Finite Group Databasebeta

← C2×#22619921 #33953846

Subgroups — C2×#22619921 #33953846

Order 18688.

2234 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989166C211yesmaximal, characteristic
2C2×#17989068C211yesmaximal, characteristic, complemented
3#22619921C2116yesmaximal, direct product factor
4C2×#17988904C211yesmaximal, characteristic, complemented
5C2×#17988931C211yesmaximal, characteristic, complemented
6C2×#17988929C211yesmaximal, characteristic, complemented
7C2×#17988909C211yesmaximal, characteristic, complemented
8C2×#17988908C211yesmaximal, characteristic, complemented
9C2×#17988919C211yesmaximal, characteristic, complemented
10C2×#17988917C211yesmaximal, characteristic, complemented
11C2×#17988626C211yesmaximal, characteristic, complemented
12C2×#106×D73C211yesmaximal, characteristic, complemented
13C2×#17988585C211yesmaximal, characteristic, complemented
14C2×#17988580C211yesmaximal, characteristic, complemented
15C2×#17988552C211yesmaximal, characteristic, complemented
16C2×#481×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C22×#11924027C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21#17989166—24no—
22#17989166C2218yes—
23C2×#14556571C2211yescharacteristic
24C2×#14556570C2211yescharacteristic
25C2×#14556568—21no—
26C2×#14556564—21no—
27C2×#14556563—21no—
28C2×#14556562—21no—
29C2×#14556562C2211yescharacteristic
30#17989068—24no—
31#17989068C2218yescomplemented
32C2×#14556556—21no—
33C2×#14556553—21no—
34C2×C4×C22⋊D73—21no—
35C2×C4×C22⋊D73—21no—
36C2×#14556550C2211yescharacteristic
37C2×#14556549C2211yescharacteristic
38C2×#14556549C2211yescharacteristic
39C2×C4⋊C4×D73C2211yescharacteristic
40C2×C4⋊C4×D73C2211yescharacteristic
41C2×C4⋊C4×D73C2211yescharacteristic
42#17988931C2218yescomplemented
43#17988929C2218yescomplemented
44#17988919C2218yescomplemented
45#17988917C2218yescomplemented
46#17988909C2218yescomplemented
47#17988908C2218yescomplemented
48#17988904C2218yescomplemented
49#17988626C2218yescomplemented
50C2×#14556525C2211yescharacteristic
51C2×#14556524C2211yescharacteristic
52C2×#14556523C2211yescharacteristic
53C2×#14556522C2211yescharacteristic
54C2×#14556522C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56#106×D73C2218yescomplemented
57#17988585C2218yescomplemented
58#17988580C2218yescomplemented
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65#17988552C2218yescomplemented
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556503C2211yescharacteristic
69C2×#121×C73C2211yescharacteristic
70C22×C4⋊C4×C73C2211yescharacteristic
71#481×C73C2218yescomplemented
72C2×#106×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C2×#11924028—24no—
78C2×#11924028—24no—
79C2×#11924028D414yes—
80C2×#11924028C2314yes—
81C2×#11924027—22no—
82C2×#11924027—24no—
83C2×#11924027—24no—
84C2×#11924027C2314yes—
85C22×Dic146D411yescharacteristic
86C22×Dic146C2311yescharacteristic
87C22×D292D411yescharacteristic
88C22×C22⋊D73—21no—
