
88C2×#11924018C2314yes—
89C2×#11924018C2314yes—
90C2×#11924017—42no—
91C2×#11924017C2314yes—
92C2×#11924016—24no—
93C2×#11924016C2314yes—
94C2×#11924015—24no—
95C2×#11924015—42no—
96C2×#11924015C2314yes—
97C2×#11924015C2314yes—
98C22×#10596831C2311yescharacteristic
99C22×#10596831C2311yescharacteristic
100#14556589—22no—
101#14556589—22no—
102#14556589C2314yes—
103#14556589C2314yes—
104#14556587—22no—
105#14556587C2314yes—
106#14556582—28no—
107#14556581—28no—
108#14556581—28no—
109#14556579—22no—
110#14556579C2314yes—
111#14556578—22no—
112#14556578C2314yes—
113#14556577—28no—
114#14556574—28no—
115#14556573—28no—
116Q8×Dic73—22no—
117Q8×Dic73—22no—
118Q8×Dic73C2314yes—
119Q8×Dic73C2314yes—
120C4×Dic146—22no—
121C4×Dic146D414yes—
122C4×Dic146C2314yes—
123C4×Dic146C2314yes—
124#14556556—28no—
125#14556556—22no—
126#14556556C2314yes—
127#14556553—22no—
128#14556553C2314yes—
129C4×C22⋊D73—28no—
130C2×C4⋊Dic73—21no—
131C2×C4⋊Dic73—21no—
132C2×C4⋊Dic73D411yescharacteristic
133C2×C4⋊Dic73C2311yescharacteristic
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×#11924007D411yescharacteristic
141C2×#11924007D411yescharacteristic
142C2×C22⋊Dic73—21no—
143C2×C22⋊Dic73—21no—
144C2×#11924005—21no—
145C2×#11924005—21no—
146C2×#11924005—21no—
147C2×C4×Dic73—21no—
148C2×C4×Dic73—21no—
149C2×C4×Dic73—21no—
150C2×C4×Dic73—21no—
151C2×C4×Dic73C2311yescharacteristic
152C2×C4×Dic73C2311yescharacteristic
153#14556524C2314yes—
154#14556520C2314yes—
155#14556520C2314yes—
156#14556516C2314yes—
157#14556514C2314yes—
158#14556513C2314yes—
159#14556512C2314yes—
160#14556502C2314yes—
161#14556501C2314yes—
162C8×Dic73C2314yes—
163C22×Q8×C73C2311yescharacteristic
164C22×Q8×C73C2311yescharacteristic
165C22×D4×C73C2311yescharacteristic
166C23×C4×C73—21no—
167C2×SD16×C73—42no—
168C2×SD16×C73—42no—
169C2×SD16×C73C2314yes—
170C2×SD16×C73C2314yes—
171C22×C8×C73C2311yescharacteristic
172C22×C8×C73C2311yescharacteristic
173C4⋊Q8×C73—22no—
174C4⋊Q8×C73C2314yes—
175C4×D4×C73—22no—
176C4×D4×C73C2314yes—
177C2×C4⋊C4×C73—21no—
178C2×C4⋊C4×C73—21no—
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C22⋊C4×C73—21no—
181C2×C42×C73C2311yescharacteristic
182C4⋊C8×C73C2314yes—
183#103×C73C2314yes—
184#103×C73C2314yes—
185C23×D73—21no—
186C2×Dic146—24no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—21no—
192C2×Dic146—21no—
193C2×Dic146C2×D414yes—
194C2×Dic146C2412yes—
195C2×Dic146C2412yes—
196C2×D292—22no—
197C2×D292—22no—
198C2×D292—21no—
199C2×D292C2412yes—
200C2×C22⋊D73—24no—
201C2×C22⋊D73—24no—
202C2×C22⋊D73—44no—
203C2×C22⋊D73—82no—
204C22×Dic73—21no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73C2×D411yescharacteristic
208C22×Dic73C2×D411yescharacteristic
209C22×Dic73C2×D411yescharacteristic
210C22×Dic73C2×D411yescharacteristic
211C2×C4×D73—24no—
212C2×C4×D73—82no—
