Finite Group Databasebeta

← C2×#22621265 #33958786

Subgroups — C2×#22621265 #33958786

Order 18688.

1930 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989141C211yesmaximal, characteristic, complemented
2C2×#17989116C211yesmaximal, characteristic
3#22621265C2116yesmaximal, direct product factor
4C2×#17988895C211yesmaximal, characteristic, complemented
5C2×#17988894C211yesmaximal, characteristic, complemented
6C2×#17988870C211yesmaximal, characteristic, complemented
7C2×#17988865C211yesmaximal, characteristic, complemented
8C2×#17988827C211yesmaximal, characteristic, complemented
9C2×#17988825C211yesmaximal, characteristic, complemented
10C2×#17988815C211yesmaximal, characteristic
11C2×#17988813C211yesmaximal, characteristic
12C2×#17988806C211yesmaximal, characteristic, complemented
13C2×#17988795C211yesmaximal, characteristic, complemented
14C2×#17988790C211yesmaximal, characteristic, complemented
15C2×C4⋊C8×D73C211yesmaximal, characteristic, complemented
16C2×#464×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924016C2211yescharacteristic
19C22×C8×D73C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21#17989141—24no—
22#17989141C2218yescomplemented
23C2×#14556590C2211yescharacteristic
24C2×#14556589C2211yescharacteristic
25#17989116—24no—
26#17989116C2218yes—
27C2×#14556584—21no—
28C2×#14556583C2211yescharacteristic
29C2×#14556581—21no—
30C2×#14556573—21no—
31C2×#14556571C2211yescharacteristic
32C2×#14556569—21no—
33C2×#14556567C2211yescharacteristic
34C2×#14556567C2211yescharacteristic
35C2×#14556562C2211yescharacteristic
36C2×Q8×Dic73C2211yescharacteristic
37C2×C4×Dic146—21no—
38C2×C4×Dic146C2211yescharacteristic
39C2×D4×Dic73C2211yescharacteristic
40C2×#14556551—21no—
41C2×#14556548—21no—
42C2×#14556547—21no—
43C2×C42×D73C2211yescharacteristic
44#17988895C2218yescomplemented
45#17988894C2218yescomplemented
46#17988870C2218yescomplemented
47#17988865C2218yescomplemented
48#17988827C2218yescomplemented
49#17988825C2218yescomplemented
50#17988815C2218yes—
51#17988813C2218yes—
52#17988806C2218yescomplemented
53#17988795C2218yescomplemented
54#17988790C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556523C2211yescharacteristic
58C2×#14556522C2211yescharacteristic
59C2×C4⋊#10596831C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C4⋊C8×D73C2218yescomplemented
63C2×#14556516C2211yescharacteristic
64C2×#14556516C2211yescharacteristic
65C2×#14556515C2211yescharacteristic
66C2×#14556515C2211yescharacteristic
67C2×#14556515C2211yescharacteristic
68C2×#14556512C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C22×SD16×C73C2211yescharacteristic
71C2×#124×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73#464×C73C2218yescomplemented
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C22×C22⋊D73—21no—
80C23×Dic73—21no—
81C22×C4×D73D411yescharacteristic
82C22×C4×D73D411yescharacteristic
83C22×C4×D73C2311yescharacteristic
84C2×#11924018—42no—
85C2×#11924018C2314yes—
86C2×#11924016—42no—
87C2×#11924016C2314yes—
88C22×#10596831C2311yescharacteristic
89C22×#10596831C2311yescharacteristic
90C2×C8×D73—42no—
91C2×C8×D73—42no—
92C2×C8×D73C2314yes—
93C2×C8×D73C2314yes—