89C22×C22⋊D73—21no—
90C22×C22⋊D73D411yescharacteristic
91C22×C22⋊D73D411yescharacteristic
92C23×Dic73—21no—
93C22×C4×D73—21no—
94C22×C4×D73—21no—
95C22×C4×D73—21no—
96C22×C4×D73C2311yescharacteristic
97C22×C4×D73C2311yescharacteristic
98C2×#11924011—24no—
99C2×#11924011C2314yes—
100C22×#10596831C2311yescharacteristic
101C22×#10596831C2311yescharacteristic
102C2×C8×D73—24no—
103C2×C8×D73C2314yes—
104#14556571—22no—
105#14556571C2314yes—
106#14556570—22no—
107#14556570C2314yes—
108#14556568—28no—
109#14556564—28no—
110#14556563—28no—
111#14556562—28no—
112#14556562—22no—
113#14556562C2314yes—
114#14556556—28no—
115#14556553—28no—
116C4×C22⋊D73—28no—
117C4×C22⋊D73—28no—
118#14556550—22no—
119#14556550C2314yes—
120#14556549—22no—
121#14556549—22no—
122#14556549C2314yes—
123#14556549C2314yes—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C4⋊C4×D73—22no—
133C4⋊C4×D73—22no—
134C4⋊C4×D73—22no—
135C4⋊C4×D73C2314yes—
136C4⋊C4×D73C2314yes—
137C4⋊C4×D73C2314yes—
138C2×C22⋊Dic73—21no—
139C2×C22⋊Dic73—21no—
140C2×C22⋊Dic73—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73—21no—
147#14556525C2314yes—
148#14556524C2314yes—
149#14556523C2314yes—
150#14556522C2314yes—
151#14556522C2314yes—
152#14556522C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556514C2314yes—
156#14556514C2314yes—
157#14556512C2314yes—
158#14556512C2314yes—
159C22⋊#10596831C2314yes—
160#14556503C2314yes—
161#14556503C2314yes—
162C22×D4×C73—21no—
163C22×D4×C73C2311yescharacteristic
164C23×C4×C73—21no—
165C23×C4×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168#121×C73—22no—
169#121×C73C2314yes—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73—22no—
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C4⋊C4×C73C2314yes—
176C2×C22⋊C4×C73—21no—
177#106×C73C2314yes—
178#106×C73C2314yes—
179#102×C73C2314yes—
180#102×C73C2314yes—
181C22⋊C8×C73C2314yes—
182C23×D73C2×D411yescharacteristic
183C23×D73C2×D411yescharacteristic
184#11924028—216no—
185#11924028—28no—
186#11924028—28no—
187#11924027—28no—
188#11924027—28no—
189#11924027—48no—
190C2×Dic146—24no—
191C2×Dic146—22no—
192C2×Dic146—22no—
193C2×Dic146—21no—
194C2×Dic146C2×D414yes—
195C2×Dic146C2412yes—
196C2×D292—24no—
197C2×D292C2×D414yes—
198C2×C22⋊D73—24no—
199C2×C22⋊D73—24no—
200C2×C22⋊D73—24no—
201C2×C22⋊D73—24no—
202C2×C22⋊D73—44no—
203C2×C22⋊D73—82no—
204C2×C22⋊D73C2×D414yes—
205C2×C22⋊D73C2×D414yes—
206C22×Dic73—21no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C22×Dic73—24no—
211C22×Dic73—44no—
212C22×Dic73C2×D411yescharacteristic
213C22×Dic73C2×D411yescharacteristic
214C2×C4×D73—22no—
215C2×C4×D73—22no—
216C2×C4×D73—24no—
217C2×C4×D73—24no—
218C2×C4×D73—24no—
219C2×C4×D73—82no—
220C2×C4×D73—82no—
221C2×C4×D73—82no—
222C2×C4×D73C2×D412yes—
223C2×C4×D73C2×D412yes—
224C2×C4×D73#4114yes—
225C2×C4×D73#4114yes—
226C2×C4×D73C2412yes—
227C2×C4×D73C2412yes—
228#11924011—28no—
229C2×#10596831—22no—
230C2×#10596831—22no—
