Finite Group Databasebeta

← C2×#22622726 #33965674

Subgroups — C2×#22622726 #33965674

Order 18688.

2134 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989320C211yesmaximal, characteristic, complemented
2C2×#17989252C211yesmaximal, characteristic, complemented
3#22622726C2116yesmaximal, direct product factor
4C2×#17988949C211yesmaximal, characteristic, complemented
5C2×#17988945C211yesmaximal, characteristic, complemented
6C2×#17988932C211yesmaximal, characteristic, complemented
7C2×#17988871C211yesmaximal, characteristic, complemented
8C2×#17988876C211yesmaximal, characteristic, complemented
9C2×#17988803C211yesmaximal, characteristic, complemented
10C2×#17988801C211yesmaximal, characteristic, complemented
11C2×#17988781C211yesmaximal, characteristic
12C2×#17988716C211yesmaximal, characteristic, complemented
13C2×#17988698C211yesmaximal, characteristic, complemented
14C2×#17988697C211yesmaximal, characteristic, complemented
15C2×#17988674C211yesmaximal, characteristic, complemented
16C2×#476×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73—21no—
18C22×#11924017C2211yescharacteristic
19C22×D584C2211yescharacteristic
20C22×#11924013C2211yescharacteristic
21#17989320—24no—
22#17989320C2218yescomplemented
23#17989252—24no—
24#17989252C2218yescomplemented
25C2×#14556590C2211yescharacteristic
26C2×#14556590C2211yescharacteristic
27C2×#14556587C2211yescharacteristic
28C2×#14556579C2211yescharacteristic
29C2×#14556578C2211yescharacteristic
30C2×#14556577—21no—
31C2×#14556574—21no—
32C2×#14556573—21no—
33C2×#14556569—21no—
34C2×#14556569—21no—
35C2×#14556567—21no—
36C2×C4×Dic146C2211yescharacteristic
37C2×#14556556C2211yescharacteristic
38C2×C4×D292C2211yescharacteristic
39C2×#14556553C2211yescharacteristic
40C2×#14556553C2211yescharacteristic
41C2×#14556553C2211yescharacteristic
42C2×C4×C22⋊D73—21no—
43#17988949C2218yescomplemented
44#17988945C2218yescomplemented
45#17988932C2218yescomplemented
46#17988876C2218yescomplemented
47#17988871C2218yescomplemented
48#17988803C2218yescomplemented
49#17988801C2218yescomplemented
50#17988781C2218yes—
51#17988716C2218yescomplemented
52#17988698C2218yescomplemented
53#17988697C2218yescomplemented
54#17988674C2218yescomplemented
55C2×#14556522C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556514C2211yescharacteristic
60C2×#14556514C2211yescharacteristic
61C2×#14556513C2211yescharacteristic
62C2×#14556512C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556502C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×C4×D4×C73C2211yescharacteristic
71#476×C73C2218yescomplemented
72C2×#106×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146D411yescharacteristic
80C22×Dic146C2311yescharacteristic
81C2×Q8×D73—28no—
82C2×Q8×D73—48no—
83C22×D292C2311yescharacteristic
84C22×D292C2311yescharacteristic
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73—21no—
89C22×C4×D73—21no—
90C22×C4×D73—21no—
91C2×#11924017—24no—
92C2×#11924017C2314yes—
93C2×D584—24no—
94C2×D584C2314yes—
95C2×#11924013—24no—
96C2×#11924013C2314yes—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99#14556590—22no—
100#14556590—22no—
101#14556590C2314yes—
102#14556590C2314yes—
103#14556587—22no—
104#14556587C2314yes—
105#14556579—22no—
106#14556579C2314yes—
107#14556578—22no—
108#14556578C2314yes—
