Finite Group Databasebeta

← C2×#22622831 #33966462

Subgroups — C2×#22622831 #33966462

Order 18688.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989296C211yesmaximal, characteristic, complemented
2C2×D4×Dic146C211yesmaximal, characteristic, complemented
3#22622831C2116yesmaximal, direct product factor
4C2×#17988996C211yesmaximal, characteristic, complemented
5C2×#17988994C211yesmaximal, characteristic, complemented
6C2×#17988984C211yesmaximal, characteristic, complemented
7C2×#17988887C211yesmaximal, characteristic, complemented
8C2×#17988885C211yesmaximal, characteristic, complemented
9C2×#17988877C211yesmaximal, characteristic, complemented
10C2×#17988875C211yesmaximal, characteristic, complemented
11C2×#17988875C211yesmaximal, characteristic, complemented
12C2×#17988865C211yesmaximal, characteristic, complemented
13C2×#17988715C211yesmaximal, characteristic, complemented
14C2×#17988699C211yesmaximal, characteristic
15C2×D8×Dic73C211yesmaximal, characteristic
16C2×#442×C73C211yesmaximal, characteristic
17C23×Dic146—21no—
18#17989296—24no—
19#17989296C2218yescomplemented
20D4×Dic146—24no—
21D4×Dic146C2218yescomplemented
22C2×#14556591C2211yescharacteristic
23C2×#14556590C2211yescharacteristic
24C2×#14556590C2211yescharacteristic
25C2×#14556590C2211yescharacteristic
26C2×#14556583C2211yescharacteristic
27C2×#14556582C2211yescharacteristic
28C2×#14556570—21no—
29C2×#14556570—21no—
30C2×#14556568—21no—
31C2×#14556568—21no—
32C2×#14556568—21no—
33C2×#14556568—21no—
34C2×C4×Dic146C2211yescharacteristic
35C2×D4×Dic73C2211yescharacteristic
36C2×D4×Dic73C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×D4×Dic73C2211yescharacteristic
39C22×#11924007—21no—
40#17988996C2218yescomplemented
41#17988994C2218yescomplemented
42#17988984C2218yescomplemented
43#17988887C2218yescomplemented
44#17988885C2218yescomplemented
45#17988877C2218yescomplemented
46#17988875C2218yescomplemented
47#17988875C2218yescomplemented
48#17988865C2218yescomplemented
49#17988715C2218yescomplemented
50#17988699C2218yes—
51D8×Dic73C2218yes—
52C2×#14556525C2211yescharacteristic
53C2×#14556525C2211yescharacteristic
54C2×#14556524C2211yescharacteristic
55C2×#14556523C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556522C2211yescharacteristic
59C2×#14556522C2211yescharacteristic
60C2×C4⋊#10596831C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C2×#14556520C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556512C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×D8×C73C2211yescharacteristic
70C2×C4×D4×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#442×C73C2218yes—
73C2×#106×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146—28no—
78C22×Dic146—21no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146—21no—
82C22×Dic146—48no—
83C22×Dic146D411yescharacteristic
84C23×Dic73—21no—
85C23×Dic73—21no—
86C23×Dic73—21no—
87C23×Dic73—21no—
88C22×#10596831C2311yescharacteristic
89C22×#10596831C2311yescharacteristic
90#14556591—22no—
91#14556591C2314yes—
92#14556590—22no—
93#14556590—22no—
94#14556590—22no—
95#14556590C2314yes—
96#14556590C2314yes—
97#14556590C2314yes—
98#14556583—22no—
99#14556583C2314yes—
100#14556582—22no—
101#14556582C2314yes—
102#14556570—28no—
103#14556570—28no—
104#14556568—28no—
105#14556568—28no—
106#14556568—28no—
107#14556568—28no—