231C2×#10596831C2412yes—
232C2×#10596831C2412yes—
233C8×D73—28no—
234C4⋊Dic73—21no—
235C4⋊Dic73—21no—
236C4⋊Dic73—21no—
237C4⋊Dic73—24no—
238C4⋊Dic73C2412yes—
239C4⋊Dic73C2412yes—
240C4⋊Dic73C2412yes—
241#11924007—24no—
242#11924007—24no—
243#11924007—24no—
244#11924007—24no—
245C22⋊Dic73—24no—
246C22⋊Dic73—24no—
247C22⋊Dic73—24no—
248#11924005—24no—
249#11924005—24no—
250#11924005—24no—
251C4×Dic73—24no—
252C4×Dic73—24no—
253C4×Dic73—24no—
254C24×C73—21no—
255C24×C73C2×D411yescharacteristic
256C2×D4×C73—24no—
257C2×D4×C73—21no—
258C2×D4×C73—22no—
259C2×D4×C73—22no—
260C2×D4×C73—82no—
261C2×D4×C73C2412yes—
262C22×C4×C73—22no—
263C22×C4×C73—22no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—24no—
268C22×C4×C73—82no—
269C22×C4×C73C2×D411yescharacteristic
270C22×C4×C73C2×D412yes—
271C22×C4×C73C2412yes—
272C22×C4×C73C2411yescharacteristic
273C2×C8×C73—22no—
274C2×C8×C73—22no—
275C2×C8×C73C2412yes—
276C2×C8×C73C2412yes—
277C4⋊C4×C73—21no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—24no—
280C4⋊C4×C73—21no—
281C4⋊C4×C73C2412yes—
282C4⋊C4×C73C2412yes—
283C4⋊C4×C73C2412yes—
284C22⋊C4×C73—24no—
285C23×C73—22no—
286C23×C73—22no—
287C23×C73—22no—
288C23×C73—22no—
289C23×C73—42no—
290C23×C73—42no—
291C23×C73—42no—
292C23×C73C22×D412yes—
293C23×C73C22×D411yescharacteristic
294C22×D73—22no—
295C22×D73—22no—
296C22×D73—22no—
297C22×D73—22no—
298C22×D73—22no—
299C22×D73#12314yes—
300C22×D73C22×D412yes—
301C22×D73C22×D412yes—
302D4×C73—22no—
303D4×C73—22no—
304D4×C73—42no—
305D4×C73—84no—
306C2×C4×C73—22no—
307C2×C4×C73—24no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—42no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73—84no—
317C2×C4×C73C22×D412yes—
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C2×#4112yes—
320C2×C4×C73C2×#4112yes—
321C2×C4×C73C2511yescharacteristic
322C22⋊D73—28no—
323C22⋊D73—28no—
324C22⋊D73—48no—
325C22⋊D73—84no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—42no—
332C2×Dic73—42no—
333C2×Dic73—42no—
334C2×Dic73—42no—
335C2×Dic73—48no—
336C2×Dic73#12314yes—
337C2×Dic73C22×D412yes—
338C2×Dic73C22×D412yes—
339D292—28no—
340C4×D73—24no—
341C4×D73—22no—
342C4×D73—22no—
343C4×D73—84no—
344C4×D73—84no—
345C4×D73—84no—
346C4×D73#12318yes—
347C4×D73C2×#4114yes—
348C4×D73C2×#4114yes—
349Dic146—28no—
350Dic146—22no—
351Dic146—22no—
352Dic146—42no—
353C8×C73—22no—
354C8×C73—22no—
355#10596831—22no—
356#10596831—22no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—22no—
360C22×C73—44no—
361C22×C73—42no—
362C22×C73—42no—
363C22×C73—42no—
364C22×C73—84no—
365C22×C73C2×#12312yes—
366C22×C73#57712yes—
367C22×C73#57712yes—
368C22×C73C23×D411yescharacteristic
369C2×D73—28no—
370C2×D73—22no—
371C2×D73—22no—
372C2×D73—22no—
373C2×D73—22no—
374C2×D73—22no—
375C2×D73—44no—
376C2×D73C2×#12314yes—
377C4×C73—22no—
378C4×C73—42no—
379C4×C73—42no—
380C4×C73—42no—
381C4×C73C2×#12312yes—
382C4×C73C22×#4111yescharacteristic
383C4×C73C22×#4111yescharacteristic