213Dic292—44no—
214#11924018—28no—
215#11924018—44no—
216#11924017—44no—
217#11924016—28no—
218#11924015—28no—
219#11924015—44no—
220C2×#10596831—22no—
221C2×#10596831#4114yes—
222C2×#10596831C2412yes—
223C2×#10596831C2412yes—
224C4⋊Dic73—21no—
225C4⋊Dic73—24no—
226C4⋊Dic73—24no—
227C4⋊Dic73C2×D414yes—
228C4⋊Dic73C2412yes—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007C2×D414yes—
236#11924007C2×D414yes—
237C22⋊Dic73—24no—
238C22⋊Dic73—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005—24no—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C4×Dic73—24no—
246C4×Dic73C2×D412yes—
247C4×Dic73C2×D412yes—
248C4×Dic73C2412yes—
249C4×Dic73C2412yes—
250C24×C73—21no—
251C2×Q8×C73—21no—
252C2×Q8×C73—21no—
253C2×Q8×C73—22no—
254C2×Q8×C73—22no—
255C2×Q8×C73—22no—
256C2×Q8×C73—22no—
257C2×Q8×C73C2412yes—
258C2×Q8×C73C2412yes—
259C2×D4×C73—21no—
260C2×D4×C73—22no—
261C2×D4×C73—22no—
262C2×D4×C73C2412yes—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—24no—
267C22×C4×C73—82no—
268C22×C4×C73C2×D411yescharacteristic
269C22×C4×C73C2×D411yescharacteristic
270C22×C4×C73C2411yescharacteristic
271SD16×C73—44no—
272SD16×C73—44no—
273C2×C8×C73—22no—
274C2×C8×C73—22no—
275C2×C8×C73C2412yes—
276C2×C8×C73C2412yes—
277C4⋊C4×C73—24no—
278C4⋊C4×C73—24no—
279C4⋊C4×C73—21no—
280C4⋊C4×C73C2412yes—
281C22⋊C4×C73—24no—
282C42×C73C2×D412yes—
283C42×C73C2412yes—
284C23×C73—22no—
285C23×C73—42no—
286C23×C73—42no—
287C23×C73—42no—
288C23×C73C22×D411yescharacteristic
289C22×D73—22no—
290C22×D73—42no—
291C22×D73—42no—
292C22×D73—42no—
293Q8×C73—22no—
294Q8×C73—22no—
295Q8×C73—22no—
296Q8×C73—22no—
297Q8×C73—42no—
298Q8×C73—42no—
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—42no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—42no—
308C2×C4×C73—42no—
309C2×C4×C73—42no—
310C2×C4×C73—84no—
311C2×C4×C73C22×D412yes—
312C2×C4×C73C22×D412yes—
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C2×#4112yes—
315C2×C4×C73H(5,𝔽2)12yes—
316C2×C4×C73C2511yescharacteristic
317C22⋊D73—48no—
318C22⋊D73—84no—
319C2×Dic73—22no—
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#13714yes—
329C2×Dic73C22×D412yes—
330C2×Dic73C22×D412yes—
331C2×Dic73C22×D412yes—
332C2×Dic73C22×D412yes—
333D292—22no—
334D292—22no—
335D292—42no—
336C4×D73—84no—
337Dic146—28no—
338Dic146—22no—
339Dic146—22no—
340Dic146—22no—
341Dic146—22no—
342Dic146—42no—
343Dic146—42no—
344C8×C73—22no—
345C8×C73—22no—
346#10596831—22no—
347#10596831C2×#4114yes—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—84no—
352C22×C73#55012yes—
353C22×C73C2×#13712yes—
354C22×C73#57712yes—
355C22×C73C23×D411yescharacteristic
356C2×D73—42no—
357C2×D73—42no—
358C2×D73—42no—
359C2×D73—84no—
360C4×C73—22no—
361C4×C73—22no—
362C4×C73—42no—
363C4×C73—42no—
364C4×C73—42no—
365C4×C73#55012yes—
