Finite Group Databasebeta

← C2×#22622646 #33965656

Subgroups — C2×#22622646 #33965656

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×#17989252C211yesmaximal, characteristic, complemented
3#22622646C2116yesmaximal, direct product factor
4C2×#17988945C211yesmaximal, characteristic, complemented
5C2×#17988936C211yesmaximal, characteristic, complemented
6C2×#17988880C211yesmaximal, characteristic, complemented
7C2×#17988879C211yesmaximal, characteristic, complemented
8C2×#17988865C211yesmaximal, characteristic, complemented
9C2×#17988801C211yesmaximal, characteristic
10C2×#17988799C211yesmaximal, characteristic
11C2×#17988791C211yesmaximal, characteristic, complemented
12C2×#17988715C211yesmaximal, characteristic, complemented
13C2×#17988690C211yesmaximal, characteristic, complemented
14C2×#17988689C211yesmaximal, characteristic, complemented
15C2×#17988667C211yesmaximal, characteristic
16C2×#489×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73—21no—
18C22×#11924017C2211yescharacteristic
19C22×#11924015C2211yescharacteristic
20C22×#11924013C2211yescharacteristic
21#17989306—24no—
22#17989306C2218yescomplemented
23#17989252—24no—
24#17989252C2218yescomplemented
25C2×#14556590C2211yescharacteristic
26C2×#14556590C2211yescharacteristic
27C2×#14556589C2211yescharacteristic
28C2×#14556584—21no—
29C2×#14556584—21no—
30C2×#14556578C2211yescharacteristic
31C2×#14556569—21no—
32C2×#14556569—21no—
33C2×#14556568—21no—
34C2×#14556567—21no—
35C2×Q8×Dic73C2211yescharacteristic
36C2×C4×Dic146C2211yescharacteristic
37C2×C4×Dic146C2211yescharacteristic
38C2×C4×D292C2211yescharacteristic
39C2×D4×Dic73C2211yescharacteristic
40C2×#14556553C2211yescharacteristic
41C2×#14556553C2211yescharacteristic
42C2×#14556547—21no—
43#17988945C2218yescomplemented
44#17988936C2218yescomplemented
45#17988880C2218yescomplemented
46#17988879C2218yescomplemented
47#17988865C2218yescomplemented
48#17988801C2218yes—
49#17988799C2218yes—
50#17988791C2218yescomplemented
51#17988715C2218yescomplemented
52#17988690C2218yescomplemented
53#17988689C2218yescomplemented
54#17988667C2218yes—
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×C4⋊#10596831C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556512C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×#124×C73C2211yescharacteristic
71#489×C73C2218yescomplemented
72C2×#103×C73C2211yescharacteristic
73C2×#103×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146D411yescharacteristic
80C22×Dic146C2311yescharacteristic
81C2×Q8×D73—28no—
82C2×Q8×D73—48no—
83C22×D292C2311yescharacteristic
84C23×Dic73—21no—
85C22×C4×D73—21no—
86C22×C4×D73—21no—
87C22×C4×D73—21no—
88C2×#11924017—24no—
89C2×#11924017C2314yes—
90C2×#11924015—24no—
91C2×#11924015C2314yes—
92C2×#11924013—24no—
93C2×#11924013C2314yes—
94C22×#10596831C2311yescharacteristic
95C22×#10596831C2311yescharacteristic
96#14556590—22no—
97#14556590—22no—
98#14556590C2314yes—
99#14556590C2314yes—
100#14556589—22no—
101#14556589C2314yes—
102#14556584—28no—
103#14556584—28no—
104#14556578—22no—
105#14556578C2314yes—
106#14556569—28no—
107#14556569—28no—
108#14556568—28no—
109#14556567—28no—
110Q8×Dic73—22no—
111Q8×Dic73C2314yes—
112C4×Dic146—22no—
113C4×Dic146D414yes—
114C4×Dic146C2314yes—
115C4×Dic146C2314yes—
116C4×D292—22no—