108C4×Dic146D414yes—
109C4×Dic146C2314yes—
110D4×Dic73—22no—
111D4×Dic73—22no—
112D4×Dic73—22no—
113D4×Dic73—22no—
114D4×Dic73C2314yes—
115D4×Dic73C2314yes—
116D4×Dic73C2314yes—
117D4×Dic73C2314yes—
118C2×C4⋊Dic73—21no—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73D411yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—28no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007D411yescharacteristic
133C2×#11924007D411yescharacteristic
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×C22⋊Dic73—21no—
138C2×C4×Dic73C2311yescharacteristic
139C2×C4×Dic73C2311yescharacteristic
140#14556525C2314yes—
141#14556525C2314yes—
142#14556524C2314yes—
143#14556523C2314yes—
144#14556523C2314yes—
145#14556522C2314yes—
146#14556522C2314yes—
147#14556522C2314yes—
148C4⋊#10596831C2314yes—
149#14556520C2314yes—
150#14556520C2314yes—
151#14556512C2314yes—
152#14556512C2314yes—
153#14556512C2314yes—
154#14556512C2314yes—
155#14556501C2314yes—
156C8×Dic73C2314yes—
157C22×D4×C73C2311yescharacteristic
158C22×D4×C73C2311yescharacteristic
159C23×C4×C73—21no—
160C23×C4×C73—21no—
161C2×D8×C73Q818yescomplemented
162C2×D8×C73C2314yes—
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C4×D4×C73—22no—
166C4×D4×C73—22no—
167C4×D4×C73C2314yes—
168C4×D4×C73C2314yes—
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C22⋊C4×C73—21no—
172C2×C22⋊C4×C73—21no—
173C2×C42×C73C2311yescharacteristic
174#106×C73C2314yes—
175#102×C73C2314yes—
176#102×C73C2314yes—
177#97×C73C2314yes—
178C2×Dic146—24no—
179C2×Dic146—24no—
180C2×Dic146—24no—
181C2×Dic146—24no—
182C2×Dic146—24no—
183C2×Dic146—432no—
184C2×Dic146—44no—
185C2×Dic146—44no—
186C2×Dic146—44no—
187C2×Dic146—82no—
188C2×Dic146C2×D414yes—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—24no—
194C22×Dic73—24no—
195C22×Dic73—24no—
196C22×Dic73—24no—
197C22×Dic73—44no—
198C22×Dic73—44no—
199C22×Dic73—44no—
200C22×Dic73—82no—
201C22×Dic73C2×D411yescharacteristic
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C2×#10596831—22no—
206C2×#10596831—22no—
207C2×#10596831C2412yes—
208C2×#10596831C2412yes—
209C4⋊Dic73—24no—
210C4⋊Dic73—21no—
211C4⋊Dic73—21no—
212C4⋊Dic73—21no—
213C4⋊Dic73—21no—
214C4⋊Dic73—24no—
215C4⋊Dic73C2×D414yes—
216C4⋊Dic73C2412yes—
217C4⋊Dic73C2412yes—
218C4⋊Dic73C2412yes—
219C4⋊Dic73C2412yes—
220#11924007—24no—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007C2×D414yes—
227#11924007C2×D414yes—
228C22⋊Dic73—24no—
229C22⋊Dic73—24no—
230C22⋊Dic73—24no—
231C22⋊Dic73—24no—
232C4×Dic73C2×D412yes—
233C4×Dic73C2×D412yes—
234C4×Dic73C2412yes—
235C4×Dic73C2412yes—
236C24×C73—21no—
237C24×C73—21no—
238C2×D4×C73—21no—
239C2×D4×C73—21no—
240C2×D4×C73—22no—
241C2×D4×C73—22no—
242C2×D4×C73C2×Q814yes—
243C2×D4×C73C2×Q814yescomplemented
244C2×D4×C73C2412yes—
245C2×D4×C73C2412yes—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—24no—
249C22×C4×C73—24no—
250C22×C4×C73—44no—
251C22×C4×C73—82no—
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2411yescharacteristic
255D8×C73C2×Q8116yescomplemented
256C2×C8×C73—22no—
257C2×C8×C73C2×Q814yescomplemented
258C2×C8×C73C2412yes—
259C2×C8×C73C2412yes—
260C4⋊C4×C73—21no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73C2412yes—
263C4⋊C4×C73C2412yes—
264C22⋊C4×C73—24no—
265C22⋊C4×C73—24no—
266C42×C73C2×D412yes—
267C42×C73C2412yes—
268C23×C73—24no—