366C4×C73C22×#4111yescharacteristic
367C4×C73C2×H(5,𝔽2)11yescharacteristic
368Dic73—22no—
369Dic73—22no—
370Dic73—22no—
371Dic73—42no—
372Dic73—42no—
373Dic73—42no—
374Dic73C2×#13714yes—
375C2×#3400—731nomaximal, Sylow
376C2×C73—82no—
377C2×C73#340014yescomplemented
378C2×C73C2×#55011yescharacteristic
379C2×C73C22×#13711yescharacteristic
380C2×C73C2×#57711yescharacteristic
381D73—82no—
382C2×#559—731no—
383C2×#557—731no—
384#3400—7316no—
385C2×#497—731no—
386C2×#497—731no—
387C2×#492—731no—
388C2×#464—731no—
389C2×#464—731no—
390C2×#462—731no—
391C2×#460—731no—
392C2×#461—731no—
393C2×#461D7311yescharacteristic, complemented
394C2×#446—731no—
395C2×#440—731no—
396C2×#440—731no—
397C2×C4×Q16—731no—
398C73C2×#340011yescharacteristic, complemented, Sylow
399C22×Q16—731no—
400C22×Q16—731no—
401C22×Q16—731no—
402C22×SD16—731no—
403C22×SD16—731no—
404C22×SD16—731no—
405C22×SD16—731no—
406C22×SD16C2×D7311yescharacteristic
407C22×SD16C2×D7311yescharacteristic
408#559—738no—
409#559—1464no—
410#557—738no—
411#557—1464no—
412C2×C4⋊Q8—731no—
413C2×C4⋊Q8—731no—
414C2×C4⋊Q8C2×D7311yescharacteristic
415C2×#127—731no—
416C2×#125—1461no—
417C2×#125—1461no—
418C2×#125—1461no—
419C2×#124—731no—
420C2×#124—731no—
421C2×#124—1461no—
422C2×#123—1461no—
423C2×#123—1461no—
424C2×C4×Q8—731no—
425C2×C4×Q8—731no—
426C2×C4×Q8—731no—
427C2×C4×Q8—731no—
428C2×C4×Q8—731no—
429C2×C4×Q8—1461no—
430C2×C4×D4—731no—
431C2×C4×D4—1461no—
432C2×C4×D4C2×D7311yescharacteristic
433#497—738no—
434#497—738no—
435#492—738no—
436#464—738no—
437#464—738no—
438#462—738no—
439#461—738no—
440#461C2×D7318yescomplemented
441#460—738no—
442#446—738no—
443#440—738no—
444#440—738no—
445C4×Q16—738no—
446C2×#107—731no—
447C2×C4⋊C8—731no—
448C2×C4⋊C8—731no—
449C2×C4⋊C8C2×D7311yescharacteristic
450C2×#103—731no—
451C2×#103—731no—
452C2×#103C2×D7311yescharacteristic
453C2×#103C2×D7311yescharacteristic
454C2×#102—731no—
455C2×#102—731no—
456C2×#97—731no—
457C2×#97—731no—
458C2×C4×C8—731no—
459C22×Q8—731no—
460C22×Q8—731no—
461C22×Q8—731no—
462C22×Q8C22×D7311yescharacteristic
463C22×Q8C22×D7311yescharacteristic
464C22×D4—731no—
465C22×D4—1461no—
466C22×D4—1461no—
467C22×D4C22×D7311yescharacteristic
468C23×C4—21no—
469C23×C4—1461no—
470C2×Q16—2922no—
471C2×Q16—2922no—
472C2×Q16—734no—
473C2×Q16—734no—
474C2×Q16—734no—
475C2×Q16—1464no—
476C2×SD16—42no—
477C2×SD16—42no—
478C2×SD16—2922no—
479C2×SD16—2922no—
480C2×SD16—734no—
481C2×SD16—734no—
482C2×SD16—734no—
483C2×SD16—734no—
484C2×SD16—1464no—
485C2×SD16—1464no—
486C2×SD16C22×D7314yes—
487C2×SD16C22×D7314yes—
488C22×C8—731no—
489C22×C8—731no—
490C22×C8C22×D7311yescharacteristic
491C22×C8C22×D7311yescharacteristic
492C4⋊Q8—22no—
493C4⋊Q8—734no—
494C4⋊Q8—734no—
495C4⋊Q8—1462no—
496C4⋊Q8—1462no—
497C4⋊Q8C22×D7314yes—
498#127—734no—
499#127—1462no—
