Finite Group Databasebeta

← C2×#22622522 #33964696

Subgroups — C2×#22622522 #33964696

Order 18688.

2146 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989300C211yesmaximal, characteristic, complemented
2C2×#17989238C211yesmaximal, characteristic, complemented
3#22622522C2116yesmaximal, direct product factor
4C2×#17988984C211yesmaximal, characteristic, complemented
5C2×#17988907C211yesmaximal, characteristic, complemented
6C2×#17988905C211yesmaximal, characteristic, complemented
7C2×#17988914C211yesmaximal, characteristic, complemented
8C2×#17988911C211yesmaximal, characteristic, complemented
9C2×#17988876C211yesmaximal, characteristic, complemented
10C2×#17988866C211yesmaximal, characteristic, complemented
11C2×#17988841C211yesmaximal, characteristic, complemented
12C2×#17988840C211yesmaximal, characteristic, complemented
13C2×#17988669C211yesmaximal, characteristic, complemented
14C2×#17988663C211yesmaximal, characteristic, complemented
15C2×#17988628C211yesmaximal, characteristic, complemented
16C2×#428×C73C211yesmaximal, characteristic, complemented
17C22×#11924028—21no—
18C22×D584C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20#17989300—24no—
21#17989300C2218yescomplemented
22#17989238—24no—
23#17989238C2218yescomplemented
24C2×#14556590C2211yescharacteristic
25C2×#14556590C2211yescharacteristic
26C2×#14556579—21no—
27C2×#14556577—21no—
28C2×#14556576—21no—
29C2×#14556574—21no—
30C2×#14556569—21no—
31C2×#14556566C2211yescharacteristic
32C2×#14556566C2211yescharacteristic
33C2×#14556565C2211yescharacteristic
34C2×#14556565C2211yescharacteristic
35C2×#14556564—21no—
36C2×#14556553C2211yescharacteristic
37C2×#14556553C2211yescharacteristic
38C2×C4×C22⋊D73C2211yescharacteristic
39C2×#14556549C2211yescharacteristic
40C2×#14556548—21no—
41C2×C4⋊C4×D73C2211yescharacteristic
42#17988984C2218yescomplemented
43#17988914C2218yescomplemented
44#17988911C2218yescomplemented
45#17988907C2218yescomplemented
46#17988905C2218yescomplemented
47#17988876C2218yescomplemented
48#17988866C2218yescomplemented
49#17988841C2218yescomplemented
50#17988840C2218yescomplemented
51#17988669C2218yescomplemented
52#17988663C2218yescomplemented
53#17988628C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556523C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556522C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556513C2211yescharacteristic
61C2×#14556513C2211yescharacteristic
62C2×#14556511C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
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×D292—21no—
82C22×D292—21no—
83C22×D292C2311yescharacteristic
84C22×D292C2311yescharacteristic
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C22⋊D73D411yescharacteristic
88C22×C4×D73—21no—
89C22×C4×D73—21no—
90C22×C4×D73—21no—
91C22×C4×D73C2311yescharacteristic
92C2×D584—24no—
93C2×D584C2314yes—
94C2×#11924011—24no—
95C2×#11924011C2314yes—
96C22×#10596831C2311yescharacteristic
97C22×#10596831C2311yescharacteristic
98#14556590—22no—
99#14556590—22no—
100#14556590C2314yes—
101#14556590C2314yes—
102#14556579—28no—
103#14556577—28no—
104#14556576—28no—
105#14556574—28no—
106#14556569—28no—
107#14556566—22no—
108#14556566—22no—
109#14556566C2314yes—
110#14556566C2314yes—
111#14556565—22no—
112#14556565—22no—
