Finite Group Databasebeta

← C2×#22623011 #33967005

Subgroups — C2×#22623011 #33967005

Order 18688.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989309C211yesmaximal, characteristic, complemented
2C2×#17989307C211yesmaximal, characteristic, complemented
3#22623011C2116yesmaximal, direct product factor
4C2×#17988981C211yesmaximal, characteristic, complemented
5C2×#17988978C211yesmaximal, characteristic, complemented
6C2×#17988968C211yesmaximal, characteristic
7C2×#17988812C211yesmaximal, characteristic, complemented
8C2×#17988808C211yesmaximal, characteristic, complemented
9C2×#17988797C211yesmaximal, characteristic, complemented
10C2×#17988796C211yesmaximal, characteristic, complemented
11C2×#17988802C211yesmaximal, characteristic
12C2×#17988801C211yesmaximal, characteristic
13C2×#17988715C211yesmaximal, characteristic, complemented
14C2×#17988686C211yesmaximal, characteristic, complemented
15C2×#17988681C211yesmaximal, characteristic, complemented
16C2×#440×C73C211yesmaximal, characteristic, complemented
17C22×Dic292C2211yescharacteristic
18C22×Dic292C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×#11924017C2211yescharacteristic
22C22×#11924017C2211yescharacteristic
23C22×#11924016C2211yescharacteristic
24C22×#11924013C2211yescharacteristic
25#17989309—24no—
26#17989309C2218yescomplemented
27#17989307—24no—
28#17989307C2218yescomplemented
29C2×#14556591C2211yescharacteristic
30C2×#14556589C2211yescharacteristic
31C2×#14556586—21no—
32C2×#14556585—21no—
33C2×#14556584—21no—
34C2×#14556584—21no—
35C2×#14556580C2211yescharacteristic
36C2×#14556579C2211yescharacteristic
37C2×#14556578C2211yescharacteristic
38C2×#14556578C2211yescharacteristic
39C2×#14556570—21no—
40C2×#14556569—21no—
41C2×C4×Dic146C2211yescharacteristic
42C2×#14556556C2211yescharacteristic
43C2×#14556556C2211yescharacteristic
44C2×#14556556C2211yescharacteristic
45C2×#14556553C2211yescharacteristic
46C2×#14556550—21no—
47C2×#14556548—21no—
48#17988981C2218yescomplemented
49#17988978C2218yescomplemented
50#17988968C2218yes—
51#17988812C2218yescomplemented
52#17988808C2218yescomplemented
53#17988802C2218yes—
54#17988801C2218yes—
55#17988797C2218yescomplemented
56#17988796C2218yescomplemented
57#17988715C2218yescomplemented
58#17988686C2218yescomplemented
59#17988681C2218yescomplemented
60C2×C4⋊#10596831C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C2×#14556520C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556514C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#440×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146D411yescharacteristic
78C22×Dic146C2311yescharacteristic
79C22×Dic146C2311yescharacteristic
80C22×Dic146C2311yescharacteristic
81C22×D292C2311yescharacteristic
82C22×C4×D73—21no—
83C2×Dic292—24no—
84C2×Dic292—42no—
85C2×Dic292C2314yes—
86C2×Dic292C2314yes—
87C2×#11924018—42no—
88C2×#11924018—42no—
89C2×#11924018C2314yes—
90C2×#11924018C2314yes—
91C2×#11924017—24no—
92C2×#11924017—42no—
93C2×#11924017C2314yes—
94C2×#11924017C2314yes—
95C2×#11924016—42no—
96C2×#11924016C2314yes—
97C2×#11924013—42no—
98C2×#11924013C2314yes—
99C22×#10596831C2311yescharacteristic
100C22×#10596831C2311yescharacteristic
101#14556591—22no—
102#14556591C2314yes—
103#14556589—22no—
