Finite Group Databasebeta

← C2×#22622511 #33964684

Subgroups — C2×#22622511 #33964684

Order 18688.

2082 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×#17989305C211yesmaximal, characteristic, complemented
2C2×#17989238C211yesmaximal, characteristic
3#22622511C2116yesmaximal, direct product factor
4C2×#17988991C211yesmaximal, characteristic, complemented
5C2×#17988924C211yesmaximal, characteristic, complemented
6C2×#17988922C211yesmaximal, characteristic, complemented
7C2×#17988913C211yesmaximal, characteristic, complemented
8C2×#17988911C211yesmaximal, characteristic, complemented
9C2×#17988871C211yesmaximal, characteristic, complemented
10C2×#17988866C211yesmaximal, characteristic, complemented
11C2×#17988834C211yesmaximal, characteristic, complemented
12C2×#17988833C211yesmaximal, characteristic, complemented
13C2×#17988674C211yesmaximal, characteristic, complemented
14C2×#17988663C211yesmaximal, characteristic, complemented
15C2×#17988626C211yesmaximal, characteristic, complemented
16C2×#428×C73C211yesmaximal, characteristic, complemented
17C22×#11924028—21no—
18C22×#11924017C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20#17989305—24no—
21#17989305C2218yescomplemented
22#17989238—24no—
23#17989238C2218yes—
24C2×#14556590C2211yescharacteristic
25C2×#14556590C2211yescharacteristic
26C2×#14556585—21no—
27C2×#14556584—21no—
28C2×#14556577—21no—
29C2×#14556576—21no—
30C2×#14556574—21no—
31C2×#14556571C2211yescharacteristic
32C2×#14556570C2211yescharacteristic
33C2×#14556569—21no—
34C2×#14556566C2211yescharacteristic
35C2×#14556565C2211yescharacteristic
36C2×C4×Dic146—21no—
37C2×#14556556C2211yescharacteristic
38C2×#14556553C2211yescharacteristic
39C2×C4×C22⋊D73C2211yescharacteristic
40C2×#14556549C2211yescharacteristic
41C2×C4⋊C4×D73C2211yescharacteristic
42#17988991C2218yescomplemented
43#17988924C2218yescomplemented
44#17988922C2218yescomplemented
45#17988913C2218yescomplemented
46#17988911C2218yescomplemented
47#17988871C2218yescomplemented
48#17988866C2218yescomplemented
49#17988834C2218yescomplemented
50#17988833C2218yescomplemented
51#17988674C2218yescomplemented
52#17988663C2218yescomplemented
53#17988626C2218yescomplemented
54C2×#14556525C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556522C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×M16×C73C2211yescharacteristic
70C2×#117×C73C2211yescharacteristic
71C22×C4⋊C4×C73C2211yescharacteristic
72#428×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#107×C73C2211yescharacteristic
75C2×#106×C73C2211yescharacteristic
76C2×#106×C73C2211yescharacteristic
77C2×#11924028—28no—
78C2×#11924028—48no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146C2311yescharacteristic
82C22×D292—21no—
83C22×D292C2311yescharacteristic
84C22×C22⋊D73—21no—
85C22×C22⋊D73D411yescharacteristic
86C22×C4×D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73C2311yescharacteristic
89C2×#11924017—24no—
90C2×#11924017C2314yes—
91C2×#11924011—24no—
92C2×#11924011C2314yes—
93C22×#10596831C2311yescharacteristic
94C22×#10596831C2311yescharacteristic
95#14556590—22no—
96#14556590—22no—
97#14556590C2314yes—
98#14556590C2314yes—
99#14556585—28no—
100#14556584—28no—
101#14556577—28no—