117C4×D292C2314yes—
118D4×Dic73—22no—
119D4×Dic73C2314yes—
120#14556553—22no—
121#14556553—22no—
122#14556553C2314yes—
123#14556553C2314yes—
124#14556547—28no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73D411yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007D411yescharacteristic
135C2×#11924007D411yescharacteristic
136C2×C22⋊Dic73—21no—
137C2×C22⋊Dic73—21no—
138C2×C22⋊Dic73—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73C2311yescharacteristic
145C2×C4×Dic73C2311yescharacteristic
146#14556525C2314yes—
147#14556524C2314yes—
148#14556524C2314yes—
149C4⋊#10596831C2314yes—
150#14556520C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556515C2314yes—
154#14556514C2314yes—
155#14556514C2314yes—
156#14556513C2314yes—
157#14556512C2314yes—
158#14556501C2314yes—
159C8×Dic73C2314yes—
160C22×Q8×C73—21no—
161C22×Q8×C73C2311yescharacteristic
162C22×D4×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C4⋊Q8×C73—22no—
166C4⋊Q8×C73C2314yes—
167#124×C73—22no—
168#124×C73C2314yes—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C22⋊C4×C73—21no—
173C2×C22⋊C4×C73—21no—
174C2×C42×C73C2311yescharacteristic
175#103×C73C2314yes—
176#103×C73C2314yes—
177#102×C73C2314yes—
178#102×C73C2314yes—
179#97×C73C2314yes—
180C23×D73—21no—
181C2×Dic146—24no—
182C2×Dic146—22no—
183C2×Dic146—22no—
184C2×Dic146—21no—
185C2×Dic146—24no—
186C2×Dic146—24no—
187C2×Dic146—44no—
188C2×Dic146—44no—
189C2×Dic146C2×D414yes—
190C2×Dic146C2412yes—
191Q8×D73—432no—
192C2×D292—21no—
193C2×D292—22no—
194C2×D292#4114yes—
195C2×D292C2412yes—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—24no—
200C22×Dic73—44no—
201C22×Dic73C2×D411yescharacteristic
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C2×C4×D73—24no—
206C2×C4×D73—24no—
207C2×C4×D73—24no—
208C2×C4×D73—44no—
209C2×C4×D73—44no—
210C2×C4×D73—44no—
211#11924017—28no—
212#11924015—28no—
213#11924013—28no—
214C2×#10596831—22no—
215C2×#10596831—22no—
216C2×#10596831C2412yes—
217C2×#10596831C2412yes—
218C4⋊Dic73—21no—
219C4⋊Dic73—21no—
220C4⋊Dic73—24no—
221C4⋊Dic73C2×D414yes—
222C4⋊Dic73C2412yes—
223C4⋊Dic73C2412yes—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007C2×D414yes—
230#11924007C2×D414yes—
231C22⋊Dic73—24no—
232C22⋊Dic73—24no—
233C22⋊Dic73—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237C4×Dic73—24no—
238C4×Dic73—24no—
239C4×Dic73C2×D412yes—
240C4×Dic73C2×D412yes—
241C4×Dic73C2412yes—
242C4×Dic73C2412yes—
243C24×C73—21no—
244C2×Q8×C73—21no—
245C2×Q8×C73—24no—
246C2×Q8×C73—22no—
247C2×Q8×C73—22no—
248C2×Q8×C73—44no—
249C2×Q8×C73C2412yes—
250C2×D4×C73—21no—
251C2×D4×C73—22no—
252C2×D4×C73—22no—
253C2×D4×C73C2412yes—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2411yescharacteristic
260C2×C8×C73—22no—
261C2×C8×C73—22no—
262C2×C8×C73C2412yes—
263C2×C8×C73C2412yes—
264C4⋊C4×C73—24no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C22⋊C4×C73—24no—
270C22⋊C4×C73—24no—
271C42×C73C2×D412yes—
272C42×C73C2412yes—
273C23×C73—22no—
274C23×C73—42no—
275C23×C73—42no—
276C23×C73—42no—
277C23×C73C22×D411yescharacteristic
278C22×D73—24no—
279C22×D73—22no—
280C22×D73—42no—
281C22×D73—42no—
282Q8×C73—22no—
283Q8×C73—22no—
284Q8×C73—48no—
285Q8×C73—42no—
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—42no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—42no—
