Finite Group Databasebeta

← C2×#22620206 #33954313

Subgroups — C2×#22620206 #33954313

Order 18688.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989209C211yesmaximal, characteristic, complemented
2C2×#17989069C211yesmaximal, characteristic, complemented
3#22620206C2116yesmaximal, direct product factor
4C2×#17988907C211yesmaximal, characteristic, complemented
5C2×#17988916C211yesmaximal, characteristic, complemented
6C2×#17988870C211yesmaximal, characteristic, complemented
7C2×#17988876C211yesmaximal, characteristic, complemented
8C2×#17988811C211yesmaximal, characteristic, complemented
9C2×#17988805C211yesmaximal, characteristic, complemented
10C2×#17988748C211yesmaximal, characteristic, complemented
11C2×#17988735C211yesmaximal, characteristic
12C2×#17988700C211yesmaximal, characteristic, complemented
13C2×C4×#11924015C211yesmaximal, characteristic, complemented
14C2×C4×#11924015C211yesmaximal, characteristic, complemented
15C2×#17988649C211yesmaximal, characteristic, complemented
16C2×#441×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924015C2211yescharacteristic
19C22×#11924015C2211yescharacteristic
20C22×D584C2211yescharacteristic
21#17989209—24no—
22#17989209C2218yescomplemented
23C2×#14556590C2211yescharacteristic
24C2×#14556585—21no—
25C2×#14556580C2211yescharacteristic
26C2×#14556579—21no—
27C2×#14556576—21no—
28C2×#14556569—21no—
29C2×#14556567C2211yescharacteristic
30C2×#14556566C2211yescharacteristic
31#17989069—24no—
32#17989069C2218yescomplemented
33C2×Q8×Dic73C2211yescharacteristic
34C2×C4×D292—21no—
35C2×C4×D292C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C2×#14556553—21no—
38C2×#14556553C2211yescharacteristic
39C2×#14556548—21no—
40C2×#14556548C2211yescharacteristic
41C2×C4⋊C4×D73—21no—
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988916C2218yescomplemented
44#17988907C2218yescomplemented
45#17988876C2218yescomplemented
46#17988870C2218yescomplemented
47#17988811C2218yescomplemented
48#17988805C2218yescomplemented
49#17988748C2218yescomplemented
50#17988735C2218yes—
51#17988700C2218yescomplemented
52C4×#11924015C2218yescomplemented
53C4×#11924015C2218yescomplemented
54#17988649C2218yescomplemented
55C2×#14556523C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C4×#10596831C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×Q8×C73C2211yescharacteristic
72#441×C73C2218yescomplemented
73C2×#106×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C2×#11924029—24no—
78C2×#11924029—22no—
79C2×#11924029—24no—
80C2×#11924029C2314yes—
81C22×Dic146—21no—
82C22×D292—21no—
83C22×D292—21no—
84C22×D292C2311yescharacteristic
85C22×D292C2311yescharacteristic
86C22×C4×D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73—21no—
89C22×C4×D73—21no—
90C22×C4×D73—21no—
91C22×C4×D73C2311yescharacteristic
92C2×#11924015—24no—
93C2×#11924015—24no—
94C2×#11924015C2314yes—
95C2×#11924015C2314yes—
96C2×D584—24no—
97C2×D584C2314yes—
98C22×#10596831C2311yescharacteristic
99C22×#10596831C2311yescharacteristic
100#14556590—22no—
101#14556590C2314yes—
102#14556585—28no—
103#14556580—22no—
104#14556580C2314yes—
105#14556579—28no—
106#14556576—28no—
107#14556569—28no—
108#14556567—22no—
109#14556567C2314yes—
110#14556566—22no—
111#14556566C2314yes—
112Q8×Dic73—22no—
113Q8×Dic73C2314yes—
114C4×D292—28no—
