Finite Group Databasebeta

← C2×#22620565 #33955801

Subgroups — C2×#22620565 #33955801

Order 18688.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989210C211yesmaximal, characteristic, complemented
2C2×#17989204C211yesmaximal, characteristic, complemented
3#22620565C2116yesmaximal, direct product factor
4C2×#17988991C211yesmaximal, characteristic, complemented
5C2×#17988968C211yesmaximal, characteristic, complemented
6C2×#17988948C211yesmaximal, characteristic, complemented
7C2×#17988945C211yesmaximal, characteristic, complemented
8C2×#17988833C211yesmaximal, characteristic, complemented
9C2×#17988826C211yesmaximal, characteristic, complemented
10C2×#17988821C211yesmaximal, characteristic
11C2×#17988688C211yesmaximal, characteristic, complemented
12C2×#17988686C211yesmaximal, characteristic, complemented
13C2×#17988679C211yesmaximal, characteristic, complemented
14C2×#17988667C211yesmaximal, characteristic, complemented
15C2×#17988545C211yesmaximal, characteristic, complemented
16C2×#468×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924017C2211yescharacteristic
19C22×#11924013C2211yescharacteristic
20C23×#10596831C2211yescharacteristic
21#17989210—24no—
22#17989210C2218yescomplemented
23#17989204—24no—
24#17989204C2218yescomplemented
25C2×#14556590C2211yescharacteristic
26C2×#14556590C2211yescharacteristic
27C2×#14556586—21no—
28C2×#14556584—21no—
29C2×#14556580C2211yescharacteristic
30C2×#14556578—21no—
31C2×#14556578C2211yescharacteristic
32C2×#14556577—21no—
33C2×#14556573—21no—
34C2×#14556572—21no—
35C2×#14556571—21no—
36C2×#14556570C2211yescharacteristic
37C2×#14556568—21no—
38C2×#14556565C2211yescharacteristic
39C2×Q8×Dic73C2211yescharacteristic
40C2×#14556556C2211yescharacteristic
41C2×D4×Dic73C2211yescharacteristic
42C2×#14556553C2211yescharacteristic
43C2×#14556550C2211yescharacteristic
44#17988991C2218yescomplemented
45#17988968C2218yescomplemented
46#17988948C2218yescomplemented
47#17988945C2218yescomplemented
48#17988833C2218yescomplemented
49#17988826C2218yescomplemented
50#17988821C2218yes—
51#17988688C2218yescomplemented
52#17988686C2218yescomplemented
53#17988679C2218yescomplemented
54#17988667C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556515C2211yescharacteristic
60C2×#14556514C2211yescharacteristic
61C2×#14556513C2211yescharacteristic
62C2×#14556512C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64#17988545C2218yescomplemented
65C2×#14556501C2211yescharacteristic
66C2×#14556501C2211yescharacteristic
67C2×C8×Dic73C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C22×M16×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#468×C73C2218yescomplemented
74C2×#107×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146C2311yescharacteristic
80C22×D292C2311yescharacteristic
81C22×C22⋊D73—21no—
82C23×Dic73—21no—
83C22×C4×D73—21no—
84C2×#11924018—24no—
85C2×#11924018C2314yes—
86C2×#11924017—24no—
87C2×#11924017C2314yes—
88C2×#11924013—24no—
89C2×#11924013C2314yes—
90C22×#10596831—24no—
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2314yes—
93C22×#10596831C2311yescharacteristic
94#14556590—22no—
95#14556590—22no—
96#14556590C2314yes—
97#14556590C2314yes—
98#14556586—28no—
99#14556584—28no—
100#14556580—22no—
101#14556580C2314yes—
