Finite Group Databasebeta

← C2×#22622751 #33965742

Subgroups — C2×#22622751 #33965742

Order 18688.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989311C211yesmaximal, characteristic, complemented
2C2×#17989296C211yesmaximal, characteristic, complemented
3#22622751C2116yesmaximal, direct product factor
4C2×#17988955C211yesmaximal, characteristic, complemented
5C2×#17988948C211yesmaximal, characteristic, complemented
6C2×#17988943C211yesmaximal, characteristic, complemented
7C2×#17988896C211yesmaximal, characteristic, complemented
8C2×#17988870C211yesmaximal, characteristic, complemented
9C2×#17988888C211yesmaximal, characteristic, complemented
10C2×#17988804C211yesmaximal, characteristic
11C2×#17988804C211yesmaximal, characteristic
12C2×#17988716C211yesmaximal, characteristic, complemented
13C2×#17988697C211yesmaximal, characteristic
14C2×#17988688C211yesmaximal, characteristic, complemented
15C2×SD16×Dic73C211yesmaximal, characteristic, complemented
16C2×#461×C73C211yesmaximal, characteristic, complemented
17C22×#11924013C2211yescharacteristic
18#17989311—24no—
19#17989311C2218yescomplemented
20#17989296—24no—
21#17989296C2218yescomplemented
22C2×#14556590C2211yescharacteristic
23C2×#14556586—21no—
24C2×#14556586—21no—
25C2×#14556583C2211yescharacteristic
26C2×#14556582C2211yescharacteristic
27C2×#14556580C2211yescharacteristic
28C2×#14556580C2211yescharacteristic
29C2×#14556571—21no—
30C2×#14556570—21no—
31C2×#14556568—21no—
32C2×#14556568—21no—
33C2×Q8×Dic73C2211yescharacteristic
34C2×Q8×Dic73C2211yescharacteristic
35C2×C4×Dic146C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×D4×Dic73C2211yescharacteristic
39C2×#14556549—21no—
40C22×#11924007—21no—
41#17988955C2218yescomplemented
42#17988948C2218yescomplemented
43#17988943C2218yescomplemented
44#17988896C2218yescomplemented
45#17988888C2218yescomplemented
46#17988870C2218yescomplemented
47#17988804C2218yes—
48#17988804C2218yes—
49#17988716C2218yescomplemented
50#17988697C2218yes—
51#17988688C2218yescomplemented
52SD16×Dic73C2218yescomplemented
53C2×#14556525C2211yescharacteristic
54C2×#14556523C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556515C2211yescharacteristic
59C2×#14556515C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556502C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C22×SD16×C73C2211yescharacteristic
71C2×C4⋊Q8×C73C2211yescharacteristic
72C2×C4×D4×C73C2211yescharacteristic
73#461×C73C2218yescomplemented
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146D411yescharacteristic
79C22×D292C2311yescharacteristic
80C23×Dic73—21no—
81C23×Dic73—21no—
82C22×C4×D73—21no—
83C2×#11924013—24no—
84C2×#11924013C2314yes—
85C22×#10596831C2311yescharacteristic
86C22×#10596831C2311yescharacteristic
87#14556590—22no—
88#14556590C2314yes—
89#14556586—28no—
90#14556586—28no—
91#14556583—22no—
92#14556583C2314yes—
93#14556582—22no—
94#14556582C2314yes—
95#14556580—22no—
96#14556580—22no—
97#14556580C2314yes—
98#14556580C2314yes—
99#14556571—28no—
100#14556570—28no—
101#14556568—28no—
102#14556568—28no—
103Q8×Dic73—22no—
104Q8×Dic73—22no—
105Q8×Dic73C2314yes—
106Q8×Dic73C2314yes—
107C4×Dic146D414yes—
108C4×Dic146C2314yes—
109C4×D292—22no—
110C4×D292C2314yes—