113#14556565C2314yes—
114#14556565C2314yes—
115#14556564—28no—
116#14556553—22no—
117#14556553—22no—
118#14556553C2314yes—
119#14556553C2314yes—
120C4×C22⋊D73D414yes—
121C4×C22⋊D73C2314yes—
122#14556549—22no—
123#14556549C2314yes—
124#14556548—28no—
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007D411yescharacteristic
131C4⋊C4×D73—22no—
132C4⋊C4×D73C2314yes—
133C2×C22⋊Dic73D411yescharacteristic
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005D411yescharacteristic
142C2×C4×Dic73—21no—
143C2×C4×Dic73C2311yescharacteristic
144#14556524C2314yes—
145#14556523C2314yes—
146#14556522C2314yes—
147#14556522C2314yes—
148#14556522C2314yes—
149#14556520C2314yes—
150#14556513C2314yes—
151#14556513C2314yes—
152#14556511C2314yes—
153#14556511C2314yes—
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×D73—21no—
182C23×D73C2×D411yescharacteristic
183#11924028—432no—
184C2×Dic146—24no—
185C2×Dic146—24no—
186C2×Dic146—44no—
187C2×Dic146—82no—
188C2×D292—22no—
189C2×D292—22no—
190C2×D292—22no—
191C2×D292—22no—
192C2×D292—24no—
193C2×D292—21no—
194C2×D292—21no—
195C2×D292—24no—
196C2×D292—44no—
197C2×D292—82no—
198C2×D292C2412yes—
199C2×D292C2412yes—
200C2×C22⋊D73—24no—
201C2×C22⋊D73—24no—
202C2×C22⋊D73—24no—
203C2×C22⋊D73—44no—
204C2×C22⋊D73—82no—
205C2×C22⋊D73C2×D414yes—
206C22×Dic73—21no—
207C22×Dic73—21no—
208C22×Dic73C2×D411yescharacteristic
209C22×Dic73C2×D411yescharacteristic
210C22×Dic73C2×D411yescharacteristic
211C2×C4×D73—22no—
212C2×C4×D73—22no—
213C2×C4×D73—24no—
214C2×C4×D73—24no—
215C2×C4×D73—24no—
216C2×C4×D73—44no—
217C2×C4×D73—44no—
218C2×C4×D73—44no—
219C2×C4×D73C2×D412yes—
220C2×C4×D73C2412yes—
221D584—28no—
222#11924011—28no—
223C2×#10596831—22no—
224C2×#10596831—22no—
225C2×#10596831C2412yes—
226C2×#10596831C2412yes—
227C4⋊Dic73—21no—
228C4⋊Dic73—21no—
229C4⋊Dic73C2412yes—
230C4⋊Dic73C2412yes—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007C2×D414yes—
235C22⋊Dic73C2×D414yes—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005—24no—
242#11924005—24no—
243#11924005C2×D414yes—
244C4×Dic73—24no—
245C4×Dic73C2×D412yes—
246C4×Dic73C2412yes—
247C24×C73C2×D411yescharacteristic
248C22×C4×C73—22no—
249C22×C4×C73—22no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—24no—
255C22×C4×C73—44no—
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2×D412yes—
258C22×C4×C73C2412yes—
259C22×C4×C73C2411yescharacteristic
260M16×C73—28no—
261C2×C8×C73—22no—
262C2×C8×C73#4114yescomplemented
263C2×C8×C73C2412yes—
264C2×C8×C73C2412yes—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73—24no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73C2412yes—
271C4⋊C4×C73C2412yes—
272C4⋊C4×C73C2412yes—
273C4⋊C4×C73C2412yes—
274C22⋊C4×C73—24no—
275C42×C73—24no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73C22×D412yes—
280C23×C73C22×D411yescharacteristic
281C22×D73—22no—
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—22no—
285C22×D73—22no—
286C22×D73—42no—
287C22×D73—42no—
288C22×D73—42no—
289C22×D73—42no—
290C22×D73—42no—
291C22×D73—42no—
292C22×D73C22×D412yes—
293C2×C4×C73—22no—
294C2×C4×C73—24no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—48no—
302C2×C4×C73—42no—
303C2×C4×C73—42no—
304C2×C4×C73—42no—
305C2×C4×C73—42no—
306C2×C4×C73C22×D412yes—