102#14556578—28no—
103#14556578—22no—
104#14556578C2314yes—
105#14556577—28no—
106#14556573—28no—
107#14556572—28no—
108#14556571—28no—
109#14556570—22no—
110#14556570C2314yes—
111#14556568—28no—
112#14556565—22no—
113#14556565C2314yes—
114Q8×Dic73—22no—
115Q8×Dic73C2314yes—
116#14556556—22no—
117#14556556C2314yes—
118D4×Dic73—22no—
119D4×Dic73C2314yes—
120#14556553—22no—
121#14556553C2314yes—
122#14556550D414yes—
123#14556550C2314yes—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73D411yescharacteristic
126C2×C4⋊Dic73D411yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×C22⋊Dic73D411yescharacteristic
138C2×C22⋊Dic73D411yescharacteristic
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73C2311yescharacteristic
146C2×C4×Dic73C2311yescharacteristic
147#14556525C2314yes—
148#14556524C2314yes—
149#14556524C2314yes—
150#14556516C2314yes—
151#14556515C2314yes—
152#14556514C2314yes—
153#14556513C2314yes—
154#14556512C2314yes—
155#14556511C2314yes—
156#14556501C2314yes—
157#14556501C2314yes—
158C8×Dic73C2314yes—
159C8×Dic73C2314yes—
160C22×Q8×C73C2311yescharacteristic
161C22×D4×C73—21no—
162C22×D4×C73C2311yescharacteristic
163C23×C4×C73C2311yescharacteristic
164C2×SD16×C73—24no—
165C2×SD16×C73C2314yes—
166C2×M16×C73—24no—
167C2×M16×C73C2314yes—
168C22×C8×C73C2311yescharacteristic
169C22×C8×C73C2311yescharacteristic
170C22⋊Q8×C73—22no—
171C22⋊Q8×C73C2314yes—
172#121×C73—22no—
173#121×C73C2314yes—
174C2×C4⋊C4×C73—21no—
175C2×C4⋊C4×C73C2311yescharacteristic
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179#107×C73C2314yes—
180#103×C73C2314yes—
181#102×C73C2314yes—
182C23×D73—21no—
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—21no—
186C2×Dic146—24no—
187C2×Dic146—24no—
188C2×Dic146—82no—
189C2×Dic146—82no—
190C2×Dic146C2412yes—
191C2×D292—22no—
192C2×D292—22no—
193C2×D292—21no—
194C2×D292C2412yes—
195C2×C22⋊D73—24no—
196C2×C22⋊D73—82no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—24no—
201C22×Dic73—82no—
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C2×C4×D73—24no—
207C2×C4×D73—82no—
208#11924018—28no—
209#11924017—28no—
210#11924013—28no—
211C2×#10596831—22no—
212C2×#10596831—28no—
213C2×#10596831#4114yes—
214C2×#10596831C2412yes—
215C2×#10596831C2412yes—
216C4⋊Dic73—21no—
217C4⋊Dic73—21no—
218C4⋊Dic73—24no—
219C4⋊Dic73C2×D414yes—
220C4⋊Dic73C2×D414yes—
221C4⋊Dic73C2412yes—
222C4⋊Dic73C2412yes—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227C22⋊Dic73—24no—
228C22⋊Dic73—24no—
229C22⋊Dic73—24no—
230C22⋊Dic73—24no—
231C22⋊Dic73C2×D414yes—
232C22⋊Dic73C2×D414yes—
233#11924005—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237C4×Dic73—24no—
238C4×Dic73—24no—
239C4×Dic73C2×D412yes—
240C4×Dic73C2×D412yes—
241C4×Dic73C2412yes—
242C4×Dic73C2412yes—
243C24×C73—21no—
244C24×C73C2×D411yescharacteristic
245C2×Q8×C73—21no—
246C2×Q8×C73—22no—
247C2×Q8×C73—22no—
248C2×Q8×C73C2412yes—
249C2×D4×C73—24no—
250C2×D4×C73—21no—
251C2×D4×C73—22no—
252C2×D4×C73—22no—
253C2×D4×C73—82no—
254C2×D4×C73C2412yes—
255C22×C4×C73—22no—
256C22×C4×C73—22no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D412yes—
262C22×C4×C73C2412yes—
263C22×C4×C73C2411yescharacteristic
264SD16×C73—28no—
265M16×C73—28no—
266C2×C8×C73—22no—
267C2×C8×C73#4114yes—
268C2×C8×C73C2412yes—
269C2×C8×C73C2412yes—