269C23×C73—24no—
270C23×C73—22no—
271C23×C73—22no—
272C23×C73—42no—
273C23×C73—42no—
274C23×C73—42no—
275C23×C73—42no—
276C23×C73C22×D411yescharacteristic
277D4×C73—24no—
278D4×C73—24no—
279D4×C73—22no—
280D4×C73—22no—
281D4×C73C22×Q814yes—
282D4×C73C22×Q814yescomplemented
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—48no—
288C2×C4×C73—42no—
289C2×C4×C73—42no—
290C2×C4×C73—84no—
291C2×C4×C73C22×D412yes—
292C2×C4×C73C22×D412yes—
293C2×C4×C73C22×D411yescharacteristic
294C2×C4×C73C22×Q812yes—
295C2×C4×C732−1+412yes—
296C2×C4×C73C2511yescharacteristic
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—48no—
305C2×Dic73—42no—
306C2×Dic73—42no—
307C2×Dic73—42no—
308C2×Dic73—42no—
309C2×Dic73—48no—
310C2×Dic73—48no—
311C2×Dic73—84no—
312C2×Dic73AGL(1,ℤ/8)14yes—
313C2×Dic73C22×D412yes—
314C2×Dic73C22×D412yes—
315C2×Dic73C22×D412yes—
316C2×Dic73C22×D412yes—
317Dic146—28no—
318Dic146—48no—
319Dic146—48no—
320Dic146—48no—
321Dic146—84no—
322C8×C73—22no—
323C8×C73C22×Q814yescomplemented
324#10596831—22no—
325#10596831—22no—
326C22×C73—24no—
327C22×C73—24no—
328C22×C73—48no—
329C22×C73—48no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—42no—
333C22×C73—42no—
334C22×C73D4×Q812yes—
335C22×C73C2×AGL(1,ℤ/8)12yes—
336C22×C73#57712yes—
337C22×C73C23×D411yescharacteristic
338C4×C73—22no—
339C4×C73—22no—
340C4×C73—42no—
341C4×C73—42no—
342C4×C73D4×Q812yes—
343C4×C73C23×Q811yescharacteristic
344C4×C73C2×2−1+411yescharacteristic
345Dic73—22no—
346Dic73—22no—
347Dic73—22no—
348Dic73—42no—
349Dic73—42no—
350Dic73—42no—
351Dic73—42no—
352Dic73C2×AGL(1,ℤ/8)14yes—
353C2×#3384—731nomaximal, Sylow
354C2×C73—44no—
355C2×C73—44no—
356C2×C73#338414yescomplemented
357C2×C73C2×D4×Q811yescharacteristic
358C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
359C2×C73C2×#57711yescharacteristic
360C2×#554—731no—
361C2×D4×Q8—731no—
362#3384—7316no—
363C2×#501—731no—
364C2×#501—731no—
365C2×#498—731no—
366C2×#478—731no—
367C2×#478—731no—
368C2×#476—731no—
369C2×#476—731no—
370C2×#476—731no—
371C2×#474—731no—
372C2×#446—731no—
373C2×#442—731no—
374C2×#442D7311yescharacteristic
375C2×C4×D8—731no—
376C73C2×#338411yescharacteristic, complemented, Sylow
377C23×Q8—1461no—
378C22×D8C2×D7311yescharacteristic
379#554—738no—
380#554—1464no—
381D4×Q8—738no—
382D4×Q8—1464no—
383C2×C4⋊Q8—731no—
384C2×C4⋊Q8—731no—
385C2×C4⋊Q8—731no—
386C2×C4⋊Q8—731no—
387C2×#125—731no—
388C2×#125—731no—
389C2×C22⋊Q8—1461no—
390C2×C22⋊Q8—1461no—
391C2×C22⋊Q8—1461no—
392C2×C22⋊Q8—1461no—
393C2×C22⋊Q8—1461no—
394C2×C22⋊Q8—1461no—
395C2×C4×Q8—731no—
396C2×C4×D4—731no—
397C2×C4×D4—731no—
398C2×C4×D4—731no—
399C2×C4×D4—731no—
400C2×C4×D4C2×D7311yescharacteristic
401C2×C4×D4C2×D7311yescharacteristic
402C22×C4⋊C4—1461no—
403#501—738no—
404#501—738no—
405#498—738no—
406#478—738no—
407#478—738no—
408#476—738no—
409#476—738no—
410#476—738no—
411#474—738no—
412#446—738no—
413#442—738no—
414#442C2×D7318yes—
415C4×D8—738no—
416C2×#107—731no—
417C2×#107—731no—
418C2×#107—731no—
419C2×#106—731no—
420C2×#106—731no—
421C2×#106—731no—
422C2×#106—731no—
423C2×#106—731no—
424C2×#106C2×D7311yescharacteristic
425C2×C4⋊C8—731no—
426C2×C4⋊C8—731no—
427C2×C4⋊C8—731no—
428C2×#102—731no—
429C2×#102—731no—
430C2×#102—731no—
431C2×#102—731no—
432C2×#102C2×D7311yescharacteristic
433C2×#102C2×D7311yescharacteristic
