Finite Group Databasebeta

← C2×#22622760 #33965751

Subgroups — C2×#22622760 #33965751

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×#17989310C211yesmaximal, characteristic, complemented
2C2×#17989297C211yesmaximal, characteristic, complemented
3#22622760C2116yesmaximal, direct product factor
4C2×#17988956C211yesmaximal, characteristic, complemented
5C2×#17988947C211yesmaximal, characteristic, complemented
6C2×#17988942C211yesmaximal, characteristic, complemented
7C2×#17988895C211yesmaximal, characteristic, complemented
8C2×#17988873C211yesmaximal, characteristic, complemented
9C2×#17988888C211yesmaximal, characteristic, complemented
10C2×#17988803C211yesmaximal, characteristic
11C2×#17988803C211yesmaximal, characteristic
12C2×#17988793C211yesmaximal, characteristic, complemented
13C2×#17988700C211yesmaximal, characteristic
14C2×#17988689C211yesmaximal, characteristic, complemented
15C2×C4×#11924017C211yesmaximal, characteristic, complemented
16C2×#446×C73C211yesmaximal, characteristic, complemented
17C22×#11924017C2211yescharacteristic
18C22×#11924017C2211yescharacteristic
19C22×D584C2211yescharacteristic
20#17989310—24no—
21#17989310C2218yescomplemented
22#17989297—24no—
23#17989297C2218yescomplemented
24C2×#14556591C2211yescharacteristic
25C2×#14556591C2211yescharacteristic
26C2×#14556586—21no—
27C2×#14556586—21no—
28C2×#14556583C2211yescharacteristic
29C2×#14556583C2211yescharacteristic
30C2×#14556579C2211yescharacteristic
31C2×#14556579C2211yescharacteristic
32C2×#14556569—21no—
33C2×#14556569—21no—
34C2×#14556567—21no—
35C2×#14556567—21no—
36C2×C4×Dic146C2211yescharacteristic
37C2×C4×Dic146C2211yescharacteristic
38C2×C4×D292C2211yescharacteristic
39C2×C4×D292C2211yescharacteristic
40C2×C4×D292C2211yescharacteristic
41C2×C4×D292C2211yescharacteristic
42C2×#14556549—21no—
43C2×C4⋊C4×D73—21no—
44#17988956C2218yescomplemented
45#17988947C2218yescomplemented
46#17988942C2218yescomplemented
47#17988895C2218yescomplemented
48#17988888C2218yescomplemented
49#17988873C2218yescomplemented
50#17988803C2218yes—
51#17988803C2218yes—
52#17988793C2218yescomplemented
53#17988700C2218yes—
54#17988689C2218yescomplemented
55C4×#11924017C2218yescomplemented
56C2×#14556525C2211yescharacteristic
57C2×#14556523C2211yescharacteristic
58C2×#14556523C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556516C2211yescharacteristic
64C2×#14556516C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556513C2211yescharacteristic
67C2×#14556513C2211yescharacteristic
68C2×#14556513C2211yescharacteristic
69C2×C4×Q8×C73C2211yescharacteristic
70#446×C73C2218yescomplemented
71C2×C4⋊C8×C73C2211yescharacteristic
72C2×C4⋊C8×C73C2211yescharacteristic
73C2×C4⋊C8×C73C2211yescharacteristic
74C2×#97×C73C2211yescharacteristic
75C2×#97×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C22×Dic146C2311yescharacteristic
80C22×D292C2311yescharacteristic
81C22×D292C2311yescharacteristic
82C22×C4×D73—21no—
83C22×C4×D73—21no—
84C22×C4×D73—21no—
85C22×C4×D73—21no—
86C2×#11924017—24no—
87C2×#11924017—24no—
88C2×#11924017C2314yes—