270C4⋊C4×C73—24no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73C2412yes—
274C4⋊C4×C73C2412yes—
275C22⋊C4×C73—24no—
276C22⋊C4×C73—24no—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73—22no—
280C23×C73—22no—
281C23×C73—42no—
282C23×C73—42no—
283C23×C73—42no—
284C23×C73C22×D412yes—
285C23×C73C22×D411yescharacteristic
286C22×D73—22no—
287C22×D73—42no—
288C22×D73—42no—
289C22×D73—42no—
290Q8×C73—22no—
291Q8×C73—22no—
292Q8×C73—42no—
293D4×C73—22no—
294D4×C73—22no—
295D4×C73—42no—
296D4×C73—84no—
297C2×C4×C73—22no—
298C2×C4×C73—24no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—42no—
305C2×C4×C73—42no—
306C2×C4×C73—42no—
307C2×C4×C73C22×D412yes—
308C2×C4×C73C22×D411yescharacteristic
309C2×C4×C73C2×#4112yes—
310C2×C4×C73C2×#4112yes—
311C2×C4×C73C2511yescharacteristic
312C22⋊D73—84no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—42no—
321C2×Dic73—42no—
322C2×Dic73—42no—
323C2×Dic73—84no—
324C2×Dic73C22×D412yes—
325C2×Dic73C22×D412yes—
326C2×Dic73C22×D412yes—
327C2×Dic73C22×D412yes—
328D292—22no—
329D292—22no—
330D292—42no—
331C4×D73—84no—
332Dic146—22no—
333Dic146—22no—
334Dic146—42no—
335Dic146—84no—
336Dic146—84no—
337C8×C73—22no—
338C8×C73C2×#4114yes—
339#10596831—22no—
340#10596831C2×#4114yes—
341C22×C73—22no—
342C22×C73—22no—
343C22×C73—22no—
344C22×C73—44no—
345C22×C73—42no—
346C22×C73—42no—
347C22×C73—42no—
348C22×C73—84no—
349C22×C73#53212yes—
350C22×C73#57612yes—
351C22×C73#57812yes—
352C22×C73C23×D411yescharacteristic
353C2×D73—42no—
354C2×D73—42no—
355C2×D73—42no—
356C2×D73—84no—
357C4×C73—22no—
358C4×C73—42no—
359C4×C73—42no—
360C4×C73—42no—
361C4×C73#53212yes—
362C4×C73C22×#4111yescharacteristic
363C4×C73C22×#4111yescharacteristic
364Dic73—22no—
365Dic73—22no—
366Dic73—22no—
367Dic73—22no—
368Dic73—42no—
369Dic73—42no—
370Dic73—42no—
371C2×#3175—731nomaximal, Sylow
372C2×C73—42no—
373C2×C73—82no—
374C2×C73#317514yescomplemented
375C2×C73C2×#53211yescharacteristic
376C2×C73C2×#57611yescharacteristic
377C2×C73C2×#57811yescharacteristic
378D73—82no—
379C2×#542—731no—
380C2×#542—731no—
381#3175—7316no—
382C2×#500—731no—
383C2×#495—731no—
384C2×#489—731no—
385C2×#489—731no—
386C2×#468—731no—
387C2×#468D7311yescharacteristic, complemented
388C2×#467—731no—
389C2×#466—731no—
390C2×#440—731no—
391C2×#440—731no—
392C2×C4×Q16—731no—
393C2×C4×D8—731no—
394C2×#405—731no—
395C73C2×#317511yescharacteristic, complemented, Sylow
396C22×Q16—731no—
397C22×SD16—731no—
398C22×SD16C2×D7311yescharacteristic
399C22×D8—731no—
400C22×M16C2×D7311yescharacteristic
401C23×C8—731no—
402#542—738no—
403#542—738no—
404#542—1464no—
405#542—1464no—
406C2×C4⋊Q8—731no—
407C2×C4⋊Q8—731no—
408C2×#126—1461no—
409C2×#126—1461no—
410C2×#124—731no—
411C2×#124—731no—
412C2×#124—1461no—
413C2×#124—1461no—
414C2×#123—1461no—
415C2×#123—1461no—
416C2×C22⋊Q8—731no—
417C2×C22⋊Q8—1461no—
418C2×C22⋊Q8—1461no—
419C2×C22⋊Q8C2×D7311yescharacteristic
420C2×#121—731no—
421C2×#121C2×D7311yescharacteristic
422C2×C4×Q8—731no—
423C2×C4×Q8—731no—
424C2×C4×D4—731no—
425C2×C4×D4—731no—
426C2×#117—731no—
427#500—738no—
428#495—738no—
429#489—738no—
430#489—738no—
431#468—738no—
432#468C2×D7318yescomplemented
433#467—738no—
434#466—738no—
435#440—738no—
436#440—738no—
437C4×Q16—738no—
438C4×D8—738no—
