Finite Group Databasebeta

← C2×#22622378 #33964522

Subgroups — C2×#22622378 #33964522

Order 18688.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989275C211yesmaximal, characteristic, complemented
2C2×#17989242C211yesmaximal, characteristic
3#22622378C2116yesmaximal, direct product factor
4C2×#17988997C211yesmaximal, characteristic, complemented
5C2×#17988924C211yesmaximal, characteristic, complemented
6C2×#17988909C211yesmaximal, characteristic, complemented
7C2×#17988919C211yesmaximal, characteristic, complemented
8C2×#17988899C211yesmaximal, characteristic, complemented
9C2×#17988883C211yesmaximal, characteristic, complemented
10C2×#17988832C211yesmaximal, characteristic, complemented
11C2×#17988815C211yesmaximal, characteristic, complemented
12C2×#17988687C211yesmaximal, characteristic, complemented
13C2×#17988657C211yesmaximal, characteristic, complemented
14C2×#17988626C211yesmaximal, characteristic, complemented
15C2×#107×D73C211yesmaximal, characteristic, complemented
16C2×#478×C73C211yesmaximal, characteristic, complemented
17C22×#11924028—21no—
18C22×#11924016C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21#17989275—24no—
22#17989275C2218yescomplemented
23#17989242—24no—
24#17989242C2218yes—
25C2×#14556591C2211yescharacteristic
26C2×#14556586—21no—
27C2×#14556582—21no—
28C2×#14556576—21no—
29C2×#14556573—21no—
30C2×#14556573—21no—
31C2×#14556571C2211yescharacteristic
32C2×#14556571C2211yescharacteristic
33C2×#14556570—21no—
34C2×#14556562C2211yescharacteristic
35C2×#14556562C2211yescharacteristic
36C2×C4×Dic146C2211yescharacteristic
37C2×C4×D292C2211yescharacteristic
38C2×#14556549—21no—
39C2×#14556549C2211yescharacteristic
40C2×C4⋊C4×D73C2211yescharacteristic
41C2×C4⋊C4×D73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988997C2218yescomplemented
44#17988924C2218yescomplemented
45#17988919C2218yescomplemented
46#17988909C2218yescomplemented
47#17988899C2218yescomplemented
48#17988883C2218yescomplemented
49#17988832C2218yescomplemented
50#17988815C2218yescomplemented
51#17988687C2218yescomplemented
52#17988657C2218yescomplemented
53#17988626C2218yescomplemented
54C2×#14556525C2211yescharacteristic
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556524C2211yescharacteristic
59#107×D73C2218yescomplemented
60C2×#14556522C2211yescharacteristic
61C2×#14556522C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556516C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556502C2211yescharacteristic
69C2×#125×C73C2211yescharacteristic
70C2×C4×D4×C73C2211yescharacteristic
71#478×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×#11924028—28no—
78C2×#11924028—48no—
79C22×Dic146—21no—
80C22×Dic146C2311yescharacteristic
81C22×D292D411yescharacteristic
82C22×C22⋊D73—21no—
83C22×C22⋊D73—21no—
84C22×C4×D73—21no—
85C22×C4×D73—21no—
86C22×C4×D73—21no—
87C22×C4×D73C2311yescharacteristic
88C22×C4×D73C2311yescharacteristic
89C2×#11924016—24no—
90C2×#11924016C2314yes—
91C2×#11924011—24no—
92C2×#11924011C2314yes—
93C22×#10596831C2311yescharacteristic
94C22×#10596831C2311yescharacteristic
95C2×C8×D73—24no—
96C2×C8×D73C2314yes—
97#14556591—22no—
98#14556591C2314yes—
99#14556586—28no—
100#14556582—28no—
101#14556576—28no—
102#14556573—28no—
103#14556573—28no—
104#14556571—22no—