307C2×C4×C73C22×D411yescharacteristic
308C2×C4×C73C2×#4112yes—
309C2×C4×C732−1+412yes—
310C2×C4×C73C2511yescharacteristic
311C22⋊D73—28no—
312C22⋊D73—48no—
313C22⋊D73—84no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—42no—
319C2×Dic73—42no—
320C2×Dic73AGL(1,ℤ/8)14yes—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324D292—22no—
325D292—22no—
326D292—22no—
327D292—22no—
328D292—48no—
329D292—42no—
330D292—42no—
331D292—84no—
332C4×D73—24no—
333C4×D73—22no—
334C4×D73—22no—
335C4×D73—48no—
336C4×D73—48no—
337C4×D73—48no—
338Dic146—48no—
339Dic146—84no—
340C8×C73—22no—
341C8×C73C2×#4114yescomplemented
342#10596831—22no—
343#10596831—22no—
344C22×C73—22no—
345C22×C73—22no—
346C22×C73—22no—
347C22×C73—44no—
348C22×C73#54712yes—
349C22×C73C2×AGL(1,ℤ/8)12yes—
350C22×C73#57712yes—
351C22×C73C23×D411yescharacteristic
352C2×D73—22no—
353C2×D73—22no—
354C2×D73—22no—
355C2×D73—44no—
356C2×D73—42no—
357C2×D73—42no—
358C2×D73—42no—
359C2×D73—42no—
360C2×D73—42no—
361C2×D73—42no—
362C2×D73—84no—
363C2×D73—84no—
364C4×C73—22no—
365C4×C73—42no—
366C4×C73—42no—
367C4×C73—42no—
368C4×C73—42no—
369C4×C73#54712yes—
370C4×C73C22×#4111yescharacteristic
371C4×C73C2×2−1+411yescharacteristic
372Dic73—22no—
373Dic73—22no—
374Dic73—42no—
375Dic73—42no—
376Dic73C2×AGL(1,ℤ/8)14yes—
377C2×#3354—731nomaximal, Sylow
378C2×C73—42no—
379C2×C73#335414yescomplemented
380C2×C73C2×#54711yescharacteristic
381C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
382C2×C73C2×#57711yescharacteristic
383D73—42no—
384D73—82no—
385D73—82no—
386C2×#555—731no—
387C2×#547—731no—
388#3354—7316no—
389C2×#498—731no—
390C2×#481—731no—
391C2×#481—731no—
392C2×#482—731no—
393C2×#482—731no—
394C2×#476—731no—
395C2×#474—731no—
396C2×#469—731no—
397C2×#469—731no—
398C2×C4×D8—731no—
399C2×#436—731no—
400C2×#428—731no—
401C2×#428D7311yescharacteristic, complemented
402C73C2×#335411yescharacteristic, complemented, Sylow
403C22×#41—1461no—
404C22×D8—731no—
405C22×M16—731no—
406C22×M16C2×D7311yescharacteristic
407#555—738no—
408#555—1464no—
409#547—738no—
410#547—1464no—
411C2×C4⋊Q8—731no—
412C2×C4⋊Q8—731no—
413C2×#124—1461no—
414C2×#124—1461no—
415C2×#123—1461no—
416C2×#123—1461no—
417C2×C22⋊Q8—1461no—
418C2×#121—731no—
419C2×#121—731no—
420C2×#121—731no—
421C2×#121—731no—
422C2×#121—1461no—
423C2×C4×D4—731no—
424C2×C4×D4—731no—
425C2×C4×D4—731no—
426C2×#117—731no—
427C2×#117—1461no—
428C2×#117C2×D7311yescharacteristic
429C22×C4⋊C4—731no—
430C22×C4⋊C4C2×D7311yescharacteristic
431#498—738no—
432#482—738no—
433#482—738no—
434#481—738no—
435#481—738no—
436#476—738no—
437#474—738no—
438#469—738no—
439#469—738no—
440C4×D8—738no—
441#436—738no—
442#428—738no—
443#428C2×D7318yescomplemented
444C2×#107—731no—
445C2×#107C2×D7311yescharacteristic
446C2×#107C2×D7311yescharacteristic
447C2×#106—731no—
448C2×#106—731no—
449C2×#106—731no—
450C2×#106—731no—
451C2×#106C2×D7311yescharacteristic
452C2×#106C2×D7311yescharacteristic
453C2×C4⋊C8—731no—
454C2×#102—731no—
455C2×#102—731no—
456C2×#102—731no—
457C2×#102—731no—
458C2×#102—731no—
459C2×#102—731no—
460C2×C22⋊C8—731no—
461C2×C22⋊C8—731no—
462C2×C4×C8—731no—
463C2×#41—2928no—
464C2×#41—1468no—
465C22×Q8—1461no—
466C22×Q8—1461no—
467C22×D4—731no—
468C22×D4—731no—
469C22×D4—731no—
470C22×D4—1461no—
471C22×D4—1461no—