115C4×D292—22no—
116C4×D292—22no—
117C4×D292C2314yes—
118C4×D292C2314yes—
119#14556553—28no—
120#14556553—22no—
121#14556553C2314yes—
122#14556548—28no—
123#14556548D414yes—
124#14556548C2314yes—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007D411yescharacteristic
132C2×#11924007D411yescharacteristic
133C4⋊C4×D73—22no—
134C4⋊C4×D73—28no—
135C4⋊C4×D73C2314yes—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005D411yescharacteristic
144C2×#11924005D411yescharacteristic
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556523C2314yes—
148#14556522C2314yes—
149#14556522C2314yes—
150#14556520C2314yes—
151#14556520C2314yes—
152#14556515C2314yes—
153#14556515C2314yes—
154#14556513C2314yes—
155#14556513C2314yes—
156#14556511C2314yes—
157#14556511C2314yes—
158#14556503C2314yes—
159#14556503C2314yes—
160C4×#10596831C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×Q8×C73C2311yescharacteristic
163C2×Q16×C73—24no—
164C2×Q16×C73C2314yes—
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C4×Q8×C73—22no—
168C4×Q8×C73—22no—
169C4×Q8×C73C2314yes—
170C4×Q8×C73C2314yes—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C42×C73—21no—
176C2×C42×C73—21no—
177C2×C42×C73C2311yescharacteristic
178#106×C73C2314yes—
179#103×C73C2314yes—
180#103×C73C2314yes—
181#97×C73C2314yes—
182C23×D73—21no—
183C23×D73—21no—
184C23×D73C2×D411yescharacteristic
185#11924029—216no—
186#11924029—28no—
187#11924029—28no—
188C2×Dic146—24no—
189C2×Dic146—82no—
190C2×D292—28no—
191C2×D292—24no—
192C2×D292—21no—
193C2×D292—22no—
194C2×D292—22no—
195C2×D292—22no—
196C2×D292—21no—
197C2×D292—24no—
198C2×D292—82no—
199C2×D292#4114yes—
200C2×D292C2412yes—
201C2×D292C2412yes—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C2×C4×D73—28no—
208C2×C4×D73—22no—
209C2×C4×D73—22no—
210C2×C4×D73—24no—
211C2×C4×D73—24no—
212C2×C4×D73—24no—
213C2×C4×D73—24no—
214C2×C4×D73—24no—
215C2×C4×D73—82no—
216C2×C4×D73—82no—
217C2×C4×D73—82no—
218C2×C4×D73—82no—
219C2×C4×D73C2×D412yes—
220C2×C4×D73C2412yes—
221#11924015—28no—
222#11924015—28no—
223D584—28no—
224C2×#10596831—22no—
225C2×#10596831—22no—
226C2×#10596831C2412yes—
227C2×#10596831C2412yes—
228C4⋊Dic73—21no—
229C4⋊Dic73—21no—
230C4⋊Dic73—24no—
231C4⋊Dic73C2412yes—
232C4⋊Dic73C2412yes—
233#11924007—24no—
234#11924007—24no—
235#11924007—24no—
236#11924007C2×D414yes—
237#11924007C2×D414yes—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005—24no—
242#11924005—24no—
243#11924005—24no—
244#11924005—24no—
245#11924005C2×D414yes—
246#11924005C2×D414yes—
247C4×Dic73—24no—
248C4×Dic73C2×D412yes—
249C4×Dic73C2412yes—
250C2×Q8×C73—21no—
251C2×Q8×C73—21no—
252C2×Q8×C73—22no—
253C2×Q8×C73—22no—
254C2×Q8×C73—22no—
255C2×Q8×C73#4114yes—
256C2×Q8×C73C2412yes—
257C2×Q8×C73C2412yes—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73C2×D411yescharacteristic
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2411yescharacteristic
265Q16×C73—28no—
266C2×C8×C73—22no—
267C2×C8×C73—22no—
268C2×C8×C73C2412yes—
269C2×C8×C73C2412yes—
270C4⋊C4×C73—24no—
271C4⋊C4×C73—24no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73C2412yes—
275C4⋊C4×C73C2412yes—
276C42×C73—24no—
277C42×C73—24no—
278C42×C73C2×D412yes—
279C42×C73C2412yes—
280C23×C73C22×D411yescharacteristic
281C22×D73—22no—
282C22×D73—24no—
283C22×D73—22no—
284C22×D73—22no—