111D4×Dic73—22no—
112D4×Dic73—22no—
113D4×Dic73C2314yes—
114D4×Dic73C2314yes—
115#14556549—28no—
116C2×C4⋊Dic73—21no—
117C2×C4⋊Dic73—21no—
118C2×C4⋊Dic73—21no—
119C2×C4⋊Dic73D411yescharacteristic
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×#11924007—21no—
124C2×#11924007—21no—
125C2×#11924007—28no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007D411yescharacteristic
129C2×#11924007D411yescharacteristic
130C2×C22⋊Dic73—21no—
131C2×C22⋊Dic73—21no—
132C2×#11924005—21no—
133C2×#11924005—21no—
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×C4×Dic73—21no—
138C2×C4×Dic73—21no—
139C2×C4×Dic73C2311yescharacteristic
140C2×C4×Dic73C2311yescharacteristic
141#14556525C2314yes—
142#14556523C2314yes—
143#14556522C2314yes—
144#14556520C2314yes—
145#14556520C2314yes—
146#14556515C2314yes—
147#14556515C2314yes—
148#14556515C2314yes—
149#14556515C2314yes—
150#14556513C2314yes—
151#14556513C2314yes—
152#14556512C2314yes—
153#14556511C2314yes—
154#14556502C2314yes—
155#14556501C2314yes—
156C8×Dic73C2314yes—
157C22×Q8×C73C2311yescharacteristic
158C22×Q8×C73C2311yescharacteristic
159C22×D4×C73C2311yescharacteristic
160C23×C4×C73—21no—
161C2×SD16×C73—24no—
162C2×SD16×C73—24no—
163C2×SD16×C73C2314yes—
164C2×SD16×C73C2314yes—
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C4⋊Q8×C73—22no—
168C4⋊Q8×C73C2314yes—
169C4×D4×C73—22no—
170C4×D4×C73C2314yes—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C22⋊C4×C73—21no—
175C2×C42×C73C2311yescharacteristic
176C4⋊C8×C73C2314yes—
177#103×C73C2314yes—
178#103×C73C2314yes—
179C23×D73—21no—
180C2×Dic146—24no—
181C2×Dic146—42no—
182C2×Dic146—82no—
183C2×Dic146C2×D414yes—
184C2×D292—22no—
185C2×D292—22no—
186C2×D292—21no—
187C2×D292C2412yes—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—24no—
192C22×Dic73—24no—
193C22×Dic73—44no—
194C22×Dic73—82no—
195C22×Dic73C2×D411yescharacteristic
196C22×Dic73C2×D411yescharacteristic
197C22×Dic73C2×D411yescharacteristic
198C22×Dic73C2×D411yescharacteristic
199C2×C4×D73—24no—
200C2×C4×D73—44no—
201#11924013—28no—
202C2×#10596831—22no—
203C2×#10596831—22no—
204C2×#10596831C2412yes—
205C2×#10596831C2412yes—
206C4⋊Dic73—21no—
207C4⋊Dic73—21no—
208C4⋊Dic73—21no—
209C4⋊Dic73—24no—
210C4⋊Dic73—24no—
211C4⋊Dic73—24no—
212C4⋊Dic73C2×D414yes—
213C4⋊Dic73C2412yes—
214C4⋊Dic73C2412yes—
215C4⋊Dic73C2412yes—
216#11924007—24no—
217#11924007—24no—
218#11924007—24no—
219#11924007—24no—
220#11924007C2×D414yes—
221#11924007C2×D414yes—
222C22⋊Dic73—24no—
223C22⋊Dic73—24no—
224#11924005—24no—
225#11924005—24no—
226#11924005—24no—
227#11924005—24no—
228#11924005—24no—
229C4×Dic73—24no—
230C4×Dic73—24no—
231C4×Dic73C2×D412yes—
232C4×Dic73C2×D412yes—
233C4×Dic73C2412yes—
234C4×Dic73C2412yes—
235C24×C73—21no—
236C2×Q8×C73—21no—
237C2×Q8×C73—21no—
238C2×Q8×C73—22no—
239C2×Q8×C73—22no—
240C2×Q8×C73—22no—
241C2×Q8×C73—22no—
242C2×Q8×C73C2412yes—
243C2×Q8×C73C2412yes—
244C2×D4×C73—21no—
245C2×D4×C73—22no—
246C2×D4×C73#4114yes—
247C2×D4×C73C2412yes—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—24no—
252C22×C4×C73—82no—
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2411yescharacteristic
256SD16×C73—28no—
257SD16×C73—28no—
258C2×C8×C73—22no—
259C2×C8×C73—22no—
260C2×C8×C73C2412yes—