94#14556590—22no—
95#14556590C2314yes—
96#14556589—22no—
97#14556589C2314yes—
98#14556584—28no—
99#14556583—22no—
100#14556583C2314yes—
101#14556581—28no—
102#14556573—28no—
103#14556571—22no—
104#14556571C2314yes—
105#14556569—28no—
106#14556567—22no—
107#14556567—22no—
108#14556567C2314yes—
109#14556567C2314yes—
110#14556562—22no—
111#14556562C2314yes—
112Q8×Dic73—22no—
113Q8×Dic73C2314yes—
114C4×Dic146—28no—
115C4×Dic146—22no—
116C4×Dic146C2314yes—
117D4×Dic73—22no—
118D4×Dic73C2314yes—
119#14556551—28no—
120#14556548—28no—
121#14556547—28no—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73C2311yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73D411yescharacteristic
143C2×C4×Dic73D411yescharacteristic
144C2×C4×Dic73C2311yescharacteristic
145C42×D73D414yes—
146C42×D73C2314yes—
147#14556525C2314yes—
148#14556524C2314yes—
149#14556523C2314yes—
150#14556522C2314yes—
151C4⋊#10596831C2314yes—
152#14556520C2314yes—
153#14556520C2314yes—
154#14556516C2314yes—
155#14556516C2314yes—
156#14556515C2314yes—
157#14556515C2314yes—
158#14556515C2314yes—
159#14556512C2314yes—
160C22×Q8×C73C2311yescharacteristic
161C22×Q8×C73C2311yescharacteristic
162C22×D4×C73C2311yescharacteristic
163C2×Q16×C73—42no—
164C2×Q16×C73C2314yes—
165C2×SD16×C73—42no—
166C2×SD16×C73C2314yes—
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169#124×C73—22no—
170#124×C73C2314yes—
171C4×Q8×C73—22no—
172C4×Q8×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73—21no—
177C2×C42×C73—21no—
178C2×C42×C73C2311yescharacteristic
179C4⋊C8×C73C2314yes—
180#103×C73C2314yes—
181#102×C73C2314yes—
182C23×D73C2×D411yescharacteristic
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—21no—
186C2×Dic146—24no—
187C2×Dic146—44no—
188C2×Dic146C2412yes—
189C2×C22⋊D73—24no—
190C2×C22⋊D73—44no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—24no—
196C22×Dic73—44no—
197C22×Dic73C2×D411yescharacteristic
198C22×Dic73C2×D411yescharacteristic
199C22×Dic73C2×D411yescharacteristic
200C2×C4×D73—24no—
201C2×C4×D73—22no—
202C2×C4×D73—22no—
203C2×C4×D73—24no—
204C2×C4×D73C2×D412yes—
205C2×C4×D73C2×D414yes—
206C2×C4×D73C2×D414yes—
207C2×C4×D73C2412yes—
208#11924018—44no—
209#11924016—44no—
210C2×#10596831—22no—
211C2×#10596831—22no—
212C2×#10596831C2412yes—
213C2×#10596831C2412yes—
214C8×D73—44no—
215C8×D73—44no—
216C4⋊Dic73—21no—
217C4⋊Dic73—21no—
218C4⋊Dic73—21no—
219C4⋊Dic73—24no—
220C4⋊Dic73—24no—
221C4⋊Dic73C2412yes—
222C4⋊Dic73C2412yes—
223C4⋊Dic73C2412yes—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232C22⋊Dic73—24no—
233C22⋊Dic73—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237C4×Dic73—24no—
238C4×Dic73—24no—
239C4×Dic73C2×D412yes—
240C4×Dic73C2×D414yes—
241C4×Dic73C2×D414yes—
242C4×Dic73C2412yes—
243C24×C73—21no—
244C2×Q8×C73—21no—
245C2×Q8×C73—21no—
246C2×Q8×C73—22no—
247C2×Q8×C73—22no—
248C2×Q8×C73—22no—
249C2×Q8×C73—22no—
250C2×Q8×C73C2412yes—
251C2×Q8×C73C2412yes—
252C2×D4×C73—21no—
253C2×D4×C73—22no—
254C2×D4×C73—22no—
255C2×D4×C73C2412yes—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2411yescharacteristic
262Q16×C73—44no—
263SD16×C73—44no—
264C2×C8×C73—22no—
265C2×C8×C73—22no—