439C2×#107—731no—
440C2×#107—731no—
441C2×#107—731no—
442C2×#107C2×D7311yescharacteristic
443C2×#103—731no—
444C2×#103—731no—
445C2×#103—731no—
446C2×#103C2×D7311yescharacteristic
447C2×#102—731no—
448C2×#102—731no—
449C2×#102—731no—
450C2×#102C2×D7311yescharacteristic
451#405—738no—
452C2×#97—731no—
453C2×#97—731no—
454C2×C4×C8—731no—
455C2×C4×C8—731no—
456C22×Q8—731no—
457C22×Q8—1461no—
458C22×Q8—1461no—
459C22×Q8C22×D7311yescharacteristic
460C22×D4—21no—
461C22×D4—731no—
462C22×D4—1461no—
463C22×D4C22×D7311yescharacteristic
464C23×C4—1461no—
465C23×C4—1461no—
466C23×C4C22×D7311yescharacteristic
467C2×Q16—734no—
468C2×Q16—1464no—
469C2×SD16—24no—
470C2×SD16—734no—
471C2×SD16—1464no—
472C2×SD16C22×D7314yes—
473C2×D8—734no—
474C2×D8—1464no—
475C2×M16—24no—
476C2×M16C22×D7314yes—
477C22×C8—731no—
478C22×C8—731no—
479C22×C8—734no—
480C22×C8—1464no—
481C22×C8C22×D7311yescharacteristic
482C22×C8C22×D7311yescharacteristic
483C4⋊Q8—734no—
484C4⋊Q8—734no—
485C4⋊Q8—1462no—
486C4⋊Q8—1462no—
487#126—1468no—
488#126—1468no—
489#124—734no—
490#124—734no—
491#124—1462no—
492#124—1462no—
493#124—1468no—
494#124—1468no—
495#123—1468no—
496#123—1468no—
497C22⋊Q8—22no—
498C22⋊Q8—734no—
499C22⋊Q8—1468no—
500C22⋊Q8—1468no—
501C22⋊Q8—1462no—
502C22⋊Q8C22×D7314yes—
503#121—22no—
504#121—734no—
505#121—1462no—
506#121C22×D7314yes—
507C4×Q8—734no—
508C4×Q8—734no—
509C4×Q8—1462no—
510C4×Q8—1462no—
511C4×D4—734no—
512C4×D4—734no—
513C4×D4—1462no—
514C4×D4—1462no—
515#117—734no—
516#117—734no—
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⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4C22×D7311yescharacteristic
528C2×C4⋊C4C22×D7311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—731no—
532C2×C22⋊C4—731no—
533C2×C22⋊C4—1461no—
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×C42—731no—
542C2×C42—731no—
543C2×C42—1461no—
544C2×C42—1461no—
545#107—734no—
546#107—734no—
547#107—734no—
548#107C22×D7314yes—
549#103—734no—
550#103—734no—
551#103—734no—
552#103C22×D7314yes—
553#102—734no—
554#102—734no—
555#102—734no—
556#102C22×D7314yes—
557#97—734no—
558#97—734no—
559C4×C8—734no—
560C4×C8—734no—
561C24—21no—
562C24—1461no—
563C24D4×D7311yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—5842no—
568C2×Q8—5842no—
569C2×Q8—732no—
570C2×Q8—1464no—
571C2×Q8—1464no—
572C2×Q8—1462no—
573C2×Q8—1462no—
574C2×Q8—1461no—
575C2×Q8C23×D7312yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—5842no—
582C2×D4—732no—
583C2×D4—1464no—
584C2×D4—1461no—
585C2×D4—1462no—
586C2×D4—1462no—
587C2×D4C23×D7312yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—5842no—
594C22×C4—5842no—
595C22×C4—731no—
596C22×C4—731no—
597C22×C4—731no—
598C22×C4—731no—
599C22×C4—1464no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4—1464no—
604C22×C4D4×D7312yes—
605C22×C4D4×D7311yescharacteristic
606C22×C4C23×D7312yes—
607C22×C4C23×D7311yescharacteristic
608Q16—1468no—
609SD16—28no—
610SD16—1468no—
611D8—1468no—
612M16—28no—
613C2×C8—22no—
614C2×C8—734no—
615C2×C8—732no—
616C2×C8—732no—
617C2×C8—1468no—
618C2×C8—1462no—
619C2×C8#1192402714yes—
620C2×C8C23×D7312yes—
621C2×C8C23×D7312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—734no—
626C4⋊C4—734no—
627C4⋊C4—732no—
628C4⋊C4—732no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1464no—
