Finite Group Databasebeta

← C2×#22622644 #33965654

Subgroups — C2×#22622644 #33965654

Order 18688.

2070 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989306C211yesmaximal, characteristic, complemented
2C2×D4×Dic146C211yesmaximal, characteristic, complemented
3#22622644C2116yesmaximal, direct product factor
4C2×#17988946C211yesmaximal, characteristic, complemented
5C2×#17988945C211yesmaximal, characteristic, complemented
6C2×#17988936C211yesmaximal, characteristic, complemented
7C2×#17988883C211yesmaximal, characteristic, complemented
8C2×#17988880C211yesmaximal, characteristic, complemented
9C2×#17988865C211yesmaximal, characteristic, complemented
10C2×#17988800C211yesmaximal, characteristic
11C2×#17988790C211yesmaximal, characteristic, complemented
12C2×#17988716C211yesmaximal, characteristic, complemented
13C2×#17988688C211yesmaximal, characteristic, complemented
14C2×#17988687C211yesmaximal, characteristic, complemented
15C2×D8×Dic73C211yesmaximal, characteristic
16C2×#463×C73C211yesmaximal, characteristic
17C23×Dic146—21no—
18C22×#11924016C2211yescharacteristic
19#17989306—24no—
20#17989306C2218yescomplemented
21D4×Dic146—24no—
22D4×Dic146C2218yescomplemented
23C2×#14556591C2211yescharacteristic
24C2×#14556590C2211yescharacteristic
25C2×#14556590C2211yescharacteristic
26C2×#14556589C2211yescharacteristic
27C2×#14556584—21no—
28C2×#14556584—21no—
29C2×#14556578C2211yescharacteristic
30C2×#14556570—21no—
31C2×#14556568—21no—
32C2×#14556568—21no—
33C2×#14556568—21no—
34C2×Q8×Dic73C2211yescharacteristic
35C2×C4×Dic146C2211yescharacteristic
36C2×C4×Dic146C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×D4×Dic73C2211yescharacteristic
39C2×D4×Dic73C2211yescharacteristic
40C2×#14556547—21no—
41#17988946C2218yescomplemented
42#17988945C2218yescomplemented
43#17988936C2218yescomplemented
44#17988883C2218yescomplemented
45#17988880C2218yescomplemented
46#17988865C2218yescomplemented
47#17988800C2218yes—
48#17988790C2218yescomplemented
49#17988716C2218yescomplemented
50#17988688C2218yescomplemented
51#17988687C2218yescomplemented
52D8×Dic73C2218yes—
53C2×#14556525C2211yescharacteristic
54C2×#14556525C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556502C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C22×D8×C73C2211yescharacteristic
71C2×#124×C73C2211yescharacteristic
72C2×C4×D4×C73C2211yescharacteristic
73#463×C73C2218yes—
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C22×Dic146—28no—
78C22×Dic146—21no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146—48no—
82C22×Dic146D411yescharacteristic
83C22×Dic146C2311yescharacteristic
84C23×Dic73—21no—
85C23×Dic73—21no—
86C23×Dic73—21no—
87C2×#11924016—24no—
88C2×#11924016C2314yes—
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2311yescharacteristic
91#14556591—22no—
92#14556591C2314yes—
93#14556590—22no—
94#14556590—22no—
95#14556590C2314yes—
96#14556590C2314yes—
97#14556589—22no—
98#14556589C2314yes—
99#14556584—28no—
100#14556584—28no—
101#14556578—22no—
102#14556578C2314yes—
103#14556570—28no—
104#14556568—28no—
105#14556568—28no—
106#14556568—28no—
107Q8×Dic73—22no—
108Q8×Dic73C2314yes—
109C4×Dic146—22no—