261C2×C8×C73C2412yes—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—24no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73C2412yes—
266C22⋊C4×C73—24no—
267C42×C73C2×D412yes—
268C42×C73C2412yes—
269C23×C73—24no—
270C23×C73—22no—
271C23×C73—42no—
272C23×C73—42no—
273C23×C73C22×D411yescharacteristic
274C22×D73—22no—
275C22×D73—42no—
276C22×D73—42no—
277C22×D73—42no—
278Q8×C73—22no—
279Q8×C73—22no—
280Q8×C73—22no—
281Q8×C73—22no—
282Q8×C73—42no—
283Q8×C73—42no—
284D4×C73—24no—
285D4×C73—22no—
286D4×C73C2×#4114yes—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73—42no—
295C2×C4×C73—84no—
296C2×C4×C73C22×D412yes—
297C2×C4×C73C22×D412yes—
298C2×C4×C73C22×D411yescharacteristic
299C2×C4×C73C2×#4112yes—
300C2×C4×C732−1+412yes—
301C2×C4×C73C2511yescharacteristic
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—48no—
310C2×Dic73—42no—
311C2×Dic73—42no—
312C2×Dic73—42no—
313C2×Dic73—84no—
314C2×Dic73C22×D412yes—
315C2×Dic73C22×D412yes—
316C2×Dic73C22×D412yes—
317C2×Dic73C22×D412yes—
318D292—22no—
319D292—22no—
320D292—42no—
321C4×D73—48no—
322Dic146—44no—
323Dic146—84no—
324C8×C73—22no—
325C8×C73—22no—
326#10596831—22no—
327#10596831—22no—
328C22×C73—24no—
329C22×C73—48no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73#54812yes—
333C22×C73#57512yes—
334C22×C73#57712yes—
335C22×C73C23×D411yescharacteristic
336C2×D73—42no—
337C2×D73—42no—
338C2×D73—42no—
339C2×D73—84no—
340C4×C73—22no—
341C4×C73—22no—
342C4×C73—42no—
343C4×C73—42no—
344C4×C73—42no—
345C4×C73#54812yes—
346C4×C73C22×#4111yescharacteristic
347C4×C73C2×2−1+411yescharacteristic
348Dic73—22no—
349Dic73—22no—
350Dic73—22no—
351Dic73—22no—
352Dic73—42no—
353Dic73—42no—
354Dic73—42no—
355C2×#3376—731nomaximal, Sylow
356C2×C73—44no—
357C2×C73#337614yescomplemented
358C2×C73C2×#54811yescharacteristic
359C2×C73C2×#57511yescharacteristic
360C2×C73C2×#57711yescharacteristic
361D73—82no—
362C2×#556—731no—
363C2×#554—731no—
364#3376—7316no—
365C2×#491—731no—
366C2×#489—731no—
367C2×#488—731no—
368C2×#479—731no—
369C2×#475—731no—
370C2×#478—731no—
371C2×#463—731no—
372C2×#463—731no—
373C2×#461D7311yescharacteristic, complemented
374C2×#446—731no—
375C2×#442—731no—
376C2×#440—731no—
377C2×C4×SD16—731no—
378C73C2×#337611yescharacteristic, complemented, Sylow
379C22×SD16C2×D7311yescharacteristic
380C22×SD16C2×D7311yescharacteristic
381C22×D8—731no—
382#556—738no—
383#556—1464no—
384#554—738no—
385#554—1464no—
386C2×C4⋊Q8—731no—
387C2×C4⋊Q8C2×D7311yescharacteristic
388C2×#126—1461no—
389C2×#126—1461no—
390C2×#125—731no—
391C2×#125—731no—
392C2×#124—731no—
393C2×#124—731no—
394C2×C22⋊Q8—1461no—
395C2×C22⋊Q8—1461no—
396C2×C22⋊Q8—1461no—
397C2×C22⋊Q8—1461no—
398C2×C4×Q8—731no—
399C2×C4×Q8—731no—
400C2×C4×Q8—731no—
401C2×C4×D4—731no—
402C2×C4×D4—731no—
403C2×C4×D4—731no—
404C2×C4×D4C2×D7311yescharacteristic
405C2×#117—1461no—
406C22×C4⋊C4—1461no—
407#491—738no—
408#489—738no—
409#488—738no—
410#479—738no—
411#478—738no—
412#475—738no—
413#463—738no—
414#463—738no—
415#461C2×D7318yescomplemented
416#446—738no—
417#442—738no—
418#440—738no—
419C4×SD16—738no—
420C2×#107—731no—
421C2×#106—731no—
422C2×#106—731no—
423C2×C4⋊C8—731no—
424C2×C4⋊C8—731no—
425C2×C4⋊C8C2×D7311yescharacteristic