104#14556589C2314yes—
105#14556586—28no—
106#14556585—28no—
107#14556584—28no—
108#14556584—28no—
109#14556580—22no—
110#14556580C2314yes—
111#14556579—22no—
112#14556579C2314yes—
113#14556578—22no—
114#14556578—22no—
115#14556578C2314yes—
116#14556578C2314yes—
117#14556570—28no—
118#14556569—28no—
119C4×Dic146D414yes—
120C4×Dic146C2314yes—
121#14556556—22no—
122#14556556—22no—
123#14556556—22no—
124#14556556C2314yes—
125#14556556C2314yes—
126#14556556C2314yes—
127#14556553—22no—
128#14556553C2314yes—
129#14556550—28no—
130#14556548—28no—
131C2×C4⋊Dic73—21no—
132C2×C4⋊Dic73—21no—
133C2×C4⋊Dic73D411yescharacteristic
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007D411yescharacteristic
140C2×#11924007D411yescharacteristic
141C2×C22⋊Dic73—21no—
142C2×C22⋊Dic73—21no—
143C2×C22⋊Dic73—21no—
144C2×C22⋊Dic73—21no—
145C2×#11924005—21no—
146C2×#11924005—21no—
147C2×#11924005—21no—
148C2×#11924005—21no—
149C2×#11924005—21no—
150C2×C4×Dic73—21no—
151C2×C4×Dic73—21no—
152C2×C4×Dic73—21no—
153C2×C4×Dic73C2311yescharacteristic
154C2×C4×Dic73C2311yescharacteristic
155C4⋊#10596831C2314yes—
156#14556520C2314yes—
157#14556520C2314yes—
158#14556514C2314yes—
159#14556514C2314yes—
160#14556514C2314yes—
161#14556511C2314yes—
162#14556501C2314yes—
163C8×Dic73C2314yes—
164C22×Q8×C73C2311yescharacteristic
165C22×D4×C73C2311yescharacteristic
166C23×C4×C73—21no—
167C2×SD16×C73—24no—
168C2×SD16×C73C2314yes—
169C22×C8×C73C2311yescharacteristic
170C22×C8×C73C2311yescharacteristic
171C4×Q8×C73—22no—
172C4×Q8×C73C2314yes—
173C4×D4×C73—22no—
174C4×D4×C73C2314yes—
175C2×C4⋊C4×C73—21no—
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C22⋊C4×C73—21no—
179C2×C42×C73—21no—
180C2×C42×C73C2311yescharacteristic
181#107×C73C2314yes—
182#103×C73C2314yes—
183#102×C73C2314yes—
184#97×C73C2314yes—
185C23×D73—21no—
186C2×Dic146—22no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—21no—
193C2×Dic146—21no—
194C2×Dic146—21no—
195C2×Dic146—42no—
196C2×Dic146C2×D414yes—
197C2×Dic146C2412yes—
198C2×Dic146C2412yes—
199C2×Dic146C2412yes—
200C2×D292—22no—
201C2×D292—22no—
202C2×D292—21no—
203C2×D292C2412yes—
204C22×Dic73—21no—
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—44no—
213Dic292—28no—
214Dic292—44no—
215#11924018—44no—
216#11924018—44no—
217#11924017—28no—
218#11924017—44no—
219#11924016—44no—
220#11924013—44no—
221C2×#10596831—22no—
222C2×#10596831—22no—
223C2×#10596831C2412yes—
224C2×#10596831C2412yes—
225C4⋊Dic73—24no—
226C4⋊Dic73—24no—
227C4⋊Dic73C2×D414yes—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007C2×D414yes—
234#11924007C2×D414yes—
235C22⋊Dic73—24no—
236C22⋊Dic73—24no—
237C22⋊Dic73—24no—
238C22⋊Dic73—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005—24no—
242#11924005—24no—
243#11924005—24no—
244C4×Dic73—24no—
245C4×Dic73—24no—
246C4×Dic73—24no—
247C4×Dic73C2×D412yes—
248C4×Dic73C2×D412yes—
249C4×Dic73C2412yes—
250C4×Dic73C2412yes—
251C24×C73—21no—
252C2×Q8×C73—21no—
253C2×Q8×C73—22no—
254C2×Q8×C73—22no—
255C2×Q8×C73C2412yes—
256C2×D4×C73—21no—
257C2×D4×C73—22no—
258C2×D4×C73—22no—
259C2×D4×C73C2412yes—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—24no—
264C22×C4×C73—44no—
265C22×C4×C73C2×D411yescharacteristic
266C22×C4×C73C2×D411yescharacteristic
267C22×C4×C73C2411yescharacteristic