632C4⋊C4—1464no—
633C4⋊C4—1464no—
634C4⋊C4—1461no—
635C4⋊C4—1461no—
636C4⋊C4C23×D7312yes—
637C4⋊C4C23×D7312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—734no—
641C22⋊C4—734no—
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—732no—
651C42—732no—
652C42—732no—
653C42—732no—
654C42—1464no—
655C42—1464no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—2922no—
664C23—2922no—
665C23—2922no—
666C23—1462no—
667C23C2×D4×D7312yes—
668C23C2×D4×D7311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—2922no—
673Q8—5844no—
674Q8—5844no—
675Q8—1462no—
676Q8—1462no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—2922no—
682D4—5844no—
683D4—1462no—
684D4—1462no—
685C2×C4—22no—
686C2×C4—24no—
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—2922no—
696C2×C4—2922no—
697C2×C4—2922no—
698C2×C4—5844no—
699C2×C4—5844no—
700C2×C4—732no—
701C2×C4—732no—
702C2×C4—732no—
703C2×C4—732no—
704C2×C4—1462no—
705C2×C4—1462no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4—1462no—
710C2×C4—1462no—
711C2×C4C2×D4×D7312yes—
712C2×C4C2×D4×D7311yescharacteristic
713C2×C4#41×D7312yes—
714C2×C4C2×#1192402712yes—
715C2×C4C24×D7311yescharacteristic
716C8—22no—
717C8—734no—
718C8—1462no—
719C8C2×#1192402714yes—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—2922no—
729C22—2922no—
730C22—2922no—
731C22—5844no—
732C22#1798913212yes—
733C22#1798939112yes—
734C22#1798940312yes—
735C22C22×D4×D7311yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—2922no—
741C4—2922no—
742C4—2922no—
743C4—1462no—
744C4—1462no—
745C4—1462no—
746C4—1462no—
747C4#1798913212yes—
748C4C2×#41×D7311yescharacteristic
749C4C22×#1192402711yescharacteristic
750C2—42no—
751C2—82no—
752C2—5842no—
753C2#2262056514yesdirect product factor
754C2C2×#1798913211yescharacteristic
755C2C2×#1798939111yescharacteristic
756C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#468×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988821C2
hypercenterC2×#468D73
hypocenterC73C2×#3175
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#17989210C2semidirect
2. C2×#17989204C2semidirect
3. #22620565C2direct (N × H)
4. C2×#17988991C2semidirect
5. C2×#17988968C2semidirect
6. C2×#17988948C2semidirect
7. C2×#17988945C2semidirect
8. C2×#17988833C2semidirect
9. C2×#17988826C2semidirect
11. C2×#17988688C2semidirect
12. C2×#17988686C2semidirect
13. C2×#17988679C2semidirect
14. C2×#17988667C2semidirect
15. C2×#17988545C2semidirect
16. C2×#468×C73C2semidirect
22. #17989210C22semidirect
24. #17989204C22semidirect
44. #17988991C22semidirect
45. #17988968C22semidirect
46. #17988948C22semidirect
47. #17988945C22semidirect
48. #17988833C22semidirect
49. #17988826C22semidirect
51. #17988688C22semidirect
52. #17988686C22semidirect
53. #17988679C22semidirect
54. #17988667C22semidirect
64. #17988545C22semidirect
73. #468×C73C22semidirect
374. C2×C73#3175semidirect
387. C2×#468D73semidirect
395. C73C2×#3175semidirect
432. #468C2×D73semidirect
753. C2#22620565direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892102
C2×#179892042
#226205652
C2×#179889912
C2×#179889682
C2×#179889482
C2×#179889452
C2×#179888332
C2×#179888262
C2×#179888212
C2×#179886882
C2×#179886862
C2×#179886792
C2×#179886672
C2×#179885452
C2×#468×C732
C2×#317573