384Dic73—22no—
385Dic73—42no—
386Dic73—42no—
387Dic73—42no—
388Dic73—42no—
389Dic73C2×#12314yes—
390C2×#3099—731nomaximal, Sylow
391C2×C73—42no—
392C2×C73—82no—
393C2×C73#309914yescomplemented
394C2×C73C22×#12311yescharacteristic
395C2×C73C2×#57711yescharacteristic
396C2×C73C2×#57711yescharacteristic
397D73—24no—
398D73—42no—
399C2×#537—731no—
400C2×#520—731no—
401#3099—7316no—
402C2×#481—731no—
403C2×#481D7311yescharacteristic, complemented
404C2×#485—731no—
405C2×#485—731no—
406C2×#482—731no—
407C2×#482—731no—
408C2×#483—731no—
409C2×#483—731no—
410C2×#428—731no—
411C22×#106—731no—
412C2×#417—731no—
413C2×#416—731no—
414C2×#408—731no—
415C73C2×#309911yescharacteristic, complemented, Sylow
416C22×#41—731no—
417C22×#41—731no—
418C22×M16—731no—
419C23×C8—731no—
420#537—738no—
421#537—1464no—
422C2×C22⋊Q8—731no—
423C2×C22⋊Q8—731no—
424C2×C22⋊Q8—1461no—
425C2×#121—731no—
426C2×#121—1461no—
427C2×#121—1461no—
428C2×#121—1461no—
429C2×#121C2×D7311yescharacteristic
430#520—738no—
431#520—1464no—
432C2×C4×Q8—1461no—
433C2×C4×D4—1461no—
434C2×C4×D4—1461no—
435C2×C4×D4—1461no—
436C2×#117—731no—
437C2×#117—731no—
438C2×#117—731no—
439C22×C4⋊C4—731no—
440C22×C4⋊C4—731no—
441C22×C4⋊C4—731no—
442C22×C4⋊C4C2×D7311yescharacteristic
443#485—738no—
444#485—738no—
445#483—738no—
446#483—738no—
447#482—738no—
448#482—738no—
449#481—738no—
450#481C2×D7318yescomplemented
451#428—738no—
452C2×#107—731no—
453C2×#107—731no—
454C2×#106—731no—
455C2×#106—731no—
456C2×#106—731no—
457C2×#106—731no—
458C2×#106—738no—
459C2×#106C2×D7311yescharacteristic
460C2×#106C2×D7311yescharacteristic
461#417—738no—
462#416—738no—
463C2×#103—731no—
464C2×#103—731no—
465C2×#103—731no—
466C2×#103—731no—
467C2×#102—731no—
468C2×#102—731no—
469C2×#102C2×D7311yescharacteristic
470C2×#102C2×D7311yescharacteristic
471#408—738no—
472C2×C22⋊C8—731no—
473C2×C22⋊C8—731no—
474C2×C22⋊C8—731no—
475C2×C22⋊C8C2×D7311yescharacteristic
476C2×#41—734no—
477C2×#41—734no—
478C2×#41—734no—
479C2×#41—1464no—
480C2×#41—1464no—
481C2×#41—1464no—
482C2×#41—1464no—
483C2×#41—1462no—
484C22×Q8—731no—
485C22×Q8—731no—
486C22×D4—21no—
487C22×D4—731no—
488C22×D4—731no—
489C22×D4—731no—
490C22×D4—1461no—
491C22×D4—1461no—
492C22×D4C22×D7311yescharacteristic
493C23×C4—21no—
494C23×C4—731no—
495C23×C4—731no—
496C23×C4—1461no—
497C23×C4—1461no—
498C23×C4—1461no—
499C23×C4—1461no—
500C23×C4C22×D7311yescharacteristic
501C2×M16—734no—
502C2×M16—1464no—
503C22×C8—731no—
504C22×C8—731no—
505C22×C8—734no—
506C22×C8—1464no—
507C22×C8C22×D7311yescharacteristic
508C22×C8C22×D7311yescharacteristic
509C22⋊Q8—734no—
510C22⋊Q8—734no—
511C22⋊Q8—1468no—
512C22⋊Q8—1462no—
513C22⋊Q8—1462no—
514#121—22no—
515#121—734no—
516#121—1468no—
517#121—1462no—
518#121—1468no—
519#121—1468no—
520#121C22×D7314yes—
521C4×Q8—1468no—
522C4×D4—1468no—
523C4×D4—1468no—
524C4×D4—1468no—
525#117—734no—
526#117—734no—
527#117—734no—
528#117—1462no—
529#117—1462no—