434C2×#97—731no—
435C2×#97C2×D7311yescharacteristic
436C2×C4×C8—731no—
437C22×Q8—2928no—
438C22×Q8—731no—
439C22×Q8—1461no—
440C22×Q8—1461no—
441C22×Q8—1461no—
442C22×Q8—1468no—
443C22×Q8—1461no—
444C22×D4C22×D7311yescharacteristic
445C22×D4C22×D7311yescharacteristic
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—1461no—
449C23×C4—1461no—
450C23×C4—1461no—
451C23×C4—1461no—
452C2×D8Dic14618yescomplemented
453C2×D8C22×D7314yes—
454C22×C8—731no—
455C22×C8—731no—
456C22×C8C22×D7311yescharacteristic
457C22×C8C22×D7311yescharacteristic
458C4⋊Q8—734no—
459C4⋊Q8—734no—
460C4⋊Q8—734no—
461C4⋊Q8—734no—
462C4⋊Q8—1462no—
463C4⋊Q8—1462no—
464C4⋊Q8—1462no—
465C4⋊Q8—1462no—
466#125—734no—
467#125—734no—
468#125—1462no—
469#125—1462no—
470C22⋊Q8—1468no—
471C22⋊Q8—1468no—
472C22⋊Q8—1468no—
473C22⋊Q8—1468no—
474C22⋊Q8—1468no—
475C22⋊Q8—1468no—
476C4×Q8—734no—
477C4×Q8—734no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—734no—
481C4×D4—734no—
482C4×D4—734no—
483C4×D4—734no—
484C4×D4—1462no—
485C4×D4—1462no—
486C4×D4—1462no—
487C4×D4—1462no—
488C4×D4C22×D7314yes—
489C4×D4C22×D7314yes—
490C2×C4⋊C4—731no—
491C2×C4⋊C4—731no—
492C2×C4⋊C4—731no—
493C2×C4⋊C4—731no—
494C2×C4⋊C4—731no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—1468no—
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—1461no—
506C2×C4⋊C4C22×D7311yescharacteristic
507C2×C4⋊C4C22×D7311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1461no—
511C2×C22⋊C4—1461no—
512C2×C22⋊C4—1461no—
513C2×C22⋊C4—1461no—
514C2×C42—731no—
515C2×C42—731no—
516C2×C42C22×D7311yescharacteristic
517#107—734no—
518#107—734no—
519#107—734no—
520#106—734no—
521#106—734no—
522#106—734no—
523#106—734no—
524#106—734no—
525#106C22×D7314yes—
526C4⋊C8—734no—
527C4⋊C8—734no—
528C4⋊C8—734no—
529#102—734no—
530#102—734no—
531#102—734no—
532#102—734no—
533#102C22×D7314yes—
534#102C22×D7314yes—
535#97—734no—
536#97C22×D7314yes—
537C4×C8—734no—
538C24—21no—
539C24—21no—
540C2×Q8—2924no—
541C2×Q8—29232no—
542C2×Q8—2924no—
543C2×Q8—2924no—
544C2×Q8—5842no—
545C2×Q8—734no—
546C2×Q8—1464no—
547C2×Q8—1464no—
548C2×Q8—1464no—
549C2×Q8—1464no—
550C2×Q8—1464no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4C2×Dic14614yes—
556C2×D4C2×Dic14614yescomplemented
557C2×D4C23×D7312yes—
558C2×D4C23×D7312yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—44no—
564C22×C4—82no—
565C22×C4—2924no—
566C22×C4—2924no—
567C22×C4—2924no—
568C22×C4—5842no—
569C22×C4—731no—
570C22×C4—731no—
571C22×C4—731no—
572C22×C4—731no—
573C22×C4—1464no—
574C22×C4—1464no—
575C22×C4—1464no—
576C22×C4—1461no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4—1461no—
580C22×C4—1464no—
581C22×C4D4×D7311yescharacteristic
582C22×C4D4×D7311yescharacteristic
583C22×C4C23×D7311yescharacteristic
584D8C2×Dic146116yescomplemented
585C2×C8—22no—
586C2×C8—732no—
587C2×C8—732no—
588C2×C8—1462no—
589C2×C8—1462no—
590C2×C8C2×Dic14614yescomplemented
591C2×C8C23×D7312yes—
592C2×C8C23×D7312yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—734no—
596C4⋊C4—734no—
597C4⋊C4—734no—
598C4⋊C4—732no—
599C4⋊C4—732no—
600C4⋊C4—732no—
601C4⋊C4—732no—
602C4⋊C4—1464no—
603C4⋊C4—1464no—
604C4⋊C4—1464no—
605C4⋊C4—1464no—
606C4⋊C4—1464no—
607C4⋊C4—1464no—
608C4⋊C4—1464no—
609C4⋊C4—1461no—
610C4⋊C4—1461no—
611C4⋊C4—1461no—
612C4⋊C4—1461no—
613C4⋊C4—1464no—
614C4⋊C4C23×D7312yes—