285C22×D73—22no—
286C22×D73—22no—
287C22×D73—42no—
288C22×D73—42no—
289C22×D73—42no—
290C22×D73—42no—
291C22×D73—42no—
292C22×D73C22×D412yes—
293Q8×C73—24no—
294Q8×C73—22no—
295Q8×C73—22no—
296Q8×C73—22no—
297Q8×C73—42no—
298Q8×C73C2×#4114yes—
299C2×C4×C73—24no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—42no—
307C2×C4×C73—42no—
308C2×C4×C73—42no—
309C2×C4×C73C22×D412yes—
310C2×C4×C73C22×D412yes—
311C2×C4×C73C22×D411yescharacteristic
312C2×C4×C73C2×#4112yes—
313C2×C4×C73C2×#4112yes—
314C2×C4×C73C2511yescharacteristic
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—42no—
321C2×Dic73—42no—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324C2×Dic73C22×D412yes—
325D292—216no—
326D292—24no—
327D292—22no—
328D292—22no—
329D292—22no—
330D292—42no—
331D292—84no—
332D292C2×#4114yes—
333C4×D73—216no—
334C4×D73—24no—
335C4×D73—22no—
336C4×D73—22no—
337C4×D73—84no—
338C4×D73—84no—
339C4×D73—84no—
340C4×D73—84no—
341Dic146—84no—
342C8×C73—22no—
343C8×C73—22no—
344#10596831—22no—
345#10596831—22no—
346C22×C73#52512yes—
347C22×C73#57712yes—
348C22×C73#57712yes—
349C22×C73C23×D411yescharacteristic
350C2×D73—22no—
351C2×D73—24no—
352C2×D73—22no—
353C2×D73—22no—
354C2×D73—44no—
355C2×D73—48no—
356C2×D73—42no—
357C2×D73—42no—
358C2×D73—42no—
359C2×D73—42no—
360C2×D73—42no—
361C2×D73—84no—
362C4×C73—24no—
363C4×C73—22no—
364C4×C73—22no—
365C4×C73—42no—
366C4×C73—42no—
367C4×C73—42no—
368C4×C73#52512yes—
369C4×C73C22×#4111yescharacteristic
370C4×C73C22×#4111yescharacteristic
371Dic73—22no—
372Dic73—22no—
373Dic73—22no—
374Dic73—42no—
375Dic73—42no—
376C2×#3125—731nomaximal, Sylow
377C2×C73#312514yescomplemented
378C2×C73C2×#52511yescharacteristic
379C2×C73C2×#57711yescharacteristic
380C2×C73C2×#57711yescharacteristic
381D73—42no—
382D73—44no—
383D73—82no—
384C2×#542—731no—
385C2×#520—731no—
386#3125—7316no—
387C2×#481—731no—
388C2×#483—731no—
389C2×#475—731no—
390C2×#476—731no—
391C2×#464—731no—
392C2×#463—731no—
393C2×#452—731no—
394C2×#449—731no—
395C2×#442—731no—
396C2×#441D7311yescharacteristic, complemented
397C2×C4×SD16—731no—
398C2×C4×SD16—731no—
399C2×#433—731no—
400C73C2×#312511yescharacteristic, complemented, Sylow
401C22×#41—731no—
402C22×Q16C2×D7311yescharacteristic
403C22×SD16—731no—
404C22×SD16—731no—
405C22×D8—731no—
406#542—738no—
407#542—1464no—
408C2×C4⋊Q8—731no—
409C2×#126—1461no—
410C2×#124—731no—
411C2×#124—1461no—
412C2×#123—1461no—
413C2×C22⋊Q8—731no—
414C2×C22⋊Q8—1461no—
415C2×#121—731no—
416#520—738no—
417#520—1464no—
418C2×C4×Q8—731no—
419C2×C4×Q8C2×D7311yescharacteristic
420C2×C4×Q8C2×D7311yescharacteristic
421C2×C4×D4—731no—
422C2×C4×D4—731no—
423C2×C4×D4—731no—
424C2×C4×D4—1461no—
425C2×C4×D4—1461no—
426C2×#117—731no—
427C2×#117—1461no—
428C22×C4⋊C4—731no—
429C22×C4⋊C4—1461no—
430#483—738no—
431#481—738no—
432#476—738no—
433#475—738no—
434#464—738no—
435#463—738no—
436#452—738no—
437#449—738no—
438#442—738no—
439#441C2×D7318yescomplemented
440C4×SD16—738no—
441C4×SD16—738no—
442#433—738no—
443C2×#106—731no—
444C2×#106—731no—
445C2×#106—731no—
446C2×#106C2×D7311yescharacteristic
447C2×C4⋊C8—731no—
448C2×C4⋊C8—731no—
449C2×#103—731no—
450C2×#103—731no—
451C2×#103C2×D7311yescharacteristic
452C2×#103C2×D7311yescharacteristic
453C2×#102—731no—
454C2×#102—731no—
455C2×#102—731no—
456C2×#102—731no—
457C2×C22⋊C8—731no—