530#117—1462no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—731no—
534C2×C4⋊C4—731no—
535C2×C4⋊C4—731no—
536C2×C4⋊C4—734no—
537C2×C4⋊C4—734no—
538C2×C4⋊C4—734no—
539C2×C4⋊C4—1462no—
540C2×C4⋊C4—1462no—
541C2×C4⋊C4—1462no—
542C2×C4⋊C4—1461no—
543C2×C4⋊C4—1461no—
544C2×C4⋊C4—1461no—
545C2×C4⋊C4—1461no—
546C2×C4⋊C4—1461no—
547C2×C4⋊C4C22×D7311yescharacteristic
548C2×C4⋊C4C22×D7311yescharacteristic
549C2×C4⋊C4C22×D7311yescharacteristic
550C2×C4⋊C4C22×D7314yes—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1461no—
553C2×C22⋊C4—1461no—
554C2×C22⋊C4—1461no—
555C2×C22⋊C4—1461no—
556C2×C22⋊C4—1461no—
557C2×C22⋊C4—1461no—
558C2×C42—1461no—
559C2×C42—1461no—
560C2×C42—1461no—
561#107—734no—
562#107—734no—
563#106—734no—
564#106—734no—
565#106—734no—
566#106—734no—
567#106C22×D7314yes—
568#106C22×D7314yes—
569#103—734no—
570#103—734no—
571#103—734no—
572#103—734no—
573#102—734no—
574#102—734no—
575#102C22×D7314yes—
576#102C22×D7314yes—
577C22⋊C8—734no—
578C22⋊C8—734no—
579C22⋊C8—734no—
580C22⋊C8C22×D7314yes—
581C24—21no—
582C24—731no—
583C24—731no—
584C24D4×D7311yescharacteristic
585#41—2928no—
586#41—1468no—
587#41—1468no—
588#41—14616no—
589#41—1468no—
590#41—1468no—
591C2×Q8—734no—
592C2×Q8—732no—
593C2×Q8—1464no—
594C2×Q8—1462no—
595C2×Q8—1462no—
596C2×Q8—1461no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—82no—
602C2×D4—2924no—
603C2×D4—5842no—
604C2×D4—734no—
605C2×D4—734no—
606C2×D4—734no—
607C2×D4—1464no—
608C2×D4—1464no—
609C2×D4—1464no—
610C2×D4—1464no—
611C2×D4—1464no—
612C2×D4C23×D7312yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—82no—
620C22×C4—2924no—
621C22×C4—5842no—
622C22×C4—5842no—
623C22×C4—5842no—
624C22×C4—731no—
625C22×C4—732no—
626C22×C4—734no—
627C22×C4—734no—
628C22×C4—732no—
629C22×C4—731no—
630C22×C4—732no—
631C22×C4—732no—
632C22×C4—1464no—
633C22×C4—1464no—
634C22×C4—1464no—
635C22×C4—1464no—
636C22×C4—1461no—
637C22×C4—1461no—
638C22×C4—1461no—
639C22×C4—1461no—
640C22×C4—1462no—
641C22×C4—1462no—
642C22×C4D4×D7312yes—
643C22×C4D4×D7311yescharacteristic
644C22×C4C23×D7312yes—
645C22×C4C23×D7311yescharacteristic
646M16—1468no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—732no—
650C2×C8—732no—
651C2×C8—1468no—
652C2×C8—1462no—
653C2×C8—1462no—
654C2×C8C23×D7312yes—
655C2×C8C23×D7312yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—732no—
661C4⋊C4—732no—
662C4⋊C4—732no—
663C4⋊C4—1464no—
664C4⋊C4—1464no—
665C4⋊C4—1464no—
666C4⋊C4—1464no—
667C4⋊C4—1464no—
668C4⋊C4—1461no—
669C4⋊C4—1461no—
670C4⋊C4—1461no—
671C4⋊C4C23×D7312yes—
672C4⋊C4C23×D7312yes—
673C4⋊C4C23×D7312yes—
674C22⋊C4—24no—
675C22⋊C4—1464no—
676C22⋊C4—1464no—
677C22⋊C4—1464no—
678C22⋊C4—1464no—
679C22⋊C4—1464no—
680C22⋊C4—1464no—
681C42—1464no—
682C42—1464no—
683C42—1464no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—732no—
692C23—734no—
693C23—732no—
694C23—1462no—
695C23—1462no—
696C23—1462no—
697C23—1462no—
698C23—1462no—