105#14556571—22no—
106#14556571C2314yes—
107#14556571C2314yes—
108#14556570—28no—
109#14556562—22no—
110#14556562—22no—
111#14556562C2314yes—
112#14556562C2314yes—
113C4×Dic146—22no—
114C4×Dic146C2314yes—
115C4×D292D414yes—
116C4×D292C2314yes—
117#14556549—22no—
118#14556549—28no—
119#14556549C2314yes—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73D411yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C4⋊C4×D73—22no—
132C4⋊C4×D73—22no—
133C4⋊C4×D73—22no—
134C4⋊C4×D73C2314yes—
135C4⋊C4×D73C2314yes—
136C4⋊C4×D73C2314yes—
137C2×C22⋊Dic73—21no—
138C2×C22⋊Dic73—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005D411yescharacteristic
143C2×#11924005D411yescharacteristic
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146#14556525C2314yes—
147#14556525C2314yes—
148#14556524C2314yes—
149#14556524C2314yes—
150#14556524C2314yes—
151#14556522C2314yes—
152#14556522C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556514C2314yes—
156#14556512C2314yes—
157#14556503C2314yes—
158#14556503C2314yes—
159#14556502C2314yes—
160C22×D4×C73C2311yescharacteristic
161C23×C4×C73—21no—
162C22×C8×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164#125×C73—22no—
165#125×C73C2314yes—
166C4×D4×C73—22no—
167C4×D4×C73C2314yes—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C22⋊C4×C73—21no—
174C2×C42×C73C2311yescharacteristic
175#107×C73C2314yes—
176#106×C73C2314yes—
177C4⋊C8×C73C2314yes—
178#102×C73C2314yes—
179#102×C73C2314yes—
180C23×D73C2×D411yescharacteristic
181C23×D73C2×D411yescharacteristic
182#11924028—432no—
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—21no—
186C2×Dic146—24no—
187C2×Dic146—44no—
188C2×Dic146C2412yes—
189C2×D292—24no—
190C2×D292C2×D414yes—
191C2×C22⋊D73—24no—
192C2×C22⋊D73—24no—
193C2×C22⋊D73—44no—
194C2×C22⋊D73—44no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C2×C4×D73—22no—
202C2×C4×D73—22no—
203C2×C4×D73—22no—
204C2×C4×D73—22no—
205C2×C4×D73—24no—
206C2×C4×D73—24no—
207C2×C4×D73—24no—
208C2×C4×D73—44no—
209C2×C4×D73—44no—
210C2×C4×D73—44no—
211C2×C4×D73C2×D412yes—
212C2×C4×D73C2×D412yes—
213C2×C4×D73C2412yes—
214C2×C4×D73C2412yes—
215#11924016—28no—
216#11924011—28no—
217C2×#10596831—22no—
218C2×#10596831#4114yescomplemented
219C2×#10596831C2412yes—
220C2×#10596831C2412yes—
221C8×D73—28no—
222C4⋊Dic73—21no—
223C4⋊Dic73—21no—
224C4⋊Dic73—21no—
225C4⋊Dic73—24no—
226C4⋊Dic73—24no—
227C4⋊Dic73—24no—
228C4⋊Dic73C2×D414yes—
229C4⋊Dic73C2412yes—
230C4⋊Dic73C2412yes—
231C4⋊Dic73C2412yes—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007—24no—
236C22⋊Dic73—24no—
237C22⋊Dic73—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005C2×D414yes—
242#11924005C2×D414yes—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C24×C73—21no—
246C2×D4×C73—21no—
247C2×D4×C73—22no—
248C2×D4×C73—22no—
249C2×D4×C73C2412yes—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—24no—
254C22×C4×C73—44no—
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2411yescharacteristic
258C2×C8×C73—22no—
259C2×C8×C73—22no—
260C2×C8×C73C2412yes—
261C2×C8×C73C2412yes—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—24no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C4⋊C4×C73C2412yes—
270C22⋊C4×C73—24no—
271C42×C73C2×D412yes—
272C42×C73C2412yes—
273C23×C73—22no—