458C2×C22⋊C8—731no—
459C2×#97C2×D7311yescharacteristic
460C2×C4×C8—731no—
461C2×#41—734no—
462C2×#41—1462no—
463C2×#41—1464no—
464C2×#41—1464no—
465C22×Q8—1461no—
466C22×Q8C22×D7311yescharacteristic
467C22×Q8C22×D7311yescharacteristic
468C22×D4—731no—
469C22×D4—731no—
470C22×D4—1461no—
471C22×D4—1461no—
472C23×C4—731no—
473C23×C4—1461no—
474C23×C4—1461no—
475C23×C4—1461no—
476C23×C4—1461no—
477C23×C4—1461no—
478C2×Q16—24no—
479C2×Q16C22×D7314yes—
480C2×SD16—734no—
481C2×SD16—734no—
482C2×SD16—1464no—
483C2×SD16—1464no—
484C2×D8—734no—
485C2×D8—1464no—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490C4⋊Q8—734no—
491C4⋊Q8—1462no—
492#126—1468no—
493#124—734no—
494#124—1468no—
495#124—1462no—
496#123—1468no—
497C22⋊Q8—734no—
498C22⋊Q8—1468no—
499C22⋊Q8—1462no—
500#121—734no—
501#121—1462no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—734no—
505C4×Q8—1462no—
506C4×Q8C22×D7314yes—
507C4×Q8C22×D7314yes—
508C4×D4—734no—
509C4×D4—734no—
510C4×D4—734no—
511C4×D4—1468no—
512C4×D4—1462no—
513C4×D4—1468no—
514C4×D4—1462no—
515C4×D4—1462no—
516#117—734no—
517#117—734no—
518#117—1468no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—731no—
525C2×C4⋊C4—734no—
526C2×C4⋊C4—1468no—
527C2×C4⋊C4—1462no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4—1461no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4—1461no—
532C2×C4⋊C4C22×D7311yescharacteristic
533C2×C4⋊C4C22×D7311yescharacteristic
534C2×C22⋊C4—731no—
535C2×C22⋊C4—731no—
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—21no—
545C2×C42—731no—
546C2×C42—1461no—
547C2×C42C22×D7311yescharacteristic
548#106—734no—
549#106—734no—
550#106—734no—
551#106C22×D7314yes—
552C4⋊C8—734no—
553C4⋊C8—734no—
554#103—734no—
555#103—734no—
556#103C22×D7314yes—
557#103C22×D7314yes—
558#102—734no—
559#102—734no—
560#102—734no—
561#102—734no—
562C22⋊C8—734no—
563C22⋊C8—734no—
564#97C22×D7314yes—
565C4×C8—734no—
566C24—731no—
567C24—1461no—
568C24—1461no—
569#41—1468no—
570#41—14616no—
571#41—1468no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—5842no—
578C2×Q8—1464no—
579C2×Q8#1192402814yes—
580C2×Q8C23×D7312yes—
581C2×Q8C23×D7312yes—
582C2×D4—5842no—
583C2×D4—734no—
584C2×D4—732no—
585C2×D4—732no—
586C2×D4—1464no—
587C2×D4—1464no—
588C2×D4—1468no—
589C2×D4—1461no—
590C2×D4—1461no—
591C2×D4—1462no—
592C2×D4—1462no—
593C2×D4—1462no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—5842no—
599C22×C4—5842no—
600C22×C4—5842no—
601C22×C4—5842no—
602C22×C4—731no—
603C22×C4—731no—
604C22×C4—731no—
605C22×C4—732no—
606C22×C4—732no—
607C22×C4—1464no—
608C22×C4—1464no—
609C22×C4—1464no—
610C22×C4—1468no—
611C22×C4—1461no—
612C22×C4—1461no—
613C22×C4—1464no—
614C22×C4—1464no—
615C22×C4—1462no—
616C22×C4—1462no—
617C22×C4D4×D7311yescharacteristic
618C22×C4D4×D7311yescharacteristic
619C22×C4C23×D7311yescharacteristic
620Q16—28no—
621SD16—1468no—
622SD16—1468no—
623D8—1468no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—732no—
627C2×C8—732no—
628C2×C8—1462no—
629C2×C8—1462no—
630C2×C8C23×D7312yes—
631C2×C8C23×D7312yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—734no—
637C4⋊C4—734no—
638C4⋊C4—732no—
639C4⋊C4—732no—
640C4⋊C4—1464no—
641C4⋊C4—1464no—
642C4⋊C4—1464no—
643C4⋊C4—1464no—
644C4⋊C4—1461no—
645C4⋊C4—1461no—
646C4⋊C4C23×D7312yes—
647C4⋊C4C23×D7312yes—
648C22⋊C4—734no—