615C4⋊C4C23×D7312yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1464no—
619C22⋊C4—1464no—
620C22⋊C4—1464no—
621C22⋊C4—1464no—
622C42—732no—
623C42—732no—
624C42—732no—
625C42—732no—
626C42D4×D7312yes—
627C42C23×D7312yes—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23C2×D4×D7311yescharacteristic
637Q8—2928no—
638Q8—2928no—
639Q8—2928no—
640Q8—5844no—
641Q8—1468no—
642D4—22no—
643D4—22no—
644D4—24no—
645D4—24no—
646D4C22×Dic14614yes—
647D4C22×Dic14614yescomplemented
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—84no—
656C2×C4—2922no—
657C2×C4—2922no—
658C2×C4—2922no—
659C2×C4—2922no—
660C2×C4—2928no—
661C2×C4—2928no—
662C2×C4—2928no—
663C2×C4—5844no—
664C2×C4—732no—
665C2×C4—734no—
666C2×C4—732no—
667C2×C4—732no—
668C2×C4—732no—
669C2×C4—1462no—
670C2×C4—1462no—
671C2×C4—1462no—
672C2×C4—1462no—
673C2×C4—1462no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4C2×D4×D7312yes—
677C2×C4C2×D4×D7312yes—
678C2×C4C2×D4×D7311yescharacteristic
679C2×C4C22×Dic14612yes—
680C2×C4#1455663812yes—
681C2×C4C24×D7311yescharacteristic
682C8—22no—
683C8—1462no—
684C8—1462no—
685C8C22×Dic14614yescomplemented
686C22—24no—
687C22—24no—
688C22—48no—
689C22—48no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22D4×Dic14612yes—
695C22AGL(1,ℤ/8)×D7312yes—
696C22#1798939712yes—
697C22C22×D4×D7311yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—2922no—
703C4—2922no—
704C4—2922no—
705C4—2922no—
706C4—734no—
707C4—1462no—
708C4—1462no—
709C4—1462no—
710C4D4×Dic14612yes—
711C4C23×Dic14611yescharacteristic
712C4C2×#1455663811yescharacteristic
713C2—44no—
714C2—44no—
715C2#2262283114yesdirect product factor
716C2C2×D4×Dic14611yescharacteristic
717C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
718C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#442×C73C2
socleC23×C73C22×D4
prime radicalC22×D8×C73C22
hypercenterC2×#442D73
hypocenterC73C2×#3384
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#17989296C2semidirect
2. C2×D4×Dic146C2semidirect
3. #22622831C2direct (N × H)
4. C2×#17988996C2semidirect
5. C2×#17988994C2semidirect
6. C2×#17988984C2semidirect
7. C2×#17988887C2semidirect
8. C2×#17988885C2semidirect
9. C2×#17988877C2semidirect
10. C2×#17988875C2semidirect
11. C2×#17988875C2semidirect
12. C2×#17988865C2semidirect
13. C2×#17988715C2semidirect
19. #17989296C22semidirect
21. D4×Dic146C22semidirect
40. #17988996C22semidirect
41. #17988994C22semidirect
42. #17988984C22semidirect
43. #17988887C22semidirect
44. #17988885C22semidirect
45. #17988877C22semidirect
46. #17988875C22semidirect
47. #17988875C22semidirect
48. #17988865C22semidirect
49. #17988715C22semidirect
161. C2×D8×C73Q8semidirect
243. C2×D4×C73C2×Q8semidirect
255. D8×C73C2×Q8semidirect
257. C2×C8×C73C2×Q8semidirect
282. D4×C73C22×Q8semidirect
323. C8×C73C22×Q8semidirect
356. C2×C73#3384semidirect
376. C73C2×#3384semidirect
452. C2×D8Dic146semidirect
556. C2×D4C2×Dic146semidirect
584. D8C2×Dic146semidirect
590. C2×C8C2×Dic146semidirect
647. D4C22×Dic146semidirect
685. C8C22×Dic146semidirect
715. C2#22622831direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892962
C2×D4×Dic1462
#226228312
C2×#179889962
C2×#179889942
C2×#179889842
C2×#179888872
C2×#179888852
C2×#179888772
C2×#179888752
C2×#179888652
C2×#179887152
C2×#179886992
C2×D8×Dic732
C2×#442×C732
C2×#338473