102#14556576—28no—
103#14556574—28no—
104#14556571—22no—
105#14556571C2314yes—
106#14556570—22no—
107#14556570C2314yes—
108#14556569—28no—
109#14556566—22no—
110#14556566C2314yes—
111#14556565—22no—
112#14556565C2314yes—
113C4×Dic146—28no—
114#14556556—22no—
115#14556556C2314yes—
116#14556553—22no—
117#14556553C2314yes—
118C4×C22⋊D73D414yes—
119C4×C22⋊D73C2314yes—
120#14556549—22no—
121#14556549C2314yes—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007D411yescharacteristic
131C4⋊C4×D73—22no—
132C4⋊C4×D73C2314yes—
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73D411yescharacteristic
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005D411yescharacteristic
141C2×C4×Dic73—21no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73C2311yescharacteristic
144#14556525C2314yes—
145#14556524C2314yes—
146#14556524C2314yes—
147#14556524C2314yes—
148#14556522C2314yes—
149#14556520C2314yes—
150#14556516C2314yes—
151#14556514C2314yes—
152#14556514C2314yes—
153#14556513C2314yes—
154#14556511C2314yes—
155#14556511C2314yes—
156C22⋊#10596831C2314yes—
157#14556503C2314yes—
158C8×Dic73C2314yes—
159C23×C4×C73—21no—
160C23×C4×C73C2311yescharacteristic
161C2×M16×C73—24no—
162C2×M16×C73C2314yes—
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165#117×C73—22no—
166#117×C73C2314yes—
167C2×C4⋊C4×C73—22no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2314yes—
174C2×C22⋊C4×C73—21no—
175C2×C42×C73—21no—
176#107×C73C2314yes—
177#107×C73C2314yes—
178#106×C73C2314yes—
179#106×C73C2314yes—
180C23×D73—21no—
181C23×D73C2×D411yescharacteristic
182#11924028—432no—
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—21no—
186C2×Dic146—24no—
187C2×Dic146—24no—
188C2×Dic146—44no—
189C2×Dic146—44no—
190C2×Dic146C2412yes—
191C2×D292—22no—
192C2×D292—22no—
193C2×D292—24no—
194C2×D292—21no—
195C2×D292—44no—
196C2×D292C2412yes—
197C2×C22⋊D73—24no—
198C2×C22⋊D73—24no—
199C2×C22⋊D73—44no—
200C2×C22⋊D73C2×D414yes—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C2×C4×D73—22no—
208C2×C4×D73—22no—
209C2×C4×D73—24no—
210C2×C4×D73—24no—
211C2×C4×D73—44no—
212C2×C4×D73—44no—
213C2×C4×D73C2×D412yes—
214C2×C4×D73C2412yes—
215#11924017—28no—
216#11924011—28no—
217C2×#10596831—22no—
218C2×#10596831—22no—
219C2×#10596831C2412yes—
220C2×#10596831C2412yes—
221C4⋊Dic73—21no—
222C4⋊Dic73—21no—
223C4⋊Dic73—24no—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007C2×D414yes—
232C22⋊Dic73—24no—
233C22⋊Dic73C2×D414yes—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005C2×D414yes—
240C4×Dic73—24no—
241C4×Dic73—24no—
242C4×Dic73C2×D412yes—
243C4×Dic73C2412yes—
244C24×C73C2×D411yescharacteristic
245C22×C4×C73—22no—
246C22×C4×C73—22no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—24no—
252C22×C4×C73—44no—
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2×D412yes—
255C22×C4×C73C2412yes—
256C22×C4×C73C2411yescharacteristic
257M16×C73—28no—
258C2×C8×C73—22no—
259C2×C8×C73#4114yescomplemented
260C2×C8×C73C2412yes—
261C2×C8×C73C2412yes—
262C4⋊C4×C73—21no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—24no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C4⋊C4×C73C2412yes—
270C4⋊C4×C73C2412yes—
271C22⋊C4×C73—24no—