649C22⋊C4—734no—
650C22⋊C4—1464no—
651C22⋊C4—1464no—
652C22⋊C4—1464no—
653C22⋊C4—1464no—
654C22⋊C4—1464no—
655C22⋊C4—1464no—
656C22⋊C4—1464no—
657C42—24no—
658C42—24no—
659C42—732no—
660C42—732no—
661C42—1464no—
662C42D4×D7312yes—
663C42C23×D7312yes—
664C23—2922no—
665C23—2922no—
666C23—2922no—
667C23—2922no—
668C23—2922no—
669C23—732no—
670C23—1462no—
671C23—1462no—
672C23—1462no—
673C23—1462no—
674C23—1464no—
675C23—1462no—
676C23C2×D4×D7311yescharacteristic
677Q8—22no—
678Q8—24no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8—5844no—
683Q8C2×#1192402814yes—
684D4—2922no—
685D4—5844no—
686D4—734no—
687D4—14616no—
688D4—1462no—
689D4—1462no—
690D4—1462no—
691D4—1464no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—2922no—
703C2×C4—2922no—
704C2×C4—5844no—
705C2×C4—5844no—
706C2×C4—5844no—
707C2×C4—5844no—
708C2×C4—732no—
709C2×C4—732no—
710C2×C4—732no—
711C2×C4—14616no—
712C2×C4—1462no—
713C2×C4—1462no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1464no—
720C2×C4C2×D4×D7312yes—
721C2×C4C2×D4×D7312yes—
722C2×C4C2×D4×D7311yescharacteristic
723C2×C4#41×D7312yes—
724C2×C4C2×#1192402812yes—
725C2×C4C24×D7311yescharacteristic
726C8—22no—
727C8—22no—
728C8—1462no—
729C8—1462no—
730C22—2928no—
731C22—2924no—
732C22—2922no—
733C22—2922no—
734C22—2922no—
735C22—2922no—
736C22—2922no—
737C22—5844no—
738C22—1462no—
739C22—1462no—
740C22—1464no—
741C22—1462no—
742C22#1798909612yes—
743C22#1798939612yes—
744C22#1798939612yes—
745C22C22×D4×D7311yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—2922no—
753C4—2922no—
754C4—1462no—
755C4—1462no—
756C4—1462no—
757C4#1798909612yes—
758C4C2×#41×D7311yescharacteristic
759C4C22×#1192402811yescharacteristic
760C2—2924no—
761C2—2922no—
762C2—5842no—
763C2#2262020614yesdirect product factor
764C2C2×#1798909611yescharacteristic
765C2C2×#1798939611yescharacteristic
766C2C2×#1798939611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#441×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988735C2
hypercenterC2×#441D73
hypocenterC73C2×#3125
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×#17989209C2semidirect
2. C2×#17989069C2semidirect
3. #22620206C2direct (N × H)
4. C2×#17988907C2semidirect
5. C2×#17988916C2semidirect
6. C2×#17988870C2semidirect
7. C2×#17988876C2semidirect
8. C2×#17988811C2semidirect
9. C2×#17988805C2semidirect
10. C2×#17988748C2semidirect
12. C2×#17988700C2semidirect
13. C2×C4×#11924015C2semidirect
14. C2×C4×#11924015C2semidirect
15. C2×#17988649C2semidirect
16. C2×#441×C73C2semidirect
22. #17989209C22semidirect
32. #17989069C22semidirect
43. #17988916C22semidirect
44. #17988907C22semidirect
45. #17988876C22semidirect
46. #17988870C22semidirect
47. #17988811C22semidirect
48. #17988805C22semidirect
49. #17988748C22semidirect
51. #17988700C22semidirect
52. C4×#11924015C22semidirect
53. C4×#11924015C22semidirect
54. #17988649C22semidirect
72. #441×C73C22semidirect
377. C2×C73#3125semidirect
396. C2×#441D73semidirect
400. C73C2×#3125semidirect
439. #441C2×D73semidirect
763. C2#22620206direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892092
C2×#179890692
#226202062
C2×#179889072
C2×#179889162
C2×#179888702
C2×#179888762
C2×#179888112
C2×#179888052
C2×#179887482
C2×#179887352
C2×#179887002
C2×C4×#119240152
C2×#179886492
C2×#441×C732
C2×#312573