472C22×D4—1461no—
473C22×D4—1461no—
474C23×C4—21no—
475C23×C4—731no—
476C23×C4—1461no—
477C23×C4—1461no—
478C23×C4—1461no—
479C23×C4C22×D7311yescharacteristic
480C2×D8—734no—
481C2×D8—1464no—
482C2×M16—24no—
483C2×M16—734no—
484C2×M16—1464no—
485C2×M16C22×D7314yes—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490C4⋊Q8—734no—
491C4⋊Q8—734no—
492C4⋊Q8—1462no—
493C4⋊Q8—1462no—
494#124—1468no—
495#124—1468no—
496#123—1468no—
497#123—1468no—
498C22⋊Q8—1468no—
499#121—734no—
500#121—734no—
501#121—734no—
502#121—734no—
503#121—1468no—
504#121—1462no—
505#121—1462no—
506#121—1462no—
507#121—1462no—
508C4×D4—734no—
509C4×D4—734no—
510C4×D4—734no—
511C4×D4—734no—
512C4×D4—1462no—
513C4×D4—1462no—
514#117—22no—
515#117—734no—
516#117—1468no—
517#117—1462no—
518#117C22×D7314yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—734no—
525C2×C4⋊C4—1462no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4C22×D7311yescharacteristic
530C2×C4⋊C4C22×D7311yescharacteristic
531C2×C4⋊C4C22×D7314yes—
532C2×C4⋊C4C22×D7311yescharacteristic
533C2×C4⋊C4C22×D7311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—731no—
536C2×C22⋊C4—731no—
537C2×C22⋊C4—1461no—
538C2×C22⋊C4—1461no—
539C2×C22⋊C4—1461no—
540C2×C22⋊C4—1461no—
541C2×C22⋊C4—1461no—
542C2×C22⋊C4—1461no—
543C2×C22⋊C4—1461no—
544C2×C42—21no—
545C2×C42—731no—
546C2×C42—1461no—
547#107—734no—
548#107C22×D7314yes—
549#107C22×D7314yes—
550#106—734no—
551#106—734no—
552#106—734no—
553#106—734no—
554#106C22×D7314yes—
555#106C22×D7314yes—
556C4⋊C8—734no—
557#102—734no—
558#102—734no—
559#102—734no—
560#102—734no—
561#102—734no—
562#102—734no—
563C22⋊C8—734no—
564C22⋊C8—734no—
565C4×C8—734no—
566C24—731no—
567C24—1461no—
568C24—1461no—
569C24D4×D7311yescharacteristic
570#41—29232no—
571C2×Q8—2924no—
572C2×Q8—5842no—
573C2×Q8—1464no—
574C2×Q8—1464no—
575C2×D4—2924no—
576C2×D4—2924no—
577C2×D4—5842no—
578C2×D4—5842no—
579C2×D4—734no—
580C2×D4—732no—
581C2×D4—732no—
582C2×D4—1464no—
583C2×D4—1464no—
584C2×D4—1464no—
585C2×D4—1464no—
586C2×D4—1464no—
587C2×D4—1461no—
588C2×D4—1461no—
589C2×D4—1462no—
590C2×D4—1462no—
591C2×D4—1462no—
592C2×D4—1462no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—44no—
601C22×C4—2924no—
602C22×C4—2924no—
603C22×C4—2924no—
604C22×C4—731no—
605C22×C4—731no—
606C22×C4—731no—
607C22×C4—732no—
608C22×C4—732no—
609C22×C4—1464no—
610C22×C4—1464no—
611C22×C4—1464no—
612C22×C4—1461no—
613C22×C4—1461no—
614C22×C4—1462no—
615C22×C4—1462no—
616C22×C4D4×D7312yes—
617C22×C4D4×D7311yescharacteristic
618C22×C4C23×D7312yes—
619C22×C4C23×D7311yescharacteristic
620D8—1468no—
621M16—28no—
622M16—1468no—
623C2×C8—22no—
624C2×C8—732no—
625C2×C8—732no—
626C2×C8—1462no—
627C2×C8—1462no—
628C2×C8#1192402814yescomplemented
629C2×C8C23×D7312yes—
630C2×C8C23×D7312yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—734no—
637C4⋊C4—732no—
638C4⋊C4—732no—
639C4⋊C4—1464no—
640C4⋊C4—1464no—
641C4⋊C4—1464no—
642C4⋊C4—1461no—
643C4⋊C4—1461no—
644C4⋊C4C23×D7312yes—
645C4⋊C4C23×D7312yes—
646C4⋊C4C23×D7312yes—
647C4⋊C4C23×D7312yes—
648C22⋊C4—24no—
649C22⋊C4—734no—
650C22⋊C4—734no—
651C22⋊C4—1464no—
652C22⋊C4—1464no—
653C22⋊C4—1464no—
654C22⋊C4—1464no—
655C22⋊C4—1464no—
656C22⋊C4—1464no—
657C22⋊C4—1464no—
658C42—24no—
659C42—732no—
660C42—732no—