89C2×#11924017C2314yes—
90C2×D584—24no—
91C2×D584C2314yes—
92#14556591—22no—
93#14556591—22no—
94#14556591C2314yes—
95#14556591C2314yes—
96#14556586—28no—
97#14556586—28no—
98#14556583—22no—
99#14556583—22no—
100#14556583C2314yes—
101#14556583C2314yes—
102#14556579—22no—
103#14556579—22no—
104#14556579C2314yes—
105#14556579C2314yes—
106#14556569—28no—
107#14556569—28no—
108#14556567—28no—
109#14556567—28no—
110C4×Dic146—22no—
111C4×Dic146—22no—
112C4×Dic146C2314yes—
113C4×Dic146C2314yes—
114C4×D292—22no—
115C4×D292—22no—
116C4×D292—22no—
117C4×D292—22no—
118C4×D292C2314yes—
119C4×D292C2314yes—
120C4×D292C2314yes—
121C4×D292C2314yes—
122#14556549—28no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C4⋊C4×D73—28no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73—21no—
147#14556525C2314yes—
148#14556523C2314yes—
149#14556523C2314yes—
150#14556516C2314yes—
151#14556516C2314yes—
152#14556516C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556516C2314yes—
156#14556513C2314yes—
157#14556513C2314yes—
158#14556513C2314yes—
159#14556513C2314yes—
160C22×Q8×C73D411yescharacteristic
161C22×C8×C73C2311yescharacteristic
162C22×C8×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C4×Q8×C73D414yes—
166C4×Q8×C73C2314yes—
167C2×C4⋊C4×C73D411yescharacteristic
168C2×C4⋊C4×C73D411yescharacteristic
169C2×C4⋊C4×C73D411yescharacteristic
170C2×C42×C73C2311yescharacteristic
171C2×C42×C73C2311yescharacteristic
172C2×C42×C73C2311yescharacteristic
173C4⋊C8×C73C2314yes—
174C4⋊C8×C73C2314yes—
175C4⋊C8×C73C2314yes—
176#97×C73C2314yes—
177#97×C73C2314yes—
178C4×C8×C73C2314yes—
179C23×D73—21no—
180C23×D73—21no—
181C2×Dic146—22no—
182C2×Dic146—22no—
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—21no—
186C2×Dic146—21no—
187C2×Dic146—24no—
188C2×Dic146—82no—
189C2×Dic146C2412yes—
190C2×Dic146C2412yes—
191C2×D292—21no—
192C2×D292—22no—
193C2×D292—22no—
194C2×D292—22no—
195C2×D292—21no—
196C2×D292#4114yes—
197C2×D292C2412yes—
198C2×D292C2412yes—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C2×C4×D73—24no—
206C2×C4×D73—24no—
207C2×C4×D73—24no—
208C2×C4×D73—24no—
209C2×C4×D73—44no—
210C2×C4×D73—44no—
211C2×C4×D73—82no—
212C2×C4×D73—82no—
213#11924017—28no—
214#11924017—28no—
215D584—28no—
216C4⋊Dic73—24no—
217C4⋊Dic73—24no—
218C4⋊Dic73—24no—
219C4⋊Dic73—21no—
220C4⋊Dic73—21no—
221C4⋊Dic73—21no—
222C4⋊Dic73—21no—
223C4⋊Dic73C2412yes—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226C4⋊Dic73C2412yes—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924005—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241C4×Dic73—24no—
242C4×Dic73—24no—
243C2×Q8×C73—42no—
244C2×Q8×C73C2×D414yes—
245C22×C4×C73C2×D411yescharacteristic
246C22×C4×C73C2×D411yescharacteristic
247C22×C4×C73C2×D411yescharacteristic
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2411yescharacteristic
252C2×C8×C73—22no—
253C2×C8×C73—22no—
254C2×C8×C73—22no—
255C2×C8×C73—22no—
256C2×C8×C73C2412yes—
257C2×C8×C73C2412yes—
258C2×C8×C73C2412yes—
259C2×C8×C73C2412yes—
260C4⋊C4×C73C2×D414yes—
261C4⋊C4×C73C2×D414yes—