110C4×Dic146D414yes—
111C4×Dic146C2314yes—
112C4×Dic146C2314yes—
113D4×Dic73—22no—
114D4×Dic73—22no—
115D4×Dic73—22no—
116D4×Dic73C2314yes—
117D4×Dic73C2314yes—
118D4×Dic73C2314yes—
119#14556547—28no—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73D411yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007D411yescharacteristic
132C2×#11924007D411yescharacteristic
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×C22⋊Dic73—21no—
138C2×C4×Dic73—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73C2311yescharacteristic
141C2×C4×Dic73C2311yescharacteristic
142#14556525C2314yes—
143#14556525C2314yes—
144#14556524C2314yes—
145#14556520C2314yes—
146#14556520C2314yes—
147#14556516C2314yes—
148#14556516C2314yes—
149#14556515C2314yes—
150#14556515C2314yes—
151#14556514C2314yes—
152#14556512C2314yes—
153#14556512C2314yes—
154#14556512C2314yes—
155#14556502C2314yes—
156#14556501C2314yes—
157C8×Dic73C2314yes—
158C22×Q8×C73C2311yescharacteristic
159C22×D4×C73C2311yescharacteristic
160C22×D4×C73C2311yescharacteristic
161C23×C4×C73—21no—
162C2×SD16×C73—24no—
163C2×SD16×C73C2314yes—
164C2×D8×C73—24no—
165C2×D8×C73C2314yes—
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168#124×C73—22no—
169#124×C73C2314yes—
170C4×D4×C73—22no—
171C4×D4×C73C2314yes—
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C22⋊C4×C73—21no—
174C2×C22⋊C4×C73—21no—
175C2×C22⋊C4×C73—21no—
176C2×C42×C73C2311yescharacteristic
177C4⋊C8×C73C2314yes—
178#103×C73C2314yes—
179#102×C73C2314yes—
180C2×Dic146—24no—
181C2×Dic146—22no—
182C2×Dic146—22no—
183C2×Dic146—21no—
184C2×Dic146—24no—
185C2×Dic146—24no—
186C2×Dic146—24no—
187C2×Dic146—432no—
188C2×Dic146—44no—
189C2×Dic146—44no—
190C2×Dic146—44no—
191C2×Dic146C2×D414yes—
192C2×Dic146C2412yes—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—24no—
198C22×Dic73—24no—
199C22×Dic73—24no—
200C22×Dic73—44no—
201C22×Dic73—44no—
202C22×Dic73—44no—
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207#11924016—28no—
208C2×#10596831—22no—
209C2×#10596831—22no—
210C2×#10596831C2412yes—
211C2×#10596831C2412yes—
212C4⋊Dic73—24no—
213C4⋊Dic73—21no—
214C4⋊Dic73—21no—
215C4⋊Dic73—21no—
216C4⋊Dic73—24no—
217C4⋊Dic73C2×D414yes—
218C4⋊Dic73C2412yes—
219C4⋊Dic73C2412yes—
220C4⋊Dic73C2412yes—
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—
232C22⋊Dic73—24no—
233C4×Dic73—24no—
234C4×Dic73—24no—
235C4×Dic73C2×D412yes—
236C4×Dic73C2×D412yes—
237C4×Dic73C2412yes—
238C4×Dic73C2412yes—
239C24×C73—21no—
240C24×C73—21no—
241C2×Q8×C73—21no—
242C2×Q8×C73—22no—
243C2×Q8×C73—22no—
244C2×Q8×C73C2412yes—
245C2×D4×C73—21no—
246C2×D4×C73—21no—
247C2×D4×C73—22no—
248C2×D4×C73—22no—
249C2×D4×C73—22no—
250C2×D4×C73#4114yes—
251C2×D4×C73C2412yes—
252C2×D4×C73C2412yes—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—24no—
256C22×C4×C73—44no—
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2411yescharacteristic
260SD16×C73—28no—
261D8×C73—28no—
262C2×C8×C73—22no—
263C2×C8×C73—22no—
264C2×C8×C73C2412yes—
265C2×C8×C73C2412yes—
266C4⋊C4×C73—21no—
267C4⋊C4×C73C2412yes—
268C22⋊C4×C73—24no—
269C22⋊C4×C73—24no—
270C22⋊C4×C73—24no—
271C42×C73C2×D412yes—
272C42×C73C2412yes—