109#14556577—28no—
110#14556574—28no—
111#14556573—28no—
112#14556569—28no—
113#14556569—28no—
114#14556567—28no—
115C4×Dic146D414yes—
116C4×Dic146C2314yes—
117#14556556—22no—
118#14556556C2314yes—
119C4×D292—22no—
120C4×D292C2314yes—
121#14556553—22no—
122#14556553—22no—
123#14556553—22no—
124#14556553C2314yes—
125#14556553C2314yes—
126#14556553C2314yes—
127C4×C22⋊D73—28no—
128C2×C4⋊Dic73D411yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007D411yescharacteristic
134C2×#11924007D411yescharacteristic
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73C2311yescharacteristic
145C2×C4×Dic73C2311yescharacteristic
146#14556522C2314yes—
147#14556520C2314yes—
148#14556520C2314yes—
149#14556516C2314yes—
150#14556514C2314yes—
151#14556514C2314yes—
152#14556513C2314yes—
153#14556512C2314yes—
154#14556511C2314yes—
155#14556511C2314yes—
156#14556511C2314yes—
157#14556502C2314yes—
158#14556501C2314yes—
159C8×Dic73C2314yes—
160C22×Q8×C73—21no—
161C22×D4×C73C2311yescharacteristic
162C23×C4×C73—21no—
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C4⋊Q8×C73—22no—
166C4⋊Q8×C73C2314yes—
167C4×D4×C73—22no—
168C4×D4×C73C2314yes—
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#106×C73C2314yes—
176#106×C73C2314yes—
177C4⋊C8×C73C2314yes—
178#102×C73C2314yes—
179#102×C73C2314yes—
180C23×D73—21no—
181C23×D73—21no—
182C2×Dic146—24no—
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—21no—
186C2×Dic146—24no—
187C2×Dic146—24no—
188C2×Dic146—44no—
189C2×Dic146—44no—
190C2×Dic146C2×D414yes—
191C2×Dic146C2412yes—
192Q8×D73—432no—
193C2×D292—21no—
194C2×D292—22no—
195C2×D292—22no—
196C2×D292—22no—
197C2×D292—21no—
198C2×D292#4114yes—
199C2×D292C2412yes—
200C2×D292C2412yes—
201C2×C22⋊D73—24no—
202C2×C22⋊D73—24no—
203C2×C22⋊D73—44no—
204C2×C22⋊D73—82no—
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—24no—
213C2×C4×D73—24no—
214C2×C4×D73—24no—
215C2×C4×D73—44no—
216C2×C4×D73—44no—
217C2×C4×D73—44no—
218C2×C4×D73—82no—
219#11924017—28no—
220D584—28no—
221#11924013—28no—
222C2×#10596831—22no—
223C2×#10596831—22no—
224C2×#10596831C2412yes—
225C2×#10596831C2412yes—
226C4⋊Dic73—21no—
227C4⋊Dic73C2×D414yes—
228C4⋊Dic73C2412yes—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007C2×D414yes—
233#11924007C2×D414yes—
234C22⋊Dic73—24no—
235C22⋊Dic73—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005—24no—
242C4×Dic73—24no—
243C4×Dic73C2×D412yes—
244C4×Dic73C2×D412yes—
245C4×Dic73C2412yes—
246C4×Dic73C2412yes—
247C24×C73—21no—
248C2×Q8×C73—24no—
249C2×Q8×C73—44no—
250C2×D4×C73—21no—
251C2×D4×C73—22no—
252C2×D4×C73—22no—
253C2×D4×C73C2412yes—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—24no—
258C22×C4×C73—82no—
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2411yescharacteristic
262C2×C8×C73—22no—
263C2×C8×C73—22no—
264C2×C8×C73C2412yes—
265C2×C8×C73C2412yes—
266C4⋊C4×C73—24no—
267C4⋊C4×C73—21no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73C2412yes—
271C4⋊C4×C73C2412yes—
272C4⋊C4×C73C2412yes—
273C22⋊C4×C73—24no—
274C42×C73C2×D412yes—
275C42×C73C2412yes—
276C23×C73—22no—
277C23×C73—42no—
278C23×C73—42no—
279C23×C73—42no—
280C23×C73C22×D411yescharacteristic
281C22×D73—24no—
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—42no—
285C22×D73—42no—
286C22×D73—42no—
287C22×D73—42no—
288C22×D73—42no—
289Q8×C73—48no—