661C42—1464no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—2922no—
666C23—2922no—
667C23—2922no—
668C23—2922no—
669C23—2922no—
670C23—2922no—
671C23—732no—
672C23—1462no—
673C23—1462no—
674C23—1462no—
675C23—1462no—
676C23—1462no—
677C23C2×D4×D7312yes—
678C23C2×D4×D7311yescharacteristic
679Q8—2928no—
680Q8—5844no—
681D4—2928no—
682D4—2928no—
683D4—2922no—
684D4—2922no—
685D4—5844no—
686D4—5844no—
687D4—1468no—
688D4—1462no—
689D4—1462no—
690D4—1462no—
691D4—1462no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—48no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—2928no—
706C2×C4—2928no—
707C2×C4—2928no—
708C2×C4—2922no—
709C2×C4—2922no—
710C2×C4—732no—
711C2×C4—734no—
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×C4—1464no—
721C2×C4C2×D4×D7312yes—
722C2×C4C2×D4×D7311yescharacteristic
723C2×C4C2×#1192402812yes—
724C2×C4#1455663912yes—
725C2×C4C24×D7311yescharacteristic
726C8—22no—
727C8—1462no—
728C8—1462no—
729C8C2×#1192402814yescomplemented
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—2924no—
735C22—2922no—
736C22—2922no—
737C22—2922no—
738C22—2922no—
739C22—2922no—
740C22—2922no—
741C22—5844no—
742C22—5844no—
743C22—1462no—
744C22—1462no—
745C22—1462no—
746C22#1798923812yes—
747C22AGL(1,ℤ/8)×D7312yes—
748C22#1798939612yes—
749C22C22×D4×D7311yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—2922no—
756C4—2922no—
757C4—734no—
758C4—1462no—
759C4—1462no—
760C4#1798923812yes—
761C4C22×#1192402811yescharacteristic
762C4C2×#1455663911yescharacteristic
763C2—42no—
764C2—2922no—
765C2—5842no—
766C2—5842no—
767C2#2262252214yesdirect product factor
768C2C2×#1798923811yescharacteristic
769C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
770C2C2×#1798939611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#428×C73C2
socleC23×C73C22×D4
hypercenterC2×#428D73
hypocenterC73C2×#3354
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×#17989300C2semidirect
2. C2×#17989238C2semidirect
3. #22622522C2direct (N × H)
4. C2×#17988984C2semidirect
5. C2×#17988907C2semidirect
6. C2×#17988905C2semidirect
7. C2×#17988914C2semidirect
8. C2×#17988911C2semidirect
9. C2×#17988876C2semidirect
10. C2×#17988866C2semidirect
11. C2×#17988841C2semidirect
12. C2×#17988840C2semidirect
13. C2×#17988669C2semidirect
14. C2×#17988663C2semidirect
15. C2×#17988628C2semidirect
16. C2×#428×C73C2semidirect
21. #17989300C22semidirect
23. #17989238C22semidirect
42. #17988984C22semidirect
43. #17988914C22semidirect
44. #17988911C22semidirect
45. #17988907C22semidirect
46. #17988905C22semidirect
47. #17988876C22semidirect
48. #17988866C22semidirect
49. #17988841C22semidirect
50. #17988840C22semidirect
51. #17988669C22semidirect
52. #17988663C22semidirect
53. #17988628C22semidirect
72. #428×C73C22semidirect
262. C2×C8×C73#41semidirect
341. C8×C73C2×#41semidirect
379. C2×C73#3354semidirect
401. C2×#428D73semidirect
402. C73C2×#3354semidirect
443. #428C2×D73semidirect
628. C2×C8#11924028semidirect
729. C8C2×#11924028semidirect
767. C2#22622522direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893002
C2×#179892382
#226225222
C2×#179889842
C2×#179889072
C2×#179889052
C2×#179889142
C2×#179889112
C2×#179888762
C2×#179888662
C2×#179888412
C2×#179888402
C2×#179886692
C2×#179886632
C2×#179886282
C2×#428×C732
C2×#335473