266C2×C8×C73C2412yes—
267C2×C8×C73C2412yes—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73C2412yes—
271C22⋊C4×C73—24no—
272C22⋊C4×C73—24no—
273C42×C73—24no—
274C42×C73C2×D412yes—
275C42×C73C2412yes—
276C23×C73—22no—
277C23×C73—42no—
278C23×C73—42no—
279C23×C73—42no—
280C23×C73C22×D411yescharacteristic
281C22×D73—22no—
282C22×D73—22no—
283C22×D73#13714yes—
284C22×D73C22×D412yes—
285Q8×C73—22no—
286Q8×C73—22no—
287Q8×C73—22no—
288Q8×C73—22no—
289Q8×C73—42no—
290Q8×C73—42no—
291D4×C73—22no—
292D4×C73—22no—
293D4×C73—42no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—42no—
300C2×C4×C73—42no—
301C2×C4×C73—42no—
302C2×C4×C73C22×D412yes—
303C2×C4×C73C22×D412yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73H(5,𝔽2)12yes—
306C2×C4×C732−1+412yes—
307C2×C4×C73C2511yescharacteristic
308C22⋊D73—48no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73—42no—
318C2×Dic73—42no—
319C2×Dic73—48no—
320C2×Dic73#13514yes—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324C4×D73—28no—
325C4×D73—24no—
326C4×D73—22no—
327C4×D73—22no—
328C4×D73—28no—
329Dic146—22no—
330Dic146—22no—
331Dic146—42no—
332Dic146—48no—
333C8×C73—22no—
334C8×C73—22no—
335#10596831—22no—
336#10596831—22no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—84no—
341C22×C73#53712yes—
342C22×C73C2×#13512yes—
343C22×C73C2×#13712yes—
344C22×C73C23×D411yescharacteristic
345C2×D73—22no—
346C2×D73—28no—
347C2×D73—22no—
348C2×D73C2×#13714yes—
349C4×C73—22no—
350C4×C73—22no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73—42no—
354C4×C73#53712yes—
355C4×C73C2×H(5,𝔽2)11yescharacteristic
356C4×C73C2×2−1+411yescharacteristic
357Dic73—22no—
358Dic73—22no—
359Dic73—42no—
360Dic73—42no—
361Dic73—42no—
362Dic73—42no—
363Dic73C2×#13514yes—
364C2×#3248—731nomaximal, Sylow
365C2×C73—82no—
366C2×C73#324814yescomplemented
367C2×C73C2×#53711yescharacteristic
368C2×C73C22×#13511yescharacteristic
369C2×C73C22×#13711yescharacteristic
370D73—24no—
371C2×#533—731no—
372C2×#529—731no—
373#3248—7316no—
374C2×#479—731no—
375C2×#479—731no—
376C2×#475—731no—
377C2×#474—731no—
378C2×#467—731no—
379C2×#467—731no—
380C2×#465—731no—
381C2×#465—731no—
382C2×#464—731no—
383C2×#464D7311yescharacteristic, complemented
384C2×#462—731no—
385C2×#461—731no—
386C22×C4⋊C8—731no—
387C73C2×#324811yescharacteristic, complemented, Sylow
388C22×Q16—731no—
389C22×Q16C2×D7311yescharacteristic
390C22×SD16—731no—
391C22×SD16C2×D7311yescharacteristic
392C23×C8—731no—
393C23×C8—731no—
394#533—738no—
395#533—1464no—
396C2×C4⋊Q8—731no—
397C2×C4⋊Q8—731no—
398#529—738no—
399#529—1464no—
400C2×#126—1461no—
401C2×#125—731no—
402C2×#125—1461no—
403C2×#124C2×D7311yescharacteristic
404C2×#123—1461no—
405C2×C22⋊Q8—731no—
406C2×C22⋊Q8—731no—
407C2×C22⋊Q8—731no—
408C2×C22⋊Q8—1461no—
409C2×#121—731no—
410C2×C4×Q8—731no—
411C2×C4×Q8—731no—
412C2×C4×Q8—1461no—
413C2×C4×Q8C2×D7311yescharacteristic
414C2×C4×D4—731no—
415C2×C4×D4—1461no—
416C2×#117—1461no—
417C2×#117—1461no—
418C22×C42—731no—
419#479—738no—
420#479—738no—
421#475—738no—
422#474—738no—
423#467—738no—
424#467—738no—
425#465—738no—
426#465—738no—
427#464—738no—
428#464C2×D7318yescomplemented
429#462—738no—