274C23×C73—42no—
275C23×C73—42no—
276C23×C73—42no—
277C23×C73C22×D411yescharacteristic
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—22no—
281C22×D73—22no—
282C22×D73—22no—
283C22×D73AGL(1,ℤ/8)14yes—
284C22×D73C22×D412yes—
285C22×D73C22×D412yes—
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—42no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—48no—
295C2×C4×C73—42no—
296C2×C4×C73—42no—
297C2×C4×C73—42no—
298C2×C4×C73C22×D412yes—
299C2×C4×C73C22×D412yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4112yes—
302C2×C4×C732−1+412yes—
303C2×C4×C73C2511yescharacteristic
304C22⋊D73—48no—
305C22⋊D73—48no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73C22×D412yes—
317C2×Dic73C22×D412yes—
318D292—28no—
319C4×D73—24no—
320C4×D73—24no—
321C4×D73—22no—
322C4×D73—22no—
323C4×D73—22no—
324C4×D73—22no—
325C4×D73—48no—
326C4×D73—48no—
327C4×D73—48no—
328Dic146—22no—
329Dic146—22no—
330Dic146—48no—
331Dic146—42no—
332C8×C73—22no—
333C8×C73—22no—
334#10596831—22no—
335#10596831C2×#4114yescomplemented
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—84no—
340C22×C73#54712yes—
341C22×C73C2×AGL(1,ℤ/8)12yes—
342C22×C73#57812yes—
343C22×C73C23×D411yescharacteristic
344C2×D73—28no—
345C2×D73—22no—
346C2×D73—22no—
347C2×D73—22no—
348C2×D73—22no—
349C2×D73—22no—
350C2×D73—44no—
351C2×D73C2×AGL(1,ℤ/8)14yes—
352C4×C73—22no—
353C4×C73—22no—
354C4×C73—42no—
355C4×C73—42no—
356C4×C73—42no—
357C4×C73#54712yes—
358C4×C73C22×#4111yescharacteristic
359C4×C73C2×2−1+411yescharacteristic
360Dic73—22no—
361Dic73—22no—
362Dic73—42no—
363Dic73—42no—
364Dic73—42no—
365Dic73—42no—
366C2×#3343—731nomaximal, Sylow
367C2×C73—82no—
368C2×C73#334314yescomplemented
369C2×C73C2×#54711yescharacteristic
370C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
371C2×C73C2×#57811yescharacteristic
372D73—24no—
373D73—42no—
374C2×#552—731no—
375C2×#547—731no—
376#3343—7316no—
377C2×#501—731no—
378C2×#484—731no—
379C2×#482—731no—
380C2×#483—731no—
381C2×#480—731no—
382C2×#477—731no—
383C2×#478D7311yescharacteristic, complemented
384C2×#468—731no—
385C2×#465—731no—
386C2×#440—731no—
387C2×#435—731no—
388C2×#428—731no—
389C22×#107—731no—
390C73C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—1461no—
392C22×SD16—731no—
393C22×M16—731no—
394C23×C8—731no—
395#552—738no—
396#552—1464no—
397#547—738no—
398#547—1464no—
399C2×C4⋊Q8—731no—
400C2×#126—1461no—
401C2×#125—1461no—
402C2×#125C2×D7311yescharacteristic
403C2×#123—1461no—
404C2×#123—1461no—
405C2×#123—1461no—
406C2×C22⋊Q8—731no—
407C2×C22⋊Q8—731no—
408C2×C22⋊Q8—1461no—
409C2×#121—731no—
410C2×#121—731no—
411C2×C4×Q8—731no—
412C2×C4×D4—731no—
413C2×C4×D4C2×D7311yescharacteristic
414C2×#117—731no—
415C2×#117—1461no—
416C22×C4⋊C4—731no—
417C22×C4⋊C4—731no—
418C22×C4⋊C4—731no—
419#501—738no—
420#484—738no—
421#483—738no—
422#482—738no—
423#480—738no—
424#478C2×D7318yescomplemented
425#477—738no—
426#468—738no—
427#465—738no—
428#440—738no—
429#435—738no—
430#428—738no—
431C2×#107—731no—
432C2×#107—731no—
433C2×#107—731no—
434C2×#107—731no—
435C2×#107—731no—
436C2×#107—738no—
437C2×#107C2×D7311yescharacteristic
438C2×#106—731no—
439C2×#106—731no—
440C2×#106C2×D7311yescharacteristic
441C2×C4⋊C8C2×D7311yescharacteristic
442C2×#103—731no—
443C2×#103—731no—
444C2×#103—731no—