272C42×C73—24no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73C22×D412yes—
277C23×C73C22×D411yescharacteristic
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—22no—
281C22×D73—22no—
282C22×D73—42no—
283C22×D73—42no—
284C22×D73—42no—
285C22×D73C22×D412yes—
286C2×C4×C73—22no—
287C2×C4×C73—24no—
288C2×C4×C73—22no—
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×C73—42no—
299C2×C4×C73C22×D412yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4112yes—
302C2×C4×C732−1+412yes—
303C2×C4×C73C2511yescharacteristic
304C22⋊D73—28no—
305C22⋊D73—48no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—42no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73AGL(1,ℤ/8)14yes—
315C2×Dic73C22×D412yes—
316C2×Dic73C22×D412yes—
317C2×Dic73C22×D412yes—
318D292—22no—
319D292—22no—
320D292—48no—
321D292—42no—
322C4×D73—24no—
323C4×D73—22no—
324C4×D73—22no—
325C4×D73—48no—
326C4×D73—48no—
327Dic146—22no—
328Dic146—22no—
329Dic146—42no—
330Dic146—48no—
331Dic146—48no—
332C8×C73—22no—
333C8×C73C2×#4114yescomplemented
334#10596831—22no—
335#10596831—22no—
336C22×C73—22no—
337C22×C73—22no—
338C22×C73—22no—
339C22×C73—44no—
340C22×C73#54712yes—
341C22×C73C2×AGL(1,ℤ/8)12yes—
342C22×C73#57812yes—
343C22×C73C23×D411yescharacteristic
344C2×D73—22no—
345C2×D73—22no—
346C2×D73—22no—
347C2×D73—44no—
348C2×D73—42no—
349C2×D73—42no—
350C2×D73—42no—
351C2×D73—84no—
352C4×C73—22no—
353C4×C73—42no—
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—
365Dic73C2×AGL(1,ℤ/8)14yes—
366C2×#3353—731nomaximal, Sylow
367C2×C73—42no—
368C2×C73#335314yescomplemented
369C2×C73C2×#54711yescharacteristic
370C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
371C2×C73C2×#57811yescharacteristic
372D73—42no—
373D73—82no—
374C2×#556—731no—
375C2×#547—731no—
376#3353—7316no—
377C2×#500—731no—
378C2×#484—731no—
379C2×#484—731no—
380C2×#482—731no—
381C2×#482—731no—
382C2×#475—731no—
383C2×#474—731no—
384C2×#468—731no—
385C2×#468—731no—
386C2×C4×SD16—731no—
387C2×#436—731no—
388C2×#428—731no—
389C2×#428D7311yescharacteristic, complemented
390C73C2×#335311yescharacteristic, complemented, Sylow
391C22×#41—1461no—
392C22×SD16—731no—
393C22×M16—731no—
394C22×M16C2×D7311yescharacteristic
395#556—738no—
396#556—1464no—
397#547—738no—
398#547—1464no—
399C2×C4⋊Q8—731no—
400C2×C4⋊Q8—731no—
401C2×#126—1461no—
402C2×#126—1461no—
403C2×#124—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×Q8—1461no—
413C2×C4×D4—731no—
414C2×C4×D4—731no—
415C2×#117—731no—
416C2×#117C2×D7311yescharacteristic
417C22×C4⋊C4—731no—
418C22×C4⋊C4C2×D7311yescharacteristic
419#500—738no—
420#484—738no—
421#484—738no—
422#482—738no—
423#482—738no—
424#475—738no—
425#474—738no—
426#468—738no—
427#468—738no—
428C4×SD16—738no—
429#436—738no—
430#428—738no—
431#428C2×D7318yescomplemented
432C2×#107—731no—
433C2×#107—731no—
434C2×#107—731no—
435C2×#107—731no—
436C2×#107C2×D7311yescharacteristic
437C2×#107C2×D7311yescharacteristic
438C2×#106—731no—
439C2×#106C2×D7311yescharacteristic
440C2×#106C2×D7311yescharacteristic
441C2×C4⋊C8—731no—
442C2×#103—731no—
443C2×#103—731no—
444C2×#103—731no—
445C2×#102—731no—
446C2×#102—731no—
447C2×#102—731no—
448C2×C22⋊C8—731no—
449C2×C22⋊C8—731no—
450C2×C4×C8—731no—
451C2×#41—2928no—
