Finite Group Databasebeta

← C2×#22622754 #33965745

Subgroups — C2×#22622754 #33965745

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×#17989309C211yesmaximal, characteristic, complemented
2C2×#17989296C211yesmaximal, characteristic, complemented
3#22622754C2116yesmaximal, direct product factor
4C2×#17988954C211yesmaximal, characteristic, complemented
5C2×#17988948C211yesmaximal, characteristic, complemented
6C2×#17988942C211yesmaximal, characteristic, complemented
7C2×#17988894C211yesmaximal, characteristic, complemented
8C2×#17988871C211yesmaximal, characteristic, complemented
9C2×#17988886C211yesmaximal, characteristic, complemented
10C2×#17988804C211yesmaximal, characteristic
11C2×#17988802C211yesmaximal, characteristic
12C2×#17988790C211yesmaximal, characteristic, complemented
13C2×#17988717C211yesmaximal, characteristic, complemented
14C2×#17988696C211yesmaximal, characteristic
15C2×#17988684C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
17C22×#11924016C2211yescharacteristic
18C22×#11924013C2211yescharacteristic
19#17989309—24no—
20#17989309C2218yescomplemented
21#17989296—24no—
22#17989296C2218yescomplemented
23C2×#14556590C2211yescharacteristic
24C2×#14556589C2211yescharacteristic
25C2×#14556586—21no—
26C2×#14556585—21no—
27C2×#14556583C2211yescharacteristic
28C2×#14556582C2211yescharacteristic
29C2×#14556580C2211yescharacteristic
30C2×#14556579C2211yescharacteristic
31C2×#14556570—21no—
32C2×#14556569—21no—
33C2×#14556568—21no—
34C2×#14556568—21no—
35C2×C4×Dic146C2211yescharacteristic
36C2×#14556556C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×D4×Dic73C2211yescharacteristic
39C2×#14556553C2211yescharacteristic
40C2×#14556548—21no—
41C22×#11924007—21no—
42#17988954C2218yescomplemented
43#17988948C2218yescomplemented
44#17988942C2218yescomplemented
45#17988894C2218yescomplemented
46#17988886C2218yescomplemented
47#17988871C2218yescomplemented
48#17988804C2218yes—
49#17988802C2218yes—
50#17988790C2218yescomplemented
51#17988717C2218yescomplemented
52#17988696C2218yes—
53#17988684C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×C4⋊#10596831C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72C4×SD16×C73C2218yescomplemented
73C2×#106×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146D411yescharacteristic
79C22×Dic146C2311yescharacteristic
80C22×D292C2311yescharacteristic
81C23×Dic73—21no—
82C23×Dic73—21no—
83C22×C4×D73—21no—
84C2×#11924016—24no—
85C2×#11924016C2314yes—
86C2×#11924013—24no—
87C2×#11924013C2314yes—
88C22×#10596831C2311yescharacteristic
89C22×#10596831C2311yescharacteristic
90#14556590—22no—
91#14556590C2314yes—
92#14556589—22no—
93#14556589C2314yes—
94#14556586—28no—
95#14556585—28no—
96#14556583—22no—
97#14556583C2314yes—
98#14556582—22no—
99#14556582C2314yes—
100#14556580—22no—
101#14556580C2314yes—
102#14556579—22no—
103#14556579C2314yes—
104#14556570—28no—
105#14556569—28no—
106#14556568—28no—
107#14556568—28no—
108C4×Dic146D414yes—
109C4×Dic146C2314yes—
110#14556556—22no—
111#14556556C2314yes—
112D4×Dic73—22no—
113D4×Dic73—22no—
114D4×Dic73C2314yes—
115D4×Dic73C2314yes—
116#14556553—22no—
117#14556553C2314yes—
118#14556548—28no—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73D411yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×#11924007—21no—
124C2×#11924007—21no—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—28no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007D411yescharacteristic
132C2×#11924007D411yescharacteristic
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73C2311yescharacteristic
142C2×C4×Dic73C2311yescharacteristic
143#14556524C2314yes—
144#14556522C2314yes—
145C4⋊#10596831C2314yes—
146#14556520C2314yes—
147#14556520C2314yes—
148#14556516C2314yes—
149#14556516C2314yes—
150#14556515C2314yes—
151#14556515C2314yes—
152#14556514C2314yes—
153#14556513C2314yes—
154#14556513C2314yes—
155#14556511C2314yes—
156#14556501C2314yes—
157#14556501C2314yes—
158C22×Q8×C73C2311yescharacteristic
159C22×D4×C73C2311yescharacteristic