426C2×#103—731no—
427C2×#103—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×#103C2×D7311yescharacteristic
431C2×#103C2×D7311yescharacteristic
432C2×#102—731no—
433C2×#102—731no—
434C2×#102—731no—
435C2×#102—731no—
436C2×#97—731no—
437C2×#97—731no—
438C2×C4×C8—731no—
439C22×Q8—731no—
440C22×Q8—1461no—
441C22×Q8C22×D7311yescharacteristic
442C22×Q8C22×D7311yescharacteristic
443C22×D4—731no—
444C22×D4C22×D7311yescharacteristic
445C23×C4—21no—
446C23×C4—1461no—
447C23×C4—1461no—
448C23×C4—1461no—
449C2×SD16—24no—
450C2×SD16—24no—
451C2×SD16C22×D7314yes—
452C2×SD16C22×D7314yes—
453C2×D8—734no—
454C2×D8—1464no—
455C22×C8—731no—
456C22×C8—731no—
457C22×C8C22×D7311yescharacteristic
458C22×C8C22×D7311yescharacteristic
459C4⋊Q8—22no—
460C4⋊Q8—734no—
461C4⋊Q8—1462no—
462C4⋊Q8C22×D7314yes—
463#126—1468no—
464#126—1468no—
465#125—734no—
466#125—734no—
467#125—1462no—
468#125—1462no—
469#124—734no—
470#124—734no—
471#124—1462no—
472#124—1462no—
473C22⋊Q8—1468no—
474C22⋊Q8—1468no—
475C22⋊Q8—1468no—
476C22⋊Q8—1468no—
477C4×Q8—734no—
478C4×Q8—734no—
479C4×Q8—734no—
480C4×Q8—734no—
481C4×Q8—1462no—
482C4×Q8—1462no—
483C4×D4—22no—
484C4×D4—734no—
485C4×D4—734no—
486C4×D4—734no—
487C4×D4—1462no—
488C4×D4—1462no—
489C4×D4—1462no—
490C4×D4C22×D7314yes—
491#117—1468no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—731no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—731no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—1468no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4—1461no—
506C2×C4⋊C4—1461no—
507C2×C4⋊C4—1461no—
508C2×C4⋊C4C22×D7311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1461no—
511C2×C22⋊C4—1461no—
512C2×C22⋊C4—1461no—
513C2×C22⋊C4—1461no—
514C2×C22⋊C4—1461no—
515C2×C22⋊C4—1461no—
516C2×C22⋊C4—1461no—
517C2×C42—731no—
518C2×C42—731no—
519C2×C42—1461no—
520C2×C42—1461no—
521C2×C42C22×D7311yescharacteristic
522#107—734no—
523#106—734no—
524#106—734no—
525C4⋊C8—734no—
526C4⋊C8—734no—
527C4⋊C8C22×D7314yes—
528#103—734no—
529#103—734no—
530#103—734no—
531#103—734no—
532#103C22×D7314yes—
533#103C22×D7314yes—
534#102—734no—
535#102—734no—
536#102—734no—
537#102—734no—
538#97—734no—
539#97—734no—
540C4×C8—734no—
541C24—21no—
542C24—1461no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—2922no—
550C2×Q8—5842no—
551C2×Q8—734no—
552C2×Q8—1464no—
553C2×Q8C23×D7312yes—
554C2×Q8C23×D7312yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—732no—
558C2×D4—1461no—
559C2×D4—1462no—
560C2×D4—1462no—
561C2×D4#1192402714yes—
562C2×D4C23×D7312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—2924no—
569C22×C4—2924no—
570C22×C4—5842no—
571C22×C4—731no—
572C22×C4—731no—
573C22×C4—731no—
574C22×C4—731no—
575C22×C4—1464no—
576C22×C4—1461no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4—1464no—
580C22×C4—1464no—
581C22×C4D4×D7311yescharacteristic
582C22×C4D4×D7311yescharacteristic
583C22×C4C23×D7311yescharacteristic
584SD16—28no—
585SD16—28no—
586D8—1468no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—732no—
590C2×C8—732no—
591C2×C8—1462no—
592C2×C8—1462no—
593C2×C8C23×D7312yes—
594C2×C8C23×D7312yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—734no—
599C4⋊C4—734no—
600C4⋊C4—734no—
601C4⋊C4—732no—
602C4⋊C4—732no—