445C2×#102—731no—
446C2×#102C2×D7311yescharacteristic
447C2×#102C2×D7311yescharacteristic
448C2×C22⋊C8—731no—
449C2×C22⋊C8—731no—
450C2×#97—731no—
451C2×#41—2928no—
452C2×#41—1468no—
453C22×Q8—731no—
454C22×Q8—1461no—
455C22×D4—731no—
456C22×D4—1461no—
457C22×D4—1461no—
458C22×D4C22×D7311yescharacteristic
459C23×C4—21no—
460C23×C4—731no—
461C23×C4—731no—
462C23×C4—1461no—
463C23×C4—1461no—
464C23×C4—1461no—
465C2×SD16—734no—
466C2×SD16—1464no—
467C2×M16—734no—
468C2×M16—1464no—
469C22×C8—731no—
470C22×C8—731no—
471C22×C8—734no—
472C22×C8—1464no—
473C22×C8C22×D7311yescharacteristic
474C22×C8C22×D7311yescharacteristic
475C4⋊Q8—734no—
476C4⋊Q8—1462no—
477#126—1468no—
478#125—22no—
479#125—1468no—
480#125C22×D7314yes—
481#123—1468no—
482#123—1468no—
483#123—1468no—
484C22⋊Q8—734no—
485C22⋊Q8—734no—
486C22⋊Q8—1462no—
487C22⋊Q8—1462no—
488C22⋊Q8—1468no—
489#121—734no—
490#121—734no—
491#121—1462no—
492#121—1462no—
493C4×Q8—734no—
494C4×Q8—1462no—
495C4×D4—22no—
496C4×D4—734no—
497C4×D4—734no—
498C4×D4C22×D7314yes—
499#117—734no—
500#117—1468no—
501#117—1462no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—734no—
509C2×C4⋊C4—734no—
510C2×C4⋊C4—734no—
511C2×C4⋊C4—1462no—
512C2×C4⋊C4—1462no—
513C2×C4⋊C4—1462no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4C22×D7311yescharacteristic
522C2×C4⋊C4C22×D7311yescharacteristic
523C2×C4⋊C4C22×D7311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—731no—
526C2×C22⋊C4—731no—
527C2×C22⋊C4—1461no—
528C2×C22⋊C4—1461no—
529C2×C22⋊C4—1461no—
530C2×C22⋊C4—1461no—
531C2×C22⋊C4—1461no—
532C2×C42—1461no—
533C2×C42—1461no—
534C2×C42C22×D7311yescharacteristic
535#107—734no—
536#107—734no—
537#107—734no—
538#107—734no—
539#107—734no—
540#107C22×D7314yes—
541#106—734no—
542#106—734no—
543#106C22×D7314yes—
544C4⋊C8C22×D7314yes—
545#103—734no—
546#103—734no—
547#103—734no—
548#102—734no—
549#102C22×D7314yes—
550#102C22×D7314yes—
551C22⋊C8—734no—
552C22⋊C8—734no—
553#97—734no—
554C24—21no—
555C24—731no—
556C24—731no—
557#41—29232no—
558C2×Q8—2924no—
559C2×Q8—732no—
560C2×Q8—1462no—
561C2×Q8—1462no—
562C2×Q8—1461no—
563C2×Q8—1464no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—2924no—
568C2×D4—2924no—
569C2×D4—734no—
570C2×D4—1464no—
571C2×D4—1464no—
572C2×D4—1464no—
573C2×D4C23×D7312yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—2924no—
580C22×C4—2924no—
581C22×C4—2924no—
582C22×C4—731no—
583C22×C4—731no—
584C22×C4—732no—
585C22×C4—732no—
586C22×C4—732no—
587C22×C4—732no—
588C22×C4—1464no—
589C22×C4—1464no—
590C22×C4—1464no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1462no—
596C22×C4—1462no—
597C22×C4—1462no—
598C22×C4—1462no—
599C22×C4D4×D7311yescharacteristic
600C22×C4D4×D7311yescharacteristic
601C22×C4C23×D7311yescharacteristic
602SD16—1468no—
603M16—1468no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—734no—
607C2×C8—732no—
608C2×C8—732no—
609C2×C8—1468no—
610C2×C8—1462no—
611C2×C8C23×D7312yes—
612C2×C8C23×D7312yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—734no—
619C4⋊C4—732no—
620C4⋊C4—732no—
621C4⋊C4—732no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1464no—
627C4⋊C4—1464no—
628C4⋊C4—1461no—
629C4⋊C4—1461no—
630C4⋊C4—1461no—
631C4⋊C4—1464no—
632C4⋊C4C23×D7312yes—
633C4⋊C4C23×D7312yes—
634C4⋊C4C23×D7312yes—