273C23×C73—24no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—42no—
277C23×C73—42no—
278C23×C73—42no—
279C23×C73—42no—
280C23×C73—42no—
281C23×C73C22×D411yescharacteristic
282Q8×C73—22no—
283Q8×C73—22no—
284Q8×C73—42no—
285D4×C73—24no—
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—22no—
289D4×C73—42no—
290D4×C73C2×#4114yes—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—48no—
296C2×C4×C73—42no—
297C2×C4×C73—42no—
298C2×C4×C73C22×D412yes—
299C2×C4×C73C22×D412yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4112yes—
302C2×C4×C732−1+412yes—
303C2×C4×C73C2511yescharacteristic
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—48no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73—48no—
317C2×Dic73—48no—
318C2×Dic73AGL(1,ℤ/8)14yes—
319C2×Dic73C22×D412yes—
320C2×Dic73C22×D412yes—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323Dic146—28no—
324Dic146—22no—
325Dic146—22no—
326Dic146—48no—
327Dic146—48no—
328Dic146—42no—
329Dic146—48no—
330C8×C73—22no—
331C8×C73—22no—
332#10596831—22no—
333#10596831—22no—
334C22×C73—24no—
335C22×C73—48no—
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—84no—
342C22×C73#54812yes—
343C22×C73C2×AGL(1,ℤ/8)12yes—
344C22×C73#57812yes—
345C22×C73C23×D411yescharacteristic
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—42no—
349C4×C73—42no—
350C4×C73#54812yes—
351C4×C73C22×#4111yescharacteristic
352C4×C73C2×2−1+411yescharacteristic
353Dic73—22no—
354Dic73—22no—
355Dic73—22no—
356Dic73—42no—
357Dic73—42no—
358Dic73—42no—
359Dic73—42no—
360Dic73C2×AGL(1,ℤ/8)14yes—
361C2×#3367—731nomaximal, Sylow
362C2×C73—44no—
363C2×C73—82no—
364C2×C73#336714yescomplemented
365C2×C73C2×#54811yescharacteristic
366C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
367C2×C73C2×#57811yescharacteristic
368C2×#556—731no—
369C2×D4×Q8—731no—
370#3367—7316no—
371C2×#489—731no—
372C2×#489—731no—
373C2×#487—731no—
374C2×#477—731no—
375C2×#477—731no—
376C2×#474—731no—
377C2×#463—731no—
378C2×#463D7311yescharacteristic
379C2×#461—731no—
380C2×#446—731no—
381C2×#440—731no—
382C2×#440—731no—
383C2×C4×D8—731no—
384C73C2×#336711yescharacteristic, complemented, Sylow
385C23×Q8—1461no—
386C22×SD16—731no—
387C22×SD16C2×D7311yescharacteristic
388C22×D8C2×D7311yescharacteristic
389#556—738no—
390#556—1464no—
391D4×Q8—738no—
392D4×Q8—1464no—
393C2×C4⋊Q8—731no—
394C2×C4⋊Q8—731no—
395C2×C4⋊Q8—731no—
396C2×C4⋊Q8—731no—
397C2×#126—1461no—
398C2×#126—1461no—
399C2×#124—731no—
400C2×#124C2×D7311yescharacteristic
401C2×C22⋊Q8—1461no—
402C2×C22⋊Q8—1461no—
403C2×C22⋊Q8—1461no—
404C2×C22⋊Q8—1461no—
405C2×C4×Q8—731no—
406C2×C4×Q8—731no—
407C2×C4×Q8—731no—
408C2×C4×D4—731no—
409C2×C4×D4—731no—
410C2×C4×D4—731no—
411C2×C4×D4C2×D7311yescharacteristic
412C2×#117—1461no—
413#489—738no—
414#489—738no—
415#487—738no—
416#477—738no—
417#477—738no—
418#474—738no—
419#463—738no—
420#463C2×D7318yes—
421#461—738no—
422#446—738no—
423#440—738no—
424#440—738no—
425C4×D8—738no—
426C2×#107—731no—
427C2×#107—731no—
428C2×#107—731no—
429C2×C4⋊C8—731no—
430C2×C4⋊C8—731no—
431C2×C4⋊C8C2×D7311yescharacteristic
432C2×#103—731no—
433C2×#103—731no—
434C2×#103—731no—
435C2×#103—731no—
436C2×#103—731no—