290D4×C73—22no—
291D4×C73—22no—
292D4×C73—42no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—42no—
299C2×C4×C73—42no—
300C2×C4×C73—42no—
301C2×C4×C73—84no—
302C2×C4×C73C22×D412yes—
303C2×C4×C73C22×D412yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73C2×#4112yes—
306C2×C4×C732−1+412yes—
307C2×C4×C73C2511yescharacteristic
308C22⋊D73—48no—
309C22⋊D73—84no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73AGL(1,ℤ/8)14yes—
318C2×Dic73C22×D412yes—
319C2×Dic73C22×D412yes—
320C2×Dic73C22×D412yes—
321C2×Dic73C22×D412yes—
322D292—24no—
323D292—22no—
324D292—22no—
325D292—22no—
326D292—42no—
327D292C2×#4114yes—
328C4×D73—48no—
329C4×D73—48no—
330C4×D73—48no—
331C4×D73—84no—
332Dic146—28no—
333Dic146—22no—
334Dic146—22no—
335Dic146—48no—
336Dic146—42no—
337Dic146—48no—
338C8×C73—22no—
339C8×C73—22no—
340#10596831—22no—
341#10596831—22no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—84no—
346C22×C73#54812yes—
347C22×C73C2×AGL(1,ℤ/8)12yes—
348C22×C73#57712yes—
349C22×C73C23×D411yescharacteristic
350C2×D73—24no—
351C2×D73—48no—
352C2×D73—42no—
353C2×D73—42no—
354C2×D73—42no—
355C2×D73—42no—
356C2×D73—42no—
357C2×D73—84no—
358C4×C73—22no—
359C4×C73—22no—
360C4×C73—42no—
361C4×C73—42no—
362C4×C73—42no—
363C4×C73#54812yes—
364C4×C73C22×#4111yescharacteristic
365C4×C73C2×2−1+411yescharacteristic
366Dic73—22no—
367Dic73—22no—
368Dic73—22no—
369Dic73—42no—
370Dic73—42no—
371Dic73C2×AGL(1,ℤ/8)14yes—
372C2×#3373—731nomaximal, Sylow
373C2×C73—82no—
374C2×C73#337314yescomplemented
375C2×C73C2×#54811yescharacteristic
376C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
377C2×C73C2×#57711yescharacteristic
378D73—44no—
379D73—82no—
380C2×#559—731no—
381C2×D4×Q8—731no—
382#3373—7316no—
383C2×#489—731no—
384C2×#489—731no—
385C2×#486—731no—
386C2×#475—731no—
387C2×#476—731no—
388C2×#476D7311yescharacteristic, complemented
389C2×#463—731no—
390C2×#463—731no—
391C2×#459—731no—
392C2×#446—731no—
393C2×#442—731no—
394C2×#442—731no—
395C2×C4×SD16—731no—
396C73C2×#337311yescharacteristic, complemented, Sylow
397C23×Q8—1461no—
398C22×SD16—731no—
399C22×D8—731no—
400C22×D8—731no—
401#559—738no—
402#559—1464no—
403D4×Q8—738no—
404D4×Q8—1464no—
405C2×C4⋊Q8—731no—
406C2×C4⋊Q8—731no—
407C2×C4⋊Q8C2×D7311yescharacteristic
408C2×#127—731no—
409C2×#124—731no—
410C2×#124—731no—
411C2×#124—1461no—
412C2×#123—1461no—
413C2×#123—1461no—
414C2×C22⋊Q8—1461no—
415C2×C22⋊Q8—1461no—
416C2×C22⋊Q8—1461no—
417C2×C4×Q8—731no—
418C2×C4×Q8—731no—
419C2×C4×D4—731no—
420C2×C4×D4—731no—
421C2×C4×D4—731no—
422C2×C4×D4—731no—
423C2×C4×D4—1461no—
424C2×C4×D4C2×D7311yescharacteristic
425#489—738no—
426#489—738no—
427#486—738no—
428#476—738no—
429#476C2×D7318yescomplemented
430#475—738no—
431#463—738no—
432#463—738no—
433#459—738no—
434#446—738no—
435#442—738no—
436#442—738no—
437C4×SD16—738no—
438C2×#106—731no—
439C2×#106C2×D7311yescharacteristic
440C2×#106C2×D7311yescharacteristic
441C2×C4⋊C8—731no—
442C2×C4⋊C8—731no—
443C2×C4⋊C8C2×D7311yescharacteristic
444C2×#103—731no—
445C2×#103—731no—
446C2×#103—731no—
447C2×#102—731no—
448C2×#102—731no—
449C2×#102—731no—
450C2×#102—731no—
451C2×#102—731no—
452C2×#102C2×D7311yescharacteristic
453C2×#102C2×D7311yescharacteristic
454C2×#97—731no—
455C2×#97—731no—
456C2×C4×C8—731no—
457C22×Q8—21no—
458C22×Q8—2928no—
459C22×Q8—731no—