635C22⋊C4—24no—
636C22⋊C4—734no—
637C22⋊C4—734no—
638C22⋊C4—1464no—
639C22⋊C4—1464no—
640C22⋊C4—1464no—
641C22⋊C4—1464no—
642C22⋊C4—1464no—
643C42—1464no—
644C42—1464no—
645C42D4×D7312yes—
646C42C23×D7312yes—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—732no—
652C23—734no—
653C23—732no—
654C23—1462no—
655C23—1462no—
656C23—1462no—
657C23—1462no—
658C23—1462no—
659C23C2×D4×D7311yescharacteristic
660Q8—2928no—
661Q8—2922no—
662Q8—1462no—
663Q8—1462no—
664D4—22no—
665D4—22no—
666D4—42no—
667D4—2928no—
668D4—2928no—
669D4—1468no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—48no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—2928no—
680C2×C4—2928no—
681C2×C4—2928no—
682C2×C4—2922no—
683C2×C4—2922no—
684C2×C4—2922no—
685C2×C4—2922no—
686C2×C4—732no—
687C2×C4—732no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4—1462no—
698C2×C4—1464no—
699C2×C4—1464no—
700C2×C4C2×D4×D7312yes—
701C2×C4C2×D4×D7312yes—
702C2×C4C2×D4×D7311yescharacteristic
703C2×C4#41×D7312yes—
704C2×C4#1455663912yes—
705C2×C4C24×D7311yescharacteristic
706C8—22no—
707C8—22no—
708C8—734no—
709C8—1462no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—2924no—
715C22—734no—
716C22—1462no—
717C22—1462no—
718C22—1462no—
719C22—1462no—
720C22—1468no—
721C22—1462no—
722C22#1798923912yes—
723C22AGL(1,ℤ/8)×D7312yes—
724C22#1798940112yes—
725C22C22×D4×D7311yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—2922no—
732C4—2922no—
733C4—2922no—
734C4—2922no—
735C4—1462no—
736C4—1462no—
737C4#1798923912yes—
738C4C2×#41×D7311yescharacteristic
739C4C2×#1455663911yescharacteristic
740C2—82no—
741C2—2922no—
742C2—1464no—
743C2#2262237814yesdirect product factor
744C2C2×#1798923911yescharacteristic
745C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
746C2C2×#1798940111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#478×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989242C2
hypercenterC2×#478D73
hypocenterC73C2×#3343
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#17989275C2semidirect
3. #22622378C2direct (N × H)
4. C2×#17988997C2semidirect
5. C2×#17988924C2semidirect
6. C2×#17988909C2semidirect
7. C2×#17988919C2semidirect
8. C2×#17988899C2semidirect
9. C2×#17988883C2semidirect
10. C2×#17988832C2semidirect
11. C2×#17988815C2semidirect
12. C2×#17988687C2semidirect
13. C2×#17988657C2semidirect
14. C2×#17988626C2semidirect
15. C2×#107×D73C2semidirect
16. C2×#478×C73C2semidirect
22. #17989275C22semidirect
43. #17988997C22semidirect
44. #17988924C22semidirect
45. #17988919C22semidirect
46. #17988909C22semidirect
47. #17988899C22semidirect
48. #17988883C22semidirect
49. #17988832C22semidirect
50. #17988815C22semidirect
51. #17988687C22semidirect
52. #17988657C22semidirect
53. #17988626C22semidirect
59. #107×D73C22semidirect
71. #478×C73C22semidirect
218. C2×#10596831#41semidirect
335. #10596831C2×#41semidirect
368. C2×C73#3343semidirect
383. C2×#478D73semidirect
390. C73C2×#3343semidirect
424. #478C2×D73semidirect
743. C2#22622378direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892752
C2×#179892422
#226223782
C2×#179889972
C2×#179889242
C2×#179889092
C2×#179889192
C2×#179888992
C2×#179888832
C2×#179888322
C2×#179888152
C2×#179886872
C2×#179886572
C2×#179886262
C2×#107×D732
C2×#478×C732
C2×#334373