437C2×#103C2×D7311yescharacteristic
438C2×#102—731no—
439C2×#102—731no—
440C2×#102—731no—
441C2×#102C2×D7311yescharacteristic
442C2×#97—731no—
443C2×#97—731no—
444C2×C4×C8—731no—
445C22×Q8—2928no—
446C22×Q8—731no—
447C22×Q8—731no—
448C22×Q8—1461no—
449C22×Q8—1461no—
450C22×Q8—1468no—
451C22×Q8—1461no—
452C22×Q8C22×D7311yescharacteristic
453C22×D4C22×D7311yescharacteristic
454C22×D4C22×D7311yescharacteristic
455C23×C4—21no—
456C23×C4—1461no—
457C23×C4—1461no—
458C23×C4—1461no—
459C2×SD16—24no—
460C2×SD16—734no—
461C2×SD16—1464no—
462C2×SD16C22×D7314yes—
463C2×D8—24no—
464C2×D8C22×D7314yes—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8C22×D7311yescharacteristic
468C22×C8C22×D7311yescharacteristic
469C4⋊Q8—734no—
470C4⋊Q8—734no—
471C4⋊Q8—734no—
472C4⋊Q8—734no—
473C4⋊Q8—1462no—
474C4⋊Q8—1462no—
475C4⋊Q8—1462no—
476C4⋊Q8—1462no—
477#126—1468no—
478#126—1468no—
479#124—22no—
480#124—734no—
481#124—1462no—
482#124C22×D7314yes—
483C22⋊Q8—1468no—
484C22⋊Q8—1468no—
485C22⋊Q8—1468no—
486C22⋊Q8—1468no—
487C4×Q8—734no—
488C4×Q8—734no—
489C4×Q8—734no—
490C4×Q8—734no—
491C4×Q8—1462no—
492C4×Q8—1462no—
493C4×D4—22no—
494C4×D4—734no—
495C4×D4—734no—
496C4×D4—734no—
497C4×D4—1462no—
498C4×D4—1462no—
499C4×D4—1462no—
500C4×D4C22×D7314yes—
501#117—1468no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—731no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4—1461no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4C22×D7311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—1461no—
520C2×C22⋊C4—1461no—
521C2×C22⋊C4—1461no—
522C2×C22⋊C4—1461no—
523C2×C22⋊C4—1461no—
524C2×C42—731no—
525C2×C42—731no—
526C2×C42—1461no—
527C2×C42—1461no—
528C2×C42C22×D7311yescharacteristic
529#107—734no—
530#107—734no—
531#107—734no—
532C4⋊C8—734no—
533C4⋊C8—734no—
534C4⋊C8C22×D7314yes—
535#103—734no—
536#103—734no—
537#103—734no—
538#103—734no—
539#103—734no—
540#103C22×D7314yes—
541#102—734no—
542#102—734no—
543#102—734no—
544#102C22×D7314yes—
545#97—734no—
546#97—734no—
547C4×C8—734no—
548C24—21no—
549C24—21no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—2924no—
554C2×Q8—29232no—
555C2×Q8—2924no—
556C2×Q8—2924no—
557C2×Q8—734no—
558C2×Q8—732no—
559C2×Q8—1464no—
560C2×Q8—1464no—
561C2×Q8—1464no—
562C2×Q8—1462no—
563C2×Q8—1462no—
564C2×Q8—1461no—
565C2×Q8—1464no—
566C2×Q8C23×D7312yes—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4#1192402714yes—
573C2×D4C23×D7312yes—
574C2×D4C23×D7312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—2924no—
580C22×C4—2924no—
581C22×C4—2924no—
582C22×C4—731no—
583C22×C4—731no—
584C22×C4—731no—
585C22×C4—731no—
586C22×C4—1464no—
587C22×C4—1464no—
588C22×C4—1464no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4D4×D7311yescharacteristic
594C22×C4D4×D7311yescharacteristic
595C22×C4C23×D7311yescharacteristic
596SD16—28no—
597SD16—1468no—
598D8—28no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—732no—
602C2×C8—732no—
603C2×C8—1462no—
604C2×C8—1462no—
605C2×C8C23×D7312yes—
606C2×C8C23×D7312yes—
607C4⋊C4—21no—
608C4⋊C4—734no—
609C4⋊C4—734no—
610C4⋊C4—734no—
611C4⋊C4—732no—
612C4⋊C4—732no—
613C4⋊C4—732no—
614C4⋊C4—1464no—
615C4⋊C4—1464no—
616C4⋊C4—1464no—