460C22×Q8—731no—
461C22×Q8—1461no—
462C22×Q8—1461no—
463C22×Q8—1468no—
464C22×D4—731no—
465C22×D4—731no—
466C22×D4—1461no—
467C22×D4—1461no—
468C22×D4C22×D7311yescharacteristic
469C23×C4—21no—
470C23×C4—1461no—
471C23×C4—1461no—
472C23×C4—1461no—
473C23×C4—1461no—
474C2×SD16—734no—
475C2×SD16—1464no—
476C2×D8—734no—
477C2×D8—734no—
478C2×D8—1464no—
479C2×D8—1464no—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8C22×D7311yescharacteristic
483C22×C8C22×D7311yescharacteristic
484C4⋊Q8—22no—
485C4⋊Q8—734no—
486C4⋊Q8—734no—
487C4⋊Q8—1462no—
488C4⋊Q8—1462no—
489C4⋊Q8C22×D7314yes—
490#127—734no—
491#127—1462no—
492#124—734no—
493#124—734no—
494#124—1462no—
495#124—1468no—
496#124—1462no—
497#123—1468no—
498#123—1468no—
499C22⋊Q8—1468no—
500C22⋊Q8—1468no—
501C22⋊Q8—1468no—
502C4×Q8—734no—
503C4×Q8—734no—
504C4×Q8—734no—
505C4×Q8—1462no—
506C4×D4—22no—
507C4×D4—734no—
508C4×D4—734no—
509C4×D4—734no—
510C4×D4—734no—
511C4×D4—1462no—
512C4×D4—1462no—
513C4×D4—1462no—
514C4×D4—1468no—
515C4×D4—1462no—
516C4×D4C22×D7314yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—731no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—1461no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4C22×D7311yescharacteristic
526C2×C4⋊C4C22×D7311yescharacteristic
527C2×C4⋊C4C22×D7311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1461no—
530C2×C22⋊C4—1461no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C22⋊C4—1461no—
537C2×C42—731no—
538C2×C42—731no—
539C2×C42—1461no—
540C2×C42C22×D7311yescharacteristic
541#106—734no—
542#106C22×D7314yes—
543#106C22×D7314yes—
544C4⋊C8—734no—
545C4⋊C8—734no—
546C4⋊C8C22×D7314yes—
547#103—734no—
548#103—734no—
549#103—734no—
550#102—734no—
551#102—734no—
552#102—734no—
553#102—734no—
554#102—734no—
555#102C22×D7314yes—
556#102C22×D7314yes—
557#97—734no—
558#97—734no—
559C4×C8—734no—
560C24—21no—
561C24—1461no—
562C24—1461no—
563C2×Q8—24no—
564C2×Q8—44no—
565C2×Q8—2924no—
566C2×Q8—2924no—
567C2×Q8—29232no—
568C2×Q8—734no—
569C2×Q8—732no—
570C2×Q8—1464no—
571C2×Q8—1464no—
572C2×Q8—1464no—
573C2×Q8—1462no—
574C2×Q8—1462no—
575C2×Q8—1461no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—2924no—
580C2×D4—5842no—
581C2×D4—734no—
582C2×D4—732no—
583C2×D4—732no—
584C2×D4—1464no—
585C2×D4—1464no—
586C2×D4—1461no—
587C2×D4—1461no—
588C2×D4—1462no—
589C2×D4—1462no—
590C2×D4—1462no—
591C2×D4C23×D7312yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—82no—
597C22×C4—2924no—
598C22×C4—2924no—
599C22×C4—2924no—
600C22×C4—5842no—
601C22×C4—731no—
602C22×C4—731no—
603C22×C4—731no—
604C22×C4—731no—
605C22×C4—1464no—
606C22×C4—1464no—
607C22×C4—1464no—
608C22×C4—1461no—
609C22×C4—1461no—
610C22×C4—1464no—
611C22×C4D4×D7311yescharacteristic
612C22×C4D4×D7311yescharacteristic
613C22×C4C23×D7311yescharacteristic
614SD16—1468no—
615D8—1468no—
616D8—1468no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—732no—
620C2×C8—732no—
621C2×C8—1462no—
622C2×C8—1462no—
623C2×C8C23×D7312yes—
624C2×C8C23×D7312yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—734no—
630C4⋊C4—734no—
631C4⋊C4—734no—
632C4⋊C4—732no—
633C4⋊C4—1464no—
634C4⋊C4—1464no—
635C4⋊C4—1464no—
636C4⋊C4—1461no—
637C4⋊C4C23×D7312yes—
638C4⋊C4C23×D7312yes—
639C4⋊C4C23×D7312yes—
640C22⋊C4—24no—
641C22⋊C4—1464no—
642C22⋊C4—1464no—
643C22⋊C4—1464no—