268SD16×C73—28no—
269C2×C8×C73—22no—
270C2×C8×C73#4114yes—
271C2×C8×C73C2412yes—
272C2×C8×C73C2412yes—
273C4⋊C4×C73—24no—
274C4⋊C4×C73—21no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73C2412yes—
277C4⋊C4×C73C2412yes—
278C22⋊C4×C73—24no—
279C42×C73—24no—
280C42×C73C2×D412yes—
281C42×C73C2412yes—
282C23×C73—22no—
283C23×C73—42no—
284C23×C73—42no—
285C23×C73—42no—
286C23×C73C22×D411yescharacteristic
287C22×D73—22no—
288C22×D73—42no—
289C22×D73—42no—
290C22×D73—42no—
291Q8×C73—22no—
292Q8×C73—22no—
293Q8×C73—42no—
294D4×C73—22no—
295D4×C73—22no—
296D4×C73—42no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—48no—
303C2×C4×C73—42no—
304C2×C4×C73—42no—
305C2×C4×C73—42no—
306C2×C4×C73C22×D412yes—
307C2×C4×C73C22×D412yes—
308C2×C4×C73C22×D411yescharacteristic
309C2×C4×C73C2×#4112yes—
310C2×C4×C73H(5,𝔽2)12yes—
311C2×C4×C73C2511yescharacteristic
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—42no—
320C2×Dic73—42no—
321C2×Dic73—42no—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324C2×Dic73C22×D412yes—
325C2×Dic73C22×D412yes—
326D292—22no—
327D292—22no—
328D292—42no—
329C4×D73—48no—
330Dic146—22no—
331Dic146—22no—
332Dic146—22no—
333Dic146—22no—
334Dic146—22no—
335Dic146—22no—
336Dic146—44no—
337Dic146—42no—
338Dic146—42no—
339Dic146—42no—
340C8×C73—22no—
341C8×C73C2×#4114yes—
342#10596831—22no—
343#10596831—22no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—42no—
347C22×C73—84no—
348C22×C73#55012yes—
349C22×C73#57512yes—
350C22×C73#57812yes—
351C22×C73C23×D411yescharacteristic
352C2×D73—42no—
353C2×D73—42no—
354C2×D73—42no—
355C2×D73—84no—
356C4×C73—22no—
357C4×C73—22no—
358C4×C73—42no—
359C4×C73—42no—
360C4×C73—42no—
361C4×C73#55012yes—
362C4×C73C22×#4111yescharacteristic
363C4×C73C2×H(5,𝔽2)11yescharacteristic
364Dic73—22no—
365Dic73—22no—
366Dic73—22no—
367Dic73—22no—
368Dic73—42no—
369Dic73—42no—
370Dic73—42no—
371C2×#3402—731nomaximal, Sylow
372C2×C73—82no—
373C2×C73#340214yescomplemented
374C2×C73C2×#55011yescharacteristic
375C2×C73C2×#57511yescharacteristic
376C2×C73C2×#57811yescharacteristic
377D73—82no—
378C2×#556—731no—
379C2×#556—731no—
380#3402—7316no—
381C2×#497—731no—
382C2×#497—731no—
383C2×#495—731no—
384C2×#464—731no—
385C2×#464—731no—
386C2×#462—731no—
387C2×#462—731no—
388C2×#463—731no—
389C2×#463—731no—
390C2×#446—731no—
391C2×#440—731no—
392C2×#440D7311yescharacteristic, complemented
393C2×C4×Q16—731no—
394C73C2×#340211yescharacteristic, complemented, Sylow
395C22×Q16—731no—
396C22×Q16—731no—
397C22×Q16—731no—
398C22×Q16—731no—
399C22×SD16—731no—
400C22×SD16—731no—
401C22×SD16—731no—
402C22×SD16C2×D7311yescharacteristic
403C22×D8—731no—
404#556—738no—
405#556—738no—
406#556—1464no—
407#556—1464no—
408C2×C4⋊Q8—731no—
409C2×C4⋊Q8—731no—
410C2×#126—1461no—
411C2×#126—1461no—
412C2×#126—1461no—
413C2×#126—1461no—
414C2×#124—731no—
415C2×#124—731no—
416C2×#124—731no—
417C2×#124—731no—
418C2×C22⋊Q8—1461no—
419C2×C22⋊Q8—1461no—
420C2×C4×Q8—731no—
421C2×C4×Q8—731no—
422C2×C4×Q8—731no—
423C2×C4×Q8—731no—
424C2×C4×Q8C2×D7311yescharacteristic
425C2×C4×D4—731no—
426C2×C4×D4C2×D7311yescharacteristic
427C2×#117—1461no—
428C2×#117—1461no—
429#497—738no—
430#497—738no—
431#495—738no—
432#464—738no—
433#464—738no—
434#463—738no—