617C4⋊C4—1464no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1461no—
621C4⋊C4—1461no—
622C4⋊C4—1461no—
623C4⋊C4—1464no—
624C4⋊C4C23×D7312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—1464no—
629C22⋊C4—1464no—
630C22⋊C4—1464no—
631C22⋊C4—1464no—
632C22⋊C4—1464no—
633C42—732no—
634C42—732no—
635C42—732no—
636C42—732no—
637C42—1464no—
638C42—1464no—
639C42D4×D7312yes—
640C42C23×D7312yes—
641C23—22no—
642C23—24no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23C2×D4×D7311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—2928no—
654Q8—2928no—
655Q8—2928no—
656Q8—2922no—
657Q8—1468no—
658Q8—1462no—
659Q8—1462no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—24no—
664D4—42no—
665D4C2×#1192402714yes—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—48no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—2922no—
674C2×C4—2922no—
675C2×C4—2922no—
676C2×C4—2922no—
677C2×C4—2928no—
678C2×C4—2928no—
679C2×C4—2928no—
680C2×C4—732no—
681C2×C4—734no—
682C2×C4—732no—
683C2×C4—732no—
684C2×C4—732no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4C2×D4×D7312yes—
693C2×C4C2×D4×D7312yes—
694C2×C4C2×D4×D7311yescharacteristic
695C2×C4C2×#1192402712yes—
696C2×C4#1455663812yes—
697C2×C4C24×D7311yescharacteristic
698C8—22no—
699C8—22no—
700C8—1462no—
701C8—1462no—
702C22—24no—
703C22—42no—
704C22—48no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#1798924312yes—
711C22AGL(1,ℤ/8)×D7312yes—
712C22#1798940112yes—
713C22C22×D4×D7311yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—2922no—
719C4—2922no—
720C4—2922no—
721C4—2922no—
722C4—734no—
723C4—1462no—
724C4—1462no—
725C4—1462no—
726C4#1798924312yes—
727C4C22×#1192402711yescharacteristic
728C4C2×#1455663811yescharacteristic
729C2—44no—
730C2—82no—
731C2#2262264414yesdirect product factor
732C2C2×#1798924311yescharacteristic
733C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
734C2C2×#1798940111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#463×C73C2
socleC23×C73C22×D4
prime radicalC22×D8×C73C22
hypercenterC2×#463D73
hypocenterC73C2×#3367
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#17989306C2semidirect
2. C2×D4×Dic146C2semidirect
3. #22622644C2direct (N × H)
4. C2×#17988946C2semidirect
5. C2×#17988945C2semidirect
6. C2×#17988936C2semidirect
7. C2×#17988883C2semidirect
8. C2×#17988880C2semidirect
9. C2×#17988865C2semidirect
11. C2×#17988790C2semidirect
12. C2×#17988716C2semidirect
13. C2×#17988688C2semidirect
14. C2×#17988687C2semidirect
20. #17989306C22semidirect
22. D4×Dic146C22semidirect
41. #17988946C22semidirect
42. #17988945C22semidirect
43. #17988936C22semidirect
44. #17988883C22semidirect
45. #17988880C22semidirect
46. #17988865C22semidirect
48. #17988790C22semidirect
49. #17988716C22semidirect
50. #17988688C22semidirect
51. #17988687C22semidirect
364. C2×C73#3367semidirect
384. C73C2×#3367semidirect
731. C2#22622644direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893062
C2×D4×Dic1462
#226226442
C2×#179889462
C2×#179889452
C2×#179889362
C2×#179888832
C2×#179888802
C2×#179888652
C2×#179888002
C2×#179887902
C2×#179887162
C2×#179886882
C2×#179886872
C2×D8×Dic732
C2×#463×C732
C2×#336773