500#125—1468no—
501#125—1468no—
502#125—1468no—
503#124—734no—
504#124—734no—
505#124—1462no—
506#124—1468no—
507#124—1462no—
508#123—1468no—
509#123—1468no—
510C4×Q8—734no—
511C4×Q8—734no—
512C4×Q8—734no—
513C4×Q8—734no—
514C4×Q8—734no—
515C4×Q8—734no—
516C4×Q8—1462no—
517C4×Q8—1462no—
518C4×Q8—1462no—
519C4×Q8—1468no—
520C4×Q8—1462no—
521C4×D4—22no—
522C4×D4—734no—
523C4×D4—1462no—
524C4×D4—1468no—
525C4×D4C22×D7314yes—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C4⋊C4—731no—
531C2×C4⋊C4—731no—
532C2×C4⋊C4—1461no—
533C2×C4⋊C4—1461no—
534C2×C4⋊C4—1461no—
535C2×C4⋊C4—1461no—
536C2×C4⋊C4—1461no—
537C2×C4⋊C4—1461no—
538C2×C4⋊C4—1461no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4C22×D7311yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—1461no—
543C2×C22⋊C4—1461no—
544C2×C22⋊C4—1461no—
545C2×C22⋊C4—1461no—
546C2×C22⋊C4—1461no—
547C2×C42—731no—
548C2×C42—731no—
549C2×C42—1461no—
550C2×C42—1461no—
551C2×C42—1461no—
552C2×C42—1461no—
553C2×C42C22×D7311yescharacteristic
554#107—734no—
555C4⋊C8—734no—
556C4⋊C8—734no—
557C4⋊C8C22×D7314yes—
558#103—734no—
559#103—734no—
560#103C22×D7314yes—
561#103C22×D7314yes—
562#102—734no—
563#102—734no—
564#97—734no—
565#97—734no—
566C4×C8—734no—
567C24—21no—
568C24—1461no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—734no—
576C2×Q8—732no—
577C2×Q8—732no—
578C2×Q8—1464no—
579C2×Q8—1462no—
580C2×Q8—1462no—
581C2×Q8—1462no—
582C2×Q8—1462no—
583C2×Q8—1461no—
584C2×Q8—1461no—
585C2×Q8C23×D7312yes—
586C2×Q8C23×D7312yes—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—2924no—
591C2×D4—5842no—
592C2×D4—732no—
593C2×D4—1464no—
594C2×D4—1464no—
595C2×D4—1461no—
596C2×D4—1462no—
597C2×D4—1462no—
598C2×D4C23×D7312yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—82no—
604C22×C4—5842no—
605C22×C4—731no—
606C22×C4—731no—
607C22×C4—731no—
608C22×C4—731no—
609C22×C4—1464no—
610C22×C4—1461no—
611C22×C4—1461no—
612C22×C4—1461no—
613C22×C4D4×D7311yescharacteristic
614C22×C4D4×D7311yescharacteristic
615C22×C4C23×D7311yescharacteristic
616Q16—2924no—
617Q16—2924no—
618Q16—1468no—
619SD16—44no—
620SD16—44no—
621SD16—2924no—
622SD16—2924no—
623SD16—1468no—
624SD16—1468no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—734no—
628C2×C8—732no—
629C2×C8—732no—
630C2×C8—1462no—
631C2×C8C23×D7312yes—
632C2×C8C23×D7312yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—734no—
637C4⋊C4—734no—
638C4⋊C4—734no—
639C4⋊C4—732no—
640C4⋊C4—1464no—
641C4⋊C4—1464no—
642C4⋊C4—1464no—
643C4⋊C4—1464no—
644C4⋊C4—1464no—
645C4⋊C4—1464no—
646C4⋊C4—1464no—
647C4⋊C4—1464no—
648C4⋊C4—1461no—
649C4⋊C4C23×D7312yes—
650C22⋊C4—24no—
651C22⋊C4—1464no—
652C22⋊C4—1464no—
653C22⋊C4—1464no—
654C22⋊C4—1464no—
655C22⋊C4—1464no—
656C42—732no—
657C42—732no—
658C42—732no—
659C42—732no—
660C42—1464no—
661C42—1464no—
662C42—1464no—