262C4⋊C4×C73C2×D414yes—
263C42×C73C2×D412yes—
264C42×C73C2×D412yes—
265C42×C73C2×D412yes—
266C42×C73C2412yes—
267C42×C73C2412yes—
268C42×C73C2412yes—
269C23×C73C22×D411yescharacteristic
270C22×D73—24no—
271C22×D73—22no—
272C22×D73—22no—
273C22×D73—42no—
274C22×D73—42no—
275C22×D73—42no—
276C22×D73—42no—
277C22×D73—42no—
278Q8×C73—44no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73C22×D412yes—
286C2×C4×C73C22×D412yes—
287C2×C4×C73C22×D412yes—
288C2×C4×C73C22×D412yes—
289C2×C4×C73C22×D412yes—
290C2×C4×C73C22×D412yes—
291C2×C4×C73C22×D411yescharacteristic
292C2×C4×C73C2×#4112yes—
293C2×C4×C732−1+412yes—
294C2×C4×C73C2511yescharacteristic
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—42no—
302C2×Dic73—42no—
303C2×Dic73—42no—
304C2×Dic73—42no—
305C2×Dic73—42no—
306C2×Dic73—42no—
307D292—24no—
308D292—22no—
309D292—22no—
310D292—22no—
311D292—42no—
312D292C2×#4114yes—
313C4×D73—48no—
314C4×D73—48no—
315C4×D73—84no—
316C4×D73—84no—
317Dic146—22no—
318Dic146—22no—
319Dic146—22no—
320Dic146—22no—
321Dic146—42no—
322Dic146—42no—
323Dic146—84no—
324C8×C73—22no—
325C8×C73—22no—
326C8×C73—22no—
327C8×C73—22no—
328C22×C73#54812yes—
329C22×C73#57512yes—
330C22×C73#57712yes—
331C22×C73C23×D411yescharacteristic
332C2×D73—24no—
333C2×D73—48no—
334C2×D73—42no—
335C2×D73—42no—
336C2×D73—42no—
337C2×D73—42no—
338C2×D73—42no—
339C2×D73—84no—
340C4×C73—22no—
341C4×C73—22no—
342C4×C73—22no—
343C4×C73—22no—
344C4×C73—22no—
345C4×C73—22no—
346C4×C73#54812yes—
347C4×C73C22×#4111yescharacteristic
348C4×C73C2×2−1+411yescharacteristic
349Dic73—42no—
350Dic73—42no—
351Dic73—42no—
352Dic73—42no—
353Dic73—42no—
354Dic73—42no—
355C2×#3376—731nomaximal, Sylow
356C2×C73#337614yescomplemented
357C2×C73C2×#54811yescharacteristic
358C2×C73C2×#57511yescharacteristic
359C2×C73C2×#57711yescharacteristic
360D73—44no—
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×#461—731no—
374C2×#446D7311yescharacteristic, complemented
375C2×#442—731no—
376C2×#440—731no—
377C2×C4×SD16—731no—
378C73C2×#337611yescharacteristic, complemented, Sylow
379C22×SD16—731no—
380C22×SD16—731no—
381C22×D8—731no—
382#556—738no—
383#556—1464no—
384#554—738no—
385#554—1464no—
386C2×C4⋊Q8—731no—
387C2×C4⋊Q8—731no—
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×Q8C2×D7311yescharacteristic
401C2×C4×D4—731no—
402C2×C4×D4—731no—
403C2×C4×D4—731no—
404C2×C4×D4—731no—
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#461—738no—
416#446C2×D7318yescomplemented
417#442—738no—
418#440—738no—
419C4×SD16—738no—
420C2×#107—731no—
421C2×#106—731no—
422C2×#106—731no—
423C2×C4⋊C8C2×D7311yescharacteristic
424C2×C4⋊C8C2×D7311yescharacteristic
425C2×C4⋊C8C2×D7311yescharacteristic
426C2×#103—731no—
427C2×#103—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×#103—731no—
431C2×#103—731no—
432C2×#102—731no—
433C2×#102—731no—
434C2×#102—731no—
435C2×#102—731no—
436C2×#97C2×D7311yescharacteristic
437C2×#97C2×D7311yescharacteristic
438C2×C4×C8C2×D7311yescharacteristic
439C22×Q8—731no—
440C22×Q8—731no—
441C22×Q8—1461no—
442C22×Q8D29211yescharacteristic