160C23×C4×C73—21no—
161C2×SD16×C73—24no—
162C2×SD16×C73C2314yes—
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C4×Q8×C73—22no—
166C4×Q8×C73C2314yes—
167C4×D4×C73—22no—
168C4×D4×C73C2314yes—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C22⋊C4×C73—21no—
173C2×C42×C73—21no—
174C2×C42×C73C2311yescharacteristic
175#106×C73C2314yes—
176#103×C73C2314yes—
177#102×C73C2314yes—
178C4×C8×C73C2314yes—
179C23×D73—21no—
180C2×Dic146—22no—
181C2×Dic146—22no—
182C2×Dic146—21no—
183C2×Dic146—24no—
184C2×Dic146—42no—
185C2×Dic146—82no—
186C2×Dic146C2×D414yes—
187C2×Dic146C2412yes—
188C2×D292—22no—
189C2×D292—22no—
190C2×D292—21no—
191C2×D292C2412yes—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—24no—
196C22×Dic73—24no—
197C22×Dic73—44no—
198C22×Dic73—82no—
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C22×Dic73C2×D411yescharacteristic
202C22×Dic73C2×D411yescharacteristic
203C2×C4×D73—24no—
204C2×C4×D73—44no—
205#11924016—28no—
206#11924013—28no—
207C2×#10596831—22no—
208C2×#10596831—22no—
209C2×#10596831C2412yes—
210C2×#10596831C2412yes—
211C4⋊Dic73—21no—
212C4⋊Dic73—21no—
213C4⋊Dic73—24no—
214C4⋊Dic73C2×D414yes—
215C4⋊Dic73C2412yes—
216C4⋊Dic73C2412yes—
217#11924007—24no—
218#11924007—24no—
219#11924007—24no—
220#11924007—24no—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007C2×D414yes—
225#11924007C2×D414yes—
226C22⋊Dic73—24no—
227C22⋊Dic73—24no—
228#11924005—24no—
229#11924005—24no—
230#11924005—24no—
231#11924005—24no—
232#11924005—24no—
233C4×Dic73—24no—
234C4×Dic73C2×D412yes—
235C4×Dic73C2×D412yes—
236C4×Dic73C2412yes—
237C4×Dic73C2412yes—
238C24×C73—21no—
239C2×Q8×C73—21no—
240C2×Q8×C73—22no—
241C2×Q8×C73—22no—
242C2×Q8×C73C2412yes—
243C2×D4×C73—21no—
244C2×D4×C73—22no—
245C2×D4×C73#4114yes—
246C2×D4×C73C2412yes—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—24no—
251C22×C4×C73—82no—
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2411yescharacteristic
255SD16×C73—28no—
256C2×C8×C73—22no—
257C2×C8×C73—22no—
258C2×C8×C73C2412yes—
259C2×C8×C73C2412yes—
260C4⋊C4×C73—24no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73—21no—
263C4⋊C4×C73C2412yes—
264C4⋊C4×C73C2412yes—
265C22⋊C4×C73—24no—
266C42×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—42no—
281D4×C73—24no—
282D4×C73—22no—
283D4×C73C2×#4114yes—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—42no—
290C2×C4×C73—42no—
291C2×C4×C73—42no—
292C2×C4×C73—84no—
293C2×C4×C73C22×D412yes—
294C2×C4×C73C22×D412yes—
295C2×C4×C73C22×D411yescharacteristic
296C2×C4×C73C2×#4112yes—
297C2×C4×C732−1+412yes—
298C2×C4×C73C2511yescharacteristic
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—48no—
307C2×Dic73—42no—
308C2×Dic73—42no—
309C2×Dic73—42no—
310C2×Dic73—84no—
311C2×Dic73C22×D412yes—
312C2×Dic73C22×D412yes—
313C2×Dic73C22×D412yes—
314C2×Dic73C22×D412yes—
315D292—22no—
316D292—22no—
317D292—42no—
318C4×D73—48no—
319Dic146—22no—
320Dic146—22no—
321Dic146—44no—
322Dic146—42no—
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×#461—731no—
374C2×#446—731no—
375C2×#442—731no—
376C2×#440—731no—
377C2×C4×SD16D7311yescharacteristic, complemented
378C73C2×#337611yescharacteristic, complemented, Sylow
379C22×SD16—731no—
380C22×SD16C2×D7311yescharacteristic
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×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#461—738no—
416#446—738no—
417#442—738no—
418#440—738no—
419C4×SD16C2×D7318yescomplemented
420C2×#107—731no—
421C2×#106—731no—
422C2×#106C2×D7311yescharacteristic
423C2×C4⋊C8—731no—
424C2×C4⋊C8—731no—
425C2×C4⋊C8—731no—
426C2×#103—731no—
427C2×#103—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×#103—731no—
431C2×#103C2×D7311yescharacteristic
432C2×#102—731no—
433C2×#102—731no—
434C2×#102—731no—
435C2×#102C2×D7311yescharacteristic
436C2×#97—731no—
437C2×#97—731no—
438C2×C4×C8C2×D7311yescharacteristic
439C22×Q8—731no—
440C22×Q8—731no—
441C22×Q8—1461no—
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—734no—
451C2×SD16—1464no—