452C2×#41—1468no—
453C22×Q8—731no—
454C22×Q8—1461no—
455C22×Q8—1461no—
456C22×D4—731no—
457C22×D4—731no—
458C22×D4—1461no—
459C22×D4—1461no—
460C23×C4—21no—
461C23×C4—731no—
462C23×C4—1461no—
463C23×C4—1461no—
464C23×C4C22×D7311yescharacteristic
465C2×SD16—734no—
466C2×SD16—1464no—
467C2×M16—24no—
468C2×M16—734no—
469C2×M16—1464no—
470C2×M16C22×D7314yes—
471C22×C8—731no—
472C22×C8—731no—
473C22×C8C22×D7311yescharacteristic
474C22×C8C22×D7311yescharacteristic
475C4⋊Q8—734no—
476C4⋊Q8—734no—
477C4⋊Q8—1462no—
478C4⋊Q8—1462no—
479#126—1468no—
480#126—1468no—
481#124—1468no—
482#123—1468no—
483#123—1468no—
484C22⋊Q8—734no—
485C22⋊Q8—734no—
486C22⋊Q8—1468no—
487C22⋊Q8—1462no—
488C22⋊Q8—1462no—
489#121—734no—
490#121—734no—
491#121—1462no—
492#121—1462no—
493C4×Q8—734no—
494C4×Q8—1468no—
495C4×Q8—1462no—
496C4×D4—734no—
497C4×D4—734no—
498C4×D4—734no—
499C4×D4—1462no—
500#117—22no—
501#117—734no—
502#117—1462no—
503#117C22×D7314yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—734no—
510C2×C4⋊C4—1462no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4C22×D7311yescharacteristic
518C2×C4⋊C4C22×D7311yescharacteristic
519C2×C4⋊C4C22×D7314yes—
520C2×C4⋊C4C22×D7311yescharacteristic
521C2×C4⋊C4C22×D7311yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—731no—
524C2×C22⋊C4—731no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C22⋊C4—1461no—
529C2×C22⋊C4—1461no—
530C2×C22⋊C4—1461no—
531C2×C42—21no—
532C2×C42—731no—
533C2×C42—1461no—
534C2×C42—1461no—
535#107—734no—
536#107—734no—
537#107—734no—
538#107—734no—
539#107C22×D7314yes—
540#107C22×D7314yes—
541#106—734no—
542#106C22×D7314yes—
543#106C22×D7314yes—
544C4⋊C8—734no—
545#103—734no—
546#103—734no—
547#103—734no—
548#102—734no—
549#102—734no—
550#102—734no—
551C22⋊C8—734no—
552C22⋊C8—734no—
553C4×C8—734no—
554C24—731no—
555C24—1461no—
556C24D4×D7311yescharacteristic
557#41—29232no—
558C2×Q8—2924no—
559C2×Q8—2924no—
560C2×Q8—732no—
561C2×Q8—1464no—
562C2×Q8—1464no—
563C2×Q8—1462no—
564C2×Q8—1462no—
565C2×Q8—1461no—
566C2×D4—2924no—
567C2×D4—2924no—
568C2×D4—734no—
569C2×D4—732no—
570C2×D4—1464no—
571C2×D4—1464no—
572C2×D4—1464no—
573C2×D4—1461no—
574C2×D4—1462no—
575C2×D4—1462no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—44no—
584C22×C4—2924no—
585C22×C4—2924no—
586C22×C4—731no—
587C22×C4—731no—
588C22×C4—731no—
589C22×C4—732no—
590C22×C4—732no—
591C22×C4—1464no—
592C22×C4—1464no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4—1462no—
597C22×C4—1462no—
598C22×C4D4×D7312yes—
599C22×C4D4×D7311yescharacteristic
600C22×C4C23×D7312yes—
601C22×C4C23×D7311yescharacteristic
602SD16—1468no—
603M16—28no—
604M16—1468no—
605C2×C8—22no—
606C2×C8—732no—
607C2×C8—732no—
608C2×C8—1462no—
609C2×C8—1462no—
610C2×C8#1192402814yescomplemented
611C2×C8C23×D7312yes—
612C2×C8C23×D7312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—734no—
619C4⋊C4—732no—
620C4⋊C4—732no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1464no—
627C4⋊C4—1461no—
628C4⋊C4—1461no—
629C4⋊C4C23×D7312yes—
630C4⋊C4C23×D7312yes—
631C4⋊C4C23×D7312yes—
632C4⋊C4C23×D7312yes—
633C22⋊C4—24no—
634C22⋊C4—734no—
635C22⋊C4—734no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C22⋊C4—1464no—
640C22⋊C4—1464no—