663C42—1464no—
664C42D4×D7312yes—
665C42C23×D7312yes—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—2922no—
671C23—2922no—
672C23—2922no—
673C23—1462no—
674C23C2×D4×D7311yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—42no—
681Q8—2922no—
682Q8—2922no—
683Q8—1468no—
684Q8—1462no—
685Q8—1462no—
686Q8—1462no—
687Q8—1462no—
688D4—22no—
689D4—22no—
690D4—42no—
691D4—2928no—
692D4—2922no—
693D4—5844no—
694D4—1462no—
695D4—1462no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—2922no—
706C2×C4—2922no—
707C2×C4—2922no—
708C2×C4—5844no—
709C2×C4—734no—
710C2×C4—732no—
711C2×C4—732no—
712C2×C4—732no—
713C2×C4—732no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4C2×D4×D7312yes—
721C2×C4C2×D4×D7312yes—
722C2×C4C2×D4×D7311yescharacteristic
723C2×C4#41×D7312yes—
724C2×C4#1455663612yes—
725C2×C4C24×D7311yescharacteristic
726C8—22no—
727C8—22no—
728C8—734no—
729C8—1462no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—2922no—
735C22—2922no—
736C22—2922no—
737C22—5844no—
738C22#1798925512yes—
739C22#137×D7312yes—
740C22#1798939312yes—
741C22C22×D4×D7311yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—2922no—
748C4—2922no—
749C4—2922no—
750C4—734no—
751C4—1462no—
752C4—1462no—
753C4—1462no—
754C4#1798925512yes—
755C4C2×#41×D7311yescharacteristic
756C4C2×#1455663611yescharacteristic
757C2—82no—
758C2—5842no—
759C2#2262297914yesdirect product factor
760C2C2×#1798925511yescharacteristic
761C2C2×#137×D7311yescharacteristic
762C2C2×#1798939311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#461×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556587C22
hypercenterC2×#461D73
hypocenterC73C2×#3400
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. C2×#17989312C2semidirect
3. #22622979C2direct (N × H)
4. C2×#17988979C2semidirect
5. C2×#17988978C2semidirect
7. C2×#17988810C2semidirect
8. C2×#17988807C2semidirect
9. C2×#17988796C2semidirect
11. C2×#17988791C2semidirect
12. C2×#17988716C2semidirect
13. C2×#17988690C2semidirect
14. C2×#17988687C2semidirect
15. C2×#17988679C2semidirect
16. C2×#461×C73C2semidirect
27. #17989312C22semidirect
47. #17988979C22semidirect
48. #17988978C22semidirect
50. #17988810C22semidirect
51. #17988807C22semidirect
52. #17988796C22semidirect
53. #17988791C22semidirect
55. #17988716C22semidirect
56. #17988690C22semidirect
57. #17988687C22semidirect
58. #17988679C22semidirect
73. #461×C73C22semidirect
377. C2×C73#3400semidirect
393. C2×#461D73semidirect
398. C73C2×#3400semidirect
440. #461C2×D73semidirect
759. C2#22622979direct (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×#179893122
#226229792
C2×#179889792
C2×#179889782
C2×#179889582
C2×#179888102
C2×#179888072
C2×#179887962
C2×#179887852
C2×#179887912
C2×#179887162
C2×#179886902
C2×#179886872
C2×#179886792
C2×#461×C732
C2×#340073