452C2×SD16C22×D7314yes—
453C2×D8—734no—
454C2×D8—1464no—
455C22×C8—731no—
456C22×C8—731no—
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—22no—
478C4×Q8—734no—
479C4×Q8—734no—
480C4×Q8—734no—
481C4×Q8—1462no—
482C4×Q8C22×D7314yes—
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—731no—
494C2×C4⋊C4—731no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—731no—
498C2×C4⋊C4—1468no—
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—1461no—
506C2×C4⋊C4—1461no—
507C2×C4⋊C4C22×D7311yescharacteristic
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—21no—
518C2×C42—731no—
519C2×C42—731no—
520C2×C42—1461no—
521C2×C42C22×D7311yescharacteristic
522#107—734no—
523#106—734no—
524#106C22×D7314yes—
525C4⋊C8—734no—
526C4⋊C8—734no—
527C4⋊C8—734no—
528#103—734no—
529#103—734no—
530#103—734no—
531#103—734no—
532#103—734no—
533#103C22×D7314yes—
534#102—734no—
535#102—734no—
536#102—734no—
537#102C22×D7314yes—
538#97—734no—
539#97—734no—
540C4×C8C22×D7314yes—
541C24—21no—
542C24—1461no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—2922no—
547C2×Q8—5842no—
548C2×Q8—734no—
549C2×Q8—732no—
550C2×Q8—1464no—
551C2×Q8—1462no—
552C2×Q8—1462no—
553C2×Q8—1461no—
554C2×Q8C23×D7312yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—732no—
558C2×D4—1461no—
559C2×D4—1462no—
560C2×D4—1462no—
561C2×D4#1192402814yes—
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—1464no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4—1461no—
580C22×C4—1464no—
581C22×C4D4×D7311yescharacteristic
582C22×C4D4×D7311yescharacteristic
583C22×C4C23×D7311yescharacteristic
584SD16—28no—
585SD16—1468no—
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—21no—
597C4⋊C4—21no—
598C4⋊C4—734no—
599C4⋊C4—734no—
600C4⋊C4—734no—
601C4⋊C4—732no—
602C4⋊C4—732no—
603C4⋊C4—1464no—
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⋊C4C23×D7312yes—
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—24no—
624C42—732no—
625C42—732no—
626C42—732no—
627C42—732no—
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—42no—
643Q8—2924no—
644Q8—2922no—
645Q8—5844no—
646Q8—1462no—
647Q8—1462no—
648D4—22no—
649D4—24no—
650D4—2922no—
651D4—1462no—
652D4—1462no—
653D4C2×#1192402814yes—
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×#1192402812yes—
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#1798924612yes—
699C22#1798938412yes—
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#1798924612yes—
715C4C22×#1192402811yescharacteristic
716C4C2×#1455663811yescharacteristic
717C2—44no—
718C2—5842no—
719C2#2262275414yesdirect product factor
720C2C2×#1798924611yescharacteristic
721C2C2×#1798938411yescharacteristic
722C2C2×#1798939311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×C4×SD16×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924013C22
hypercenterC2×C4×SD16D73
hypocenterC73C2×#3376
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#17989309C2semidirect
2. C2×#17989296C2semidirect
3. #22622754C2direct (N × H)
4. C2×#17988954C2semidirect
5. C2×#17988948C2semidirect
6. C2×#17988942C2semidirect
7. C2×#17988894C2semidirect
8. C2×#17988871C2semidirect
9. C2×#17988886C2semidirect
12. C2×#17988790C2semidirect
13. C2×#17988717C2semidirect
15. C2×#17988684C2semidirect
16. C2×C4×SD16×C73C2semidirect
20. #17989309C22semidirect
22. #17989296C22semidirect
42. #17988954C22semidirect
43. #17988948C22semidirect
44. #17988942C22semidirect
45. #17988894C22semidirect
46. #17988886C22semidirect
47. #17988871C22semidirect
50. #17988790C22semidirect
51. #17988717C22semidirect
53. #17988684C22semidirect
72. C4×SD16×C73C22semidirect
357. C2×C73#3376semidirect
377. C2×C4×SD16D73semidirect
378. C73C2×#3376semidirect
419. C4×SD16C2×D73semidirect
719. C2#22622754direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893092
C2×#179892962
#226227542
C2×#179889542
C2×#179889482
C2×#179889422
C2×#179888942
C2×#179888712
C2×#179888862
C2×#179888042
C2×#179888022
C2×#179887902
C2×#179887172
C2×#179886962
C2×#179886842
C2×C4×SD16×C732
C2×#337673