603C4⋊C4—732no—
604C4⋊C4—1464no—
605C4⋊C4—1464no—
606C4⋊C4—1464no—
607C4⋊C4—1464no—
608C4⋊C4—1464no—
609C4⋊C4—1464no—
610C4⋊C4—1464no—
611C4⋊C4—1461no—
612C4⋊C4—1461no—
613C4⋊C4—1461no—
614C4⋊C4C23×D7312yes—
615C22⋊C4—24no—
616C22⋊C4—1464no—
617C22⋊C4—1464no—
618C22⋊C4—1464no—
619C22⋊C4—1464no—
620C22⋊C4—1464no—
621C22⋊C4—1464no—
622C22⋊C4—1464no—
623C42—732no—
624C42—732no—
625C42—732no—
626C42—732no—
627C42—1464no—
628C42—1464no—
629C42D4×D7312yes—
630C42C23×D7312yes—
631C23—22no—
632C23—24no—
633C23—42no—
634C23—42no—
635C23—2922no—
636C23—2922no—
637C23—2922no—
638C23—1462no—
639C23C2×D4×D7311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—42no—
645Q8—42no—
646Q8—2924no—
647Q8—5844no—
648D4—22no—
649D4—24no—
650D4—2922no—
651D4—1462no—
652D4—1462no—
653D4C2×#1192402714yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—2928no—
664C2×C4—2922no—
665C2×C4—2922no—
666C2×C4—2922no—
667C2×C4—2928no—
668C2×C4—5844no—
669C2×C4—732no—
670C2×C4—732no—
671C2×C4—732no—
672C2×C4—732no—
673C2×C4—1462no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4—1462no—
680C2×C4C2×D4×D7312yes—
681C2×C4C2×D4×D7312yes—
682C2×C4C2×D4×D7311yescharacteristic
683C2×C4C2×#1192402712yes—
684C2×C4#1455663812yes—
685C2×C4C24×D7311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1462no—
689C8—1462no—
690C22—24no—
691C22—48no—
692C22—42no—
693C22—42no—
694C22—2922no—
695C22—2922no—
696C22—2922no—
697C22—5844no—
698C22#1798924312yes—
699C22#1798938612yes—
700C22#1798939312yes—
701C22C22×D4×D7311yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—2922no—
708C4—2922no—
709C4—2922no—
710C4—1462no—
711C4—1462no—
712C4—1462no—
713C4—1462no—
714C4#1798924312yes—
715C4C22×#1192402711yescharacteristic
716C4C2×#1455663811yescharacteristic
717C2—44no—
718C2—5842no—
719C2#2262275114yesdirect product factor
720C2C2×#1798924311yescharacteristic
721C2C2×#1798938611yescharacteristic
722C2C2×#1798939311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#461×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924013C22
hypercenterC2×#461D73
hypocenterC73C2×#3376
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#17989311C2semidirect
2. C2×#17989296C2semidirect
3. #22622751C2direct (N × H)
4. C2×#17988955C2semidirect
5. C2×#17988948C2semidirect
6. C2×#17988943C2semidirect
7. C2×#17988896C2semidirect
8. C2×#17988870C2semidirect
9. C2×#17988888C2semidirect
12. C2×#17988716C2semidirect
14. C2×#17988688C2semidirect
15. C2×SD16×Dic73C2semidirect
16. C2×#461×C73C2semidirect
19. #17989311C22semidirect
21. #17989296C22semidirect
41. #17988955C22semidirect
42. #17988948C22semidirect
43. #17988943C22semidirect
44. #17988896C22semidirect
45. #17988888C22semidirect
46. #17988870C22semidirect
49. #17988716C22semidirect
51. #17988688C22semidirect
52. SD16×Dic73C22semidirect
73. #461×C73C22semidirect
357. C2×C73#3376semidirect
373. C2×#461D73semidirect
378. C73C2×#3376semidirect
415. #461C2×D73semidirect
719. C2#22622751direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893112
C2×#179892962
#226227512
C2×#179889552
C2×#179889482
C2×#179889432
C2×#179888962
C2×#179888702
C2×#179888882
C2×#179888042
C2×#179887162
C2×#179886972
C2×#179886882
C2×SD16×Dic732
C2×#461×C732
C2×#337673