435#463—738no—
436#462—738no—
437#462—738no—
438#446—738no—
439#440—738no—
440#440C2×D7318yescomplemented
441C4×Q16—738no—
442C2×#107C2×D7311yescharacteristic
443C2×C4⋊C8—731no—
444C2×C4⋊C8—731no—
445C2×C4⋊C8—731no—
446C2×#103—731no—
447C2×#103—731no—
448C2×#103—731no—
449C2×#103C2×D7311yescharacteristic
450C2×#102—731no—
451C2×#102C2×D7311yescharacteristic
452C2×#97—731no—
453C2×#97C2×D7311yescharacteristic
454C2×C4×C8—731no—
455C22×Q8—731no—
456C22×Q8—731no—
457C22×Q8—731no—
458C22×Q8—731no—
459C22×Q8C22×D7311yescharacteristic
460C22×D4—731no—
461C22×D4C22×D7311yescharacteristic
462C23×C4—21no—
463C23×C4—1461no—
464C2×Q16—2922no—
465C2×Q16—2922no—
466C2×Q16—2922no—
467C2×Q16—734no—
468C2×Q16—734no—
469C2×Q16—734no—
470C2×Q16—734no—
471C2×Q16—1464no—
472C2×SD16—24no—
473C2×SD16—2922no—
474C2×SD16—2922no—
475C2×SD16—734no—
476C2×SD16—734no—
477C2×SD16—734no—
478C2×SD16—1464no—
479C2×SD16C22×D7314yes—
480C2×D8—2922no—
481C2×D8—734no—
482C22×C8—731no—
483C22×C8—731no—
484C22×C8C22×D7311yescharacteristic
485C22×C8C22×D7311yescharacteristic
486C4⋊Q8—734no—
487C4⋊Q8—734no—
488C4⋊Q8—1462no—
489C4⋊Q8—1462no—
490#126—1468no—
491#126—1468no—
492#126—1468no—
493#126—1468no—
494#124—734no—
495#124—734no—
496#124—734no—
497#124—734no—
498#124—1462no—
499#124—1462no—
500#124—1462no—
501#124—1462no—
502C22⋊Q8—1468no—
503C22⋊Q8—1468no—
504C4×Q8—22no—
505C4×Q8—734no—
506C4×Q8—734no—
507C4×Q8—734no—
508C4×Q8—734no—
509C4×Q8—734no—
510C4×Q8—1462no—
511C4×Q8—1462no—
512C4×Q8—1462no—
513C4×Q8C22×D7314yes—
514C4×D4—22no—
515C4×D4—734no—
516C4×D4—1462no—
517C4×D4C22×D7314yes—
518#117—1468no—
519#117—1468no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4—1461no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4C22×D7311yescharacteristic
532C2×C4⋊C4C22×D7311yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C22⋊C4—1461no—
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×C42—21no—
544C2×C42—731no—
545C2×C42—731no—
546C2×C42—1461no—
547C2×C42—1461no—
548C2×C42—1461no—
549C2×C42C22×D7311yescharacteristic
550#107C22×D7314yes—
551C4⋊C8—734no—
552C4⋊C8—734no—
553C4⋊C8—734no—
554#103—734no—
555#103—734no—
556#103—734no—
557#103C22×D7314yes—
558#102—734no—
559#102C22×D7314yes—
560#97—734no—
561#97C22×D7314yes—
562C4×C8—734no—
563C24—21no—
564C24—1461no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—2922no—
569C2×Q8—734no—
570C2×Q8—732no—
571C2×Q8—732no—
572C2×Q8—732no—
573C2×Q8—1462no—
574C2×Q8—1462no—
575C2×Q8—1462no—
576C2×Q8—1462no—
577C2×Q8—1462no—
578C2×Q8—1462no—
579C2×Q8—1461no—
580C2×Q8—1461no—
581C2×Q8—1461no—
582C2×Q8C23×D7312yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—732no—
587C2×D4—1461no—
588C2×D4—1462no—
589C2×D4—1462no—
590C2×D4C23×D7312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—2924no—
597C22×C4—731no—
598C22×C4—731no—
599C22×C4—731no—
600C22×C4—731no—
601C22×C4—1464no—
602C22×C4—1461no—
603C22×C4—1461no—
604C22×C4—1461no—
605C22×C4D4×D7311yescharacteristic
606C22×C4D4×D7311yescharacteristic
607C22×C4C23×D7311yescharacteristic
608Q16—2924no—
609Q16—2924no—
610Q16—2924no—
611Q16—1468no—
612SD16—28no—
613SD16—2924no—
614SD16—2924no—
615SD16—1468no—
616D8—2924no—
617C2×C8—22no—
618C2×C8—732no—
619C2×C8—732no—
620C2×C8—1462no—
621C2×C8—1462no—
622C2×C8#1192402814yes—