430#461—738no—
431C2×#107—731no—
432C2×#107—731no—
433C2×#106—731no—
434C2×#106—731no—
435C2×C4⋊C8—731no—
436C2×C4⋊C8—731no—
437C2×C4⋊C8—731no—
438C2×C4⋊C8—738no—
439C2×C4⋊C8C2×D7311yescharacteristic
440C2×#103—731no—
441C2×#103—731no—
442C2×#103—731no—
443C2×#103—731no—
444C2×#103—731no—
445C2×#103C2×D7311yescharacteristic
446C2×#102—731no—
447C2×#102C2×D7311yescharacteristic
448C22×Q8—731no—
449C22×Q8—1461no—
450C22×Q8C22×D7311yescharacteristic
451C22×Q8C22×D7311yescharacteristic
452C22×D4—1461no—
453C22×D4C22×D7311yescharacteristic
454C23×C4—731no—
455C23×C4—731no—
456C23×C4—731no—
457C23×C4—1461no—
458C2×Q16—42no—
459C2×Q16—2922no—
460C2×Q16—734no—
461C2×Q16C22×D7314yes—
462C2×SD16—42no—
463C2×SD16—2922no—
464C2×SD16—734no—
465C2×SD16C22×D7314yes—
466C22×C8—2922no—
467C22×C8—2922no—
468C22×C8—734no—
469C22×C8—734no—
470C22×C8—731no—
471C22×C8—731no—
472C22×C8C22×D7311yescharacteristic
473C22×C8C22×D7311yescharacteristic
474C4⋊Q8—734no—
475C4⋊Q8—734no—
476C4⋊Q8—1462no—
477C4⋊Q8—1462no—
478#126—1468no—
479#125—734no—
480#125—1468no—
481#125—1462no—
482#124—22no—
483#124C22×D7314yes—
484#123—1468no—
485C22⋊Q8—734no—
486C22⋊Q8—734no—
487C22⋊Q8—734no—
488C22⋊Q8—1462no—
489C22⋊Q8—1468no—
490C22⋊Q8—1462no—
491C22⋊Q8—1462no—
492#121—734no—
493#121—1462no—
494C4×Q8—22no—
495C4×Q8—734no—
496C4×Q8—734no—
497C4×Q8—1468no—
498C4×Q8—1462no—
499C4×Q8—1462no—
500C4×Q8C22×D7314yes—
501C4×D4—734no—
502C4×D4—1462no—
503C4×D4—1468no—
504#117—1468no—
505#117—1468no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—731no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4C22×D7311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C42—21no—
529C2×C42—731no—
530C2×C42—731no—
531C2×C42—731no—
532C2×C42—734no—
533C2×C42—734no—
534C2×C42—1461no—
535C2×C42—1461no—
536C2×C42C22×D7311yescharacteristic
537#107—734no—
538#107—734no—
539#106—734no—
540#106—734no—
541C4⋊C8—734no—
542C4⋊C8—734no—
543C4⋊C8—734no—
544C4⋊C8C22×D7314yes—
545#103—734no—
546#103—734no—
547#103—734no—
548#103—734no—
549#103—734no—
550#103C22×D7314yes—
551#102—734no—
552#102C22×D7314yes—
553C24—21no—
554C24—731no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—2924no—
562C2×Q8—732no—
563C2×Q8—1464no—
564C2×Q8—1462no—
565C2×Q8—1462no—
566C2×Q8—1461no—
567C2×Q8C23×D7312yes—
568C2×Q8C23×D7312yes—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—2924no—
573C2×D4—1464no—
574C2×D4C23×D7312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—2924no—
579C22×C4—731no—
580C22×C4—731no—
581C22×C4—731no—
582C22×C4—734no—
583C22×C4—734no—
584C22×C4—732no—
585C22×C4—732no—
586C22×C4—1464no—
587C22×C4—1464no—
588C22×C4—1464no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1462no—
594C22×C4—1462no—
595C22×C4D4×D7311yescharacteristic
596C22×C4D4×D7311yescharacteristic
597C22×C4C23×D7311yescharacteristic
598Q16—44no—
599Q16—2924no—
600SD16—44no—
601SD16—2924no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—2924no—
605C2×C8—2924no—
606C2×C8—732no—
607C2×C8—732no—
608C2×C8—1462no—
609C2×C8—1462no—
610C2×C8C23×D7312yes—
611C2×C8C23×D7312yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—732no—
615C4⋊C4—732no—
616C4⋊C4—732no—