641C22⋊C4—1464no—
642C42—24no—
643C42—732no—
644C42—732no—
645C42—1464no—
646C42—1464no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—2922no—
651C23—2922no—
652C23—2922no—
653C23—732no—
654C23—1462no—
655C23—1462no—
656C23—1462no—
657C23—1462no—
658C23C2×D4×D7312yes—
659C23C2×D4×D7311yescharacteristic
660Q8—2928no—
661Q8—2928no—
662Q8—2922no—
663Q8—1462no—
664Q8—1462no—
665D4—2928no—
666D4—2928no—
667D4—2922no—
668D4—1468no—
669D4—1462no—
670D4—1462no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—48no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—2928no—
685C2×C4—2928no—
686C2×C4—2922no—
687C2×C4—2922no—
688C2×C4—2922no—
689C2×C4—732no—
690C2×C4—734no—
691C2×C4—732no—
692C2×C4—732no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1462no—
700C2×C4—1464no—
701C2×C4C2×D4×D7312yes—
702C2×C4C2×D4×D7311yescharacteristic
703C2×C4C2×#1192402812yes—
704C2×C4#1455663912yes—
705C2×C4C24×D7311yescharacteristic
706C8—22no—
707C8—1462no—
708C8—1462no—
709C8C2×#1192402814yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—2924no—
715C22—2922no—
716C22—2922no—
717C22—2922no—
718C22—5844no—
719C22—1462no—
720C22—1462no—
721C22—1462no—
722C22#1798923812yes—
723C22AGL(1,ℤ/8)×D7312yes—
724C22#1798940312yes—
725C22C22×D4×D7311yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—2922no—
732C4—2922no—
733C4—2922no—
734C4—734no—
735C4—1462no—
736C4—1462no—
737C4#1798923812yes—
738C4C22×#1192402811yescharacteristic
739C4C2×#1455663911yescharacteristic
740C2—42no—
741C2—2922no—
742C2—5842no—
743C2#2262251114yesdirect product factor
744C2C2×#1798923811yescharacteristic
745C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
746C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#428×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989238C2
hypercenterC2×#428D73
hypocenterC73C2×#3353
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#17989305C2semidirect
3. #22622511C2direct (N × H)
4. C2×#17988991C2semidirect
5. C2×#17988924C2semidirect
6. C2×#17988922C2semidirect
7. C2×#17988913C2semidirect
8. C2×#17988911C2semidirect
9. C2×#17988871C2semidirect
10. C2×#17988866C2semidirect
11. C2×#17988834C2semidirect
12. C2×#17988833C2semidirect
13. C2×#17988674C2semidirect
14. C2×#17988663C2semidirect
15. C2×#17988626C2semidirect
16. C2×#428×C73C2semidirect
21. #17989305C22semidirect
42. #17988991C22semidirect
43. #17988924C22semidirect
44. #17988922C22semidirect
45. #17988913C22semidirect
46. #17988911C22semidirect
47. #17988871C22semidirect
48. #17988866C22semidirect
49. #17988834C22semidirect
50. #17988833C22semidirect
51. #17988674C22semidirect
52. #17988663C22semidirect
53. #17988626C22semidirect
72. #428×C73C22semidirect
259. C2×C8×C73#41semidirect
333. C8×C73C2×#41semidirect
368. C2×C73#3353semidirect
389. C2×#428D73semidirect
390. C73C2×#3353semidirect
431. #428C2×D73semidirect
610. C2×C8#11924028semidirect
709. C8C2×#11924028semidirect
743. C2#22622511direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893052
C2×#179892382
#226225112
C2×#179889912
C2×#179889242
C2×#179889222
C2×#179889132
C2×#179889112
C2×#179888712
C2×#179888662
C2×#179888342
C2×#179888332
C2×#179886742
C2×#179886632
C2×#179886262
C2×#428×C732
C2×#335373