623C2×C8C23×D7312yes—
624C2×C8C23×D7312yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—734no—
629C4⋊C4—734no—
630C4⋊C4—734no—
631C4⋊C4—1464no—
632C4⋊C4—1464no—
633C4⋊C4—1464no—
634C4⋊C4—1464no—
635C4⋊C4—1464no—
636C4⋊C4—1464no—
637C4⋊C4—1464no—
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—
649C22⋊C4—1464no—
650C42—24no—
651C42—732no—
652C42—732no—
653C42—732no—
654C42—732no—
655C42—1464no—
656C42—1464no—
657C42—1464no—
658C42D4×D7312yes—
659C42C23×D7312yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—2922no—
665C23—2922no—
666C23—2922no—
667C23—1462no—
668C23C2×D4×D7311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—2924no—
673Q8—2922no—
674Q8—2922no—
675Q8—2922no—
676Q8—1462no—
677Q8—1462no—
678Q8—1462no—
679Q8—1462no—
680Q8—1462no—
681Q8—1462no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—2922no—
686D4—1462no—
687D4—1462no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—48no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—2928no—
698C2×C4—2922no—
699C2×C4—2922no—
700C2×C4—2922no—
701C2×C4—732no—
702C2×C4—732no—
703C2×C4—732no—
704C2×C4—732no—
705C2×C4—1462no—
706C2×C4—1462no—
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×C4C2×#1192402812yes—
716C2×C4#1455663712yes—
717C2×C4C24×D7311yescharacteristic
718C8—22no—
719C8—1462no—
720C8—1462no—
721C8C2×#1192402814yes—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—2922no—
727C22—2922no—
728C22—2922no—
729C22—5844no—
730C22#1798925812yes—
731C22#1798938312yes—
732C22#1798940312yes—
733C22C22×D4×D7311yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—2922no—
740C4—2922no—
741C4—2922no—
742C4—1462no—
743C4—1462no—
744C4—1462no—
745C4—1462no—
746C4#1798925812yes—
747C4C22×#1192402811yescharacteristic
748C4C2×#1455663711yescharacteristic
749C2—82no—
750C2—5842no—
751C2#2262301114yesdirect product factor
752C2C2×#1798925811yescharacteristic
753C2C2×#1798938311yescharacteristic
754C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#440×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924013C22
hypercenterC2×#440D73
hypocenterC73C2×#3402
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#17989309C2semidirect
2. C2×#17989307C2semidirect
3. #22623011C2direct (N × H)
4. C2×#17988981C2semidirect
5. C2×#17988978C2semidirect
7. C2×#17988812C2semidirect
8. C2×#17988808C2semidirect
9. C2×#17988797C2semidirect
10. C2×#17988796C2semidirect
13. C2×#17988715C2semidirect
14. C2×#17988686C2semidirect
15. C2×#17988681C2semidirect
16. C2×#440×C73C2semidirect
26. #17989309C22semidirect
28. #17989307C22semidirect
48. #17988981C22semidirect
49. #17988978C22semidirect
51. #17988812C22semidirect
52. #17988808C22semidirect
55. #17988797C22semidirect
56. #17988796C22semidirect
57. #17988715C22semidirect
58. #17988686C22semidirect
59. #17988681C22semidirect
72. #440×C73C22semidirect
373. C2×C73#3402semidirect
392. C2×#440D73semidirect
394. C73C2×#3402semidirect
440. #440C2×D73semidirect
751. C2#22623011direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893092
C2×#179893072
#226230112
C2×#179889812
C2×#179889782
C2×#179889682
C2×#179888122
C2×#179888082
C2×#179887972
C2×#179887962
C2×#179888022
C2×#179888012
C2×#179887152
C2×#179886862
C2×#179886812
C2×#440×C732
C2×#340273