617C4⋊C4—1464no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1464no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1464no—
627C4⋊C4—1461no—
628C4⋊C4—1461no—
629C4⋊C4—1461no—
630C4⋊C4C23×D7312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1464no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C42—24no—
639C42—734no—
640C42—732no—
641C42—734no—
642C42—732no—
643C42—1464no—
644C42—1464no—
645C42D4×D7312yes—
646C42C23×D7312yes—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—734no—
652C23—732no—
653C23—1462no—
654C23—1462no—
655C23C2×D4×D7311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—2928no—
663Q8—2922no—
664Q8—1462no—
665Q8—1462no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—2928no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—2922no—
679C2×C4—2922no—
680C2×C4—2922no—
681C2×C4—2922no—
682C2×C4—2928no—
683C2×C4—732no—
684C2×C4—734no—
685C2×C4—732no—
686C2×C4—732no—
687C2×C4—1468no—
688C2×C4—1468no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4—1464no—
698C2×C4C2×D4×D7312yes—
699C2×C4C2×D4×D7312yes—
700C2×C4C2×D4×D7311yescharacteristic
701C2×C4#1455663612yes—
702C2×C4#1455663812yes—
703C2×C4C24×D7311yescharacteristic
704C8—22no—
705C8—22no—
706C8—1462no—
707C8—1462no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—84no—
712C22—734no—
713C22—1462no—
714C22—1468no—
715C22—1462no—
716C22#1798916612yes—
717C22#135×D7312yes—
718C22#137×D7312yes—
719C22C22×D4×D7311yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—2922no—
726C4—2922no—
727C4—2922no—
728C4—2922no—
729C4—734no—
730C4—1462no—
731C4—1462no—
732C4#1798916612yes—
733C4C2×#1455663611yescharacteristic
734C4C2×#1455663811yescharacteristic
735C2—82no—
736C2—1464no—
737C2#2262126514yesdirect product factor
738C2C2×#1798916611yescharacteristic
739C2C2×#135×D7311yescharacteristic
740C2C2×#137×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#464×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556562C22
hypercenterC2×#464D73
hypocenterC73C2×#3248
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#17989141C2semidirect
3. #22621265C2direct (N × H)
4. C2×#17988895C2semidirect
5. C2×#17988894C2semidirect
6. C2×#17988870C2semidirect
7. C2×#17988865C2semidirect
8. C2×#17988827C2semidirect
9. C2×#17988825C2semidirect
12. C2×#17988806C2semidirect
13. C2×#17988795C2semidirect
14. C2×#17988790C2semidirect
15. C2×C4⋊C8×D73C2semidirect
16. C2×#464×C73C2semidirect
22. #17989141C22semidirect
44. #17988895C22semidirect
45. #17988894C22semidirect
46. #17988870C22semidirect
47. #17988865C22semidirect
48. #17988827C22semidirect
49. #17988825C22semidirect
52. #17988806C22semidirect
53. #17988795C22semidirect
54. #17988790C22semidirect
62. C4⋊C8×D73C22semidirect
73. #464×C73C22semidirect
366. C2×C73#3248semidirect
383. C2×#464D73semidirect
387. C73C2×#3248semidirect
428. #464C2×D73semidirect
737. C2#22621265direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891412
C2×#179891162
#226212652
C2×#179888952
C2×#179888942
C2×#179888702
C2×#179888652
C2×#179888272
C2×#179888252
C2×#179888152
C2×#179888132
C2×#179888062
C2×#179887952
C2×#179887902
C2×C4⋊C8×D732
C2×#464×C732
C2×#324873