443C22×D4—731no—
444C22×D4—731no—
445C23×C4—1461no—
446C23×C4—1461no—
447C23×C4—1461no—
448C23×C4—1461no—
449C2×SD16—734no—
450C2×SD16—734no—
451C2×SD16—1464no—
452C2×SD16—1464no—
453C2×D8—734no—
454C2×D8—1464no—
455C22×C8C22×D7311yescharacteristic
456C22×C8C22×D7311yescharacteristic
457C22×C8C22×D7311yescharacteristic
458C22×C8C22×D7311yescharacteristic
459C4⋊Q8—734no—
460C4⋊Q8—734no—
461C4⋊Q8—1462no—
462C4⋊Q8—1462no—
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—1462no—
480C4×Q8—1462no—
481C4×Q8D29214yes—
482C4×Q8C22×D7314yes—
483C4×D4—734no—
484C4×D4—734no—
485C4×D4—734no—
486C4×D4—734no—
487C4×D4—1462no—
488C4×D4—1462no—
489C4×D4—1462no—
490C4×D4—1462no—
491#117—1468no—
492C2×C4⋊C4—731no—
493C2×C4⋊C4—731no—
494C2×C4⋊C4—731no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—1461no—
497C2×C4⋊C4—1461no—
498C2×C4⋊C4—1461no—
499C2×C4⋊C4—1461no—
500C2×C4⋊C4—1461no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4—1468no—
506C2×C4⋊C4D29211yescharacteristic
507C2×C4⋊C4D29211yescharacteristic
508C2×C4⋊C4D29211yescharacteristic
509C2×C22⋊C4—1461no—
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—1461no—
518C2×C42—1461no—
519C2×C42C22×D7311yescharacteristic
520C2×C42C22×D7311yescharacteristic
521C2×C42C22×D7311yescharacteristic
522#107—734no—
523#106—734no—
524#106—734no—
525C4⋊C8C22×D7314yes—
526C4⋊C8C22×D7314yes—
527C4⋊C8C22×D7314yes—
528#103—734no—
529#103—734no—
530#103—734no—
531#103—734no—
532#103—734no—
533#103—734no—
534#102—734no—
535#102—734no—
536#102—734no—
537#102—734no—
538#97C22×D7314yes—
539#97C22×D7314yes—
540C4×C8C22×D7314yes—
541C24—1461no—
542C24—1461no—
543C2×Q8—42no—
544C2×Q8—5842no—
545C2×Q8—732no—
546C2×Q8—732no—
547C2×Q8—1462no—
548C2×Q8—1462no—
549C2×Q8—1462no—
550C2×Q8—1462no—
551C2×Q8—1461no—
552C2×Q8—1461no—
553C2×Q8—1464no—
554C2×Q8C2×D29214yes—
555C2×D4—734no—
556C2×D4—732no—
557C2×D4—732no—
558C2×D4—1461no—
559C2×D4—1461no—
560C2×D4—1462no—
561C2×D4—1462no—
562C2×D4—1462no—
563C22×C4—2924no—
564C22×C4—2924no—
565C22×C4—5842no—
566C22×C4—5842no—
567C22×C4—1461no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1464no—
574C22×C4—1464no—
575C22×C4—1464no—
576C22×C4—1464no—
577C22×C4C2×D29211yescharacteristic
578C22×C4C2×D29211yescharacteristic
579C22×C4C2×D29211yescharacteristic
580C22×C4C2×D29211yescharacteristic
581C22×C4C2×D29211yescharacteristic
582C22×C4C2×D29211yescharacteristic
583C22×C4C23×D7311yescharacteristic
584SD16—1468no—
585SD16—1468no—
586D8—1468no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8C23×D7312yes—
592C2×C8C23×D7312yes—
593C2×C8C23×D7312yes—
594C2×C8C23×D7312yes—
595C4⋊C4—732no—
596C4⋊C4—732no—
597C4⋊C4—732no—
598C4⋊C4—732no—
599C4⋊C4—1464no—
600C4⋊C4—1464no—
601C4⋊C4—1464no—
602C4⋊C4—1464no—
603C4⋊C4—1464no—
604C4⋊C4—1464no—
605C4⋊C4—1461no—
606C4⋊C4—1461no—
607C4⋊C4—1461no—
608C4⋊C4—1461no—
609C4⋊C4—1464no—
610C4⋊C4—1464no—
611C4⋊C4—1464no—
612C4⋊C4C2×D29214yes—
613C4⋊C4C2×D29214yes—
614C4⋊C4C2×D29214yes—
615C22⋊C4—1464no—
616C22⋊C4—1464no—
617C22⋊C4—1464no—
618C22⋊C4—1464no—
619C22⋊C4—1464no—