699C23C2×D4×D7312yes—
700C23C2×D4×D7311yescharacteristic
701Q8—2922no—
702Q8—1468no—
703Q8—1462no—
704Q8—1462no—
705D4—22no—
706D4—22no—
707D4—42no—
708D4—84no—
709D4—2928no—
710D4—5844no—
711D4—1468no—
712D4—1468no—
713D4—1468no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—84no—
725C2×C4—2922no—
726C2×C4—2922no—
727C2×C4—2922no—
728C2×C4—2922no—
729C2×C4—2928no—
730C2×C4—5844no—
731C2×C4—5844no—
732C2×C4—5844no—
733C2×C4—732no—
734C2×C4—734no—
735C2×C4—734no—
736C2×C4—734no—
737C2×C4—738no—
738C2×C4—732no—
739C2×C4—1462no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1462no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1462no—
746C2×C4—1464no—
747C2×C4C2×D4×D7312yes—
748C2×C4C2×D4×D7311yescharacteristic
749C2×C4#41×D7312yes—
750C2×C4#41×D7312yes—
751C2×C4C24×D7311yescharacteristic
752C8—22no—
753C8—22no—
754C8—1462no—
755C8—1462no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—84no—
764C22—2924no—
765C22—734no—
766C22—1462no—
767C22—1462no—
768C22—1462no—
769C22—1468no—
770C22—1462no—
771C22—1462no—
772C22#123×D7312yes—
773C22#1798939312yes—
774C22#1798939712yes—
775C22C22×D4×D7311yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—2922no—
781C4—2922no—
782C4—2922no—
783C4—2922no—
784C4—734no—
785C4—1462no—
786C4#123×D7312yes—
787C4C2×#41×D7311yescharacteristic
788C4C2×#41×D7311yescharacteristic
789C2—42no—
790C2—82no—
791C2—2922no—
792C2—1464no—
793C2#2261992114yesdirect product factor
794C2C2×#123×D7311yescharacteristic
795C2C2×#1798939311yescharacteristic
796C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#481×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989166C2
hypercenterC2×#481D73
hypocenterC73C2×#3099
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#17989068C2semidirect
3. #22619921C2direct (N × H)
4. C2×#17988904C2semidirect
5. C2×#17988931C2semidirect
6. C2×#17988929C2semidirect
7. C2×#17988909C2semidirect
8. C2×#17988908C2semidirect
9. C2×#17988919C2semidirect
10. C2×#17988917C2semidirect
11. C2×#17988626C2semidirect
12. C2×#106×D73C2semidirect
13. C2×#17988585C2semidirect
14. C2×#17988580C2semidirect
15. C2×#17988552C2semidirect
16. C2×#481×C73C2semidirect
31. #17989068C22semidirect
42. #17988931C22semidirect
43. #17988929C22semidirect
44. #17988919C22semidirect
45. #17988917C22semidirect
46. #17988909C22semidirect
47. #17988908C22semidirect
48. #17988904C22semidirect
49. #17988626C22semidirect
56. #106×D73C22semidirect
57. #17988585C22semidirect
58. #17988580C22semidirect
65. #17988552C22semidirect
71. #481×C73C22semidirect
393. C2×C73#3099semidirect
403. C2×#481D73semidirect
415. C73C2×#3099semidirect
450. #481C2×D73semidirect
793. C2#22619921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891662
C2×#179890682
#226199212
C2×#179889042
C2×#179889312
C2×#179889292
C2×#179889092
C2×#179889082
C2×#179889192
C2×#179889172
C2×#179886262
C2×#106×D732
C2×#179885852
C2×#179885802
C2×#179885522
C2×#481×C732
C2×#309973