644C22⋊C4—1464no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C22⋊C4—1464no—
648C22⋊C4—1464no—
649C42—732no—
650C42—732no—
651C42—732no—
652C42—732no—
653C42—1464no—
654C42D4×D7312yes—
655C42C23×D7312yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—2922no—
661C23—2922no—
662C23—2922no—
663C23—2922no—
664C23—2922no—
665C23—1462no—
666C23—1462no—
667C23—1464no—
668C23C2×D4×D7311yescharacteristic
669Q8—48no—
670Q8—2928no—
671Q8—2928no—
672Q8—2922no—
673Q8—1468no—
674Q8—1462no—
675Q8—1462no—
676D4—22no—
677D4—22no—
678D4—42no—
679D4—2928no—
680D4—2922no—
681D4—5844no—
682D4—734no—
683D4—1462no—
684D4—1462no—
685D4—1462no—
686D4—1464no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—84no—
696C2×C4—2928no—
697C2×C4—2928no—
698C2×C4—2928no—
699C2×C4—2922no—
700C2×C4—2922no—
701C2×C4—5844no—
702C2×C4—732no—
703C2×C4—734no—
704C2×C4—732no—
705C2×C4—732no—
706C2×C4—732no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4—1462no—
710C2×C4—1462no—
711C2×C4—1462no—
712C2×C4C2×D4×D7312yes—
713C2×C4C2×D4×D7312yes—
714C2×C4C2×D4×D7311yescharacteristic
715C2×C4#41×D7312yes—
716C2×C4#1455663912yes—
717C2×C4C24×D7311yescharacteristic
718C8—22no—
719C8—22no—
720C8—1462no—
721C8—1462no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—2928no—
727C22—2922no—
728C22—2922no—
729C22—2922no—
730C22—2922no—
731C22—2922no—
732C22—5844no—
733C22—1464no—
734C22#1798924712yes—
735C22AGL(1,ℤ/8)×D7312yes—
736C22#1798939312yes—
737C22C22×D4×D7311yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—2922no—
744C4—2922no—
745C4—734no—
746C4—1462no—
747C4—1462no—
748C4—1462no—
749C4#1798924712yes—
750C4C2×#41×D7311yescharacteristic
751C4C2×#1455663911yescharacteristic
752C2—82no—
753C2—2924no—
754C2—5842no—
755C2#2262272614yesdirect product factor
756C2C2×#1798924711yescharacteristic
757C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
758C2C2×#1798939311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#476×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988781C2
hypercenterC2×#476D73
hypocenterC73C2×#3373
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#17989320C2semidirect
2. C2×#17989252C2semidirect
3. #22622726C2direct (N × H)
4. C2×#17988949C2semidirect
5. C2×#17988945C2semidirect
6. C2×#17988932C2semidirect
7. C2×#17988871C2semidirect
8. C2×#17988876C2semidirect
9. C2×#17988803C2semidirect
10. C2×#17988801C2semidirect
12. C2×#17988716C2semidirect
13. C2×#17988698C2semidirect
14. C2×#17988697C2semidirect
15. C2×#17988674C2semidirect
16. C2×#476×C73C2semidirect
22. #17989320C22semidirect
24. #17989252C22semidirect
43. #17988949C22semidirect
44. #17988945C22semidirect
45. #17988932C22semidirect
46. #17988876C22semidirect
47. #17988871C22semidirect
48. #17988803C22semidirect
49. #17988801C22semidirect
51. #17988716C22semidirect
52. #17988698C22semidirect
53. #17988697C22semidirect
54. #17988674C22semidirect
71. #476×C73C22semidirect
374. C2×C73#3373semidirect
388. C2×#476D73semidirect
396. C73C2×#3373semidirect
429. #476C2×D73semidirect
755. C2#22622726direct (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×#179892522
#226227262
C2×#179889492
C2×#179889452
C2×#179889322
C2×#179888712
C2×#179888762
C2×#179888032
C2×#179888012
C2×#179887812
C2×#179887162
C2×#179886982
C2×#179886972
C2×#179886742
C2×#476×C732
C2×#337373