620C22⋊C4—1464no—
621C22⋊C4—1464no—
622C22⋊C4—1464no—
623C42—1464no—
624C42—1464no—
625C42C2×D29212yes—
626C42C2×D29212yes—
627C42C2×D29212yes—
628C42C23×D7312yes—
629C42C23×D7312yes—
630C42C23×D7312yes—
631C23—2922no—
632C23—2922no—
633C23—2922no—
634C23—2922no—
635C23—2922no—
636C23—1462no—
637C23—1462no—
638C23—1464no—
639C23C22×D29211yescharacteristic
640Q8—44no—
641Q8—2922no—
642Q8—2922no—
643Q8—5844no—
644Q8—1462no—
645Q8—1462no—
646Q8—1462no—
647Q8—1462no—
648D4—2922no—
649D4—734no—
650D4—1462no—
651D4—1462no—
652D4—1462no—
653D4—1464no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—2928no—
661C2×C4—2928no—
662C2×C4—2922no—
663C2×C4—2922no—
664C2×C4—2922no—
665C2×C4—2922no—
666C2×C4—2922no—
667C2×C4—2922no—
668C2×C4—5844no—
669C2×C4—5844no—
670C2×C4—1462no—
671C2×C4—1462no—
672C2×C4—1462no—
673C2×C4—1462no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4C22×D29212yes—
677C2×C4C22×D29212yes—
678C2×C4C22×D29212yes—
679C2×C4C22×D29212yes—
680C2×C4C22×D29212yes—
681C2×C4C22×D29212yes—
682C2×C4C22×D29211yescharacteristic
683C2×C4#41×D7312yes—
684C2×C4#1455663912yes—
685C2×C4C24×D7311yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C22—2928no—
691C22—2922no—
692C22—2922no—
693C22—2922no—
694C22—2922no—
695C22—2922no—
696C22—5844no—
697C22—1464no—
698C22#1798924912yes—
699C22#1798938712yes—
700C22#1798939912yes—
701C22C23×D29211yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—2922no—
709C4—2922no—
710C4—2922no—
711C4—2922no—
712C4—2922no—
713C4—2922no—
714C4#1798924912yes—
715C4C2×#41×D7311yescharacteristic
716C4C2×#1455663911yescharacteristic
717C2—2924no—
718C2—5842no—
719C2#2262276014yesdirect product factor
720C2C2×#1798924911yescharacteristic
721C2C2×#1798938711yescharacteristic
722C2C2×#1798939911yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#446×C73C2
socleC23×C73C22×D4
prime radicalC22×D584C22
hypercenterC2×#446D73
hypocenterC73C2×#3376
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#17989310C2semidirect
2. C2×#17989297C2semidirect
3. #22622760C2direct (N × H)
4. C2×#17988956C2semidirect
5. C2×#17988947C2semidirect
6. C2×#17988942C2semidirect
7. C2×#17988895C2semidirect
8. C2×#17988873C2semidirect
9. C2×#17988888C2semidirect
12. C2×#17988793C2semidirect
14. C2×#17988689C2semidirect
15. C2×C4×#11924017C2semidirect
16. C2×#446×C73C2semidirect
21. #17989310C22semidirect
23. #17989297C22semidirect
44. #17988956C22semidirect
45. #17988947C22semidirect
46. #17988942C22semidirect
47. #17988895C22semidirect
48. #17988888C22semidirect
49. #17988873C22semidirect
52. #17988793C22semidirect
54. #17988689C22semidirect
55. C4×#11924017C22semidirect
70. #446×C73C22semidirect
356. C2×C73#3376semidirect
374. C2×#446D73semidirect
378. C73C2×#3376semidirect
416. #446C2×D73semidirect
719. C2#22622760direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893102
C2×#179892972
#226227602
C2×#179889562
C2×#179889472
C2×#179889422
C2×#179888952
C2×#179888732
C2×#179888882
C2×#179888032
C2×#179887932
C2×#179887002
C2×#179886892
C2×C4×#119240172
C2×#446×C732
C2×#337673