295C2×C4×C73—42no—
296C2×C4×C73—42no—
297C2×C4×C73C22×D412yes—
298C2×C4×C73C22×D412yes—
299C2×C4×C73C22×D411yescharacteristic
300C2×C4×C73C2×#4112yes—
301C2×C4×C732−1+412yes—
302C2×C4×C73C2511yescharacteristic
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—42no—
310C2×Dic73—42no—
311C2×Dic73—42no—
312C2×Dic73—48no—
313C2×Dic73AGL(1,ℤ/8)14yes—
314C2×Dic73C22×D412yes—
315C2×Dic73C22×D412yes—
316C2×Dic73C22×D412yes—
317C2×Dic73C22×D412yes—
318D292—24no—
319D292—22no—
320D292C2×#4114yes—
321C4×D73—48no—
322C4×D73—48no—
323C4×D73—48no—
324Dic146—28no—
325Dic146—22no—
326Dic146—22no—
327Dic146—48no—
328Dic146—42no—
329Dic146—48no—
330C8×C73—22no—
331C8×C73—22no—
332#10596831—22no—
333#10596831—22no—
334C22×C73—42no—
335C22×C73—42no—
336C22×C73—42no—
337C22×C73—84no—
338C22×C73#54812yes—
339C22×C73C2×AGL(1,ℤ/8)12yes—
340C22×C73#57812yes—
341C22×C73C23×D411yescharacteristic
342C2×D73—24no—
343C2×D73—48no—
344C2×D73—42no—
345C2×D73—42no—
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—42no—
349C4×C73—42no—
350C4×C73—42no—
351C4×C73#54812yes—
352C4×C73C22×#4111yescharacteristic
353C4×C73C2×2−1+411yescharacteristic
354Dic73—22no—
355Dic73—22no—
356Dic73—22no—
357Dic73—42no—
358Dic73—42no—
359Dic73—42no—
360Dic73C2×AGL(1,ℤ/8)14yes—
361C2×#3367—731nomaximal, Sylow
362C2×C73—82no—
363C2×C73#336714yescomplemented
364C2×C73C2×#54811yescharacteristic
365C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
366C2×C73C2×#57811yescharacteristic
367D73—44no—
368C2×#556—731no—
369C2×D4×Q8—731no—
370#3367—7316no—
371C2×#489—731no—
372C2×#489D7311yescharacteristic, complemented
373C2×#487—731no—
374C2×#477—731no—
375C2×#477—731no—
376C2×#474—731no—
377C2×#463—731no—
378C2×#463—731no—
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×SD16—731no—
388C22×D8—731no—
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⋊Q8C2×D7311yescharacteristic
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×D4—731no—
412C2×#117—1461no—
413#489—738no—
414#489C2×D7318yescomplemented
415#487—738no—
416#477—738no—
417#477—738no—
418#474—738no—
419#463—738no—
420#463—738no—
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⋊C8—731no—
432C2×#103—731no—
433C2×#103—731no—
434C2×#103—731no—
435C2×#103—731no—
436C2×#103C2×D7311yescharacteristic
437C2×#103C2×D7311yescharacteristic
438C2×#102—731no—
439C2×#102—731no—
440C2×#102C2×D7311yescharacteristic
441C2×#102C2×D7311yescharacteristic
442C2×#97—731no—
443C2×#97C2×D7311yescharacteristic
444C2×C4×C8—731no—
445C22×Q8—21no—
446C22×Q8—2928no—
447C22×Q8—731no—
448C22×Q8—731no—
449C22×Q8—1461no—
450C22×Q8—1461no—
451C22×Q8—1468no—
452C22×Q8C22×D7311yescharacteristic
453C22×D4—731no—
454C22×D4C22×D7311yescharacteristic
455C23×C4—1461no—
456C23×C4—1461no—
457C23×C4—1461no—
458C23×C4—1461no—
459C2×SD16—734no—
460C2×SD16—734no—
461C2×SD16—1464no—
462C2×SD16—1464no—
463C2×D8—734no—
464C2×D8—1464no—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8C22×D7311yescharacteristic
468C22×C8C22×D7311yescharacteristic
469C4⋊Q8—22no—
470C4⋊Q8—734no—
471C4⋊Q8—734no—
472C4⋊Q8—734no—
473C4⋊Q8—1462no—
474C4⋊Q8—1462no—
475C4⋊Q8—1462no—
476C4⋊Q8C22×D7314yes—
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—734no—
494C4×D4—734no—
495C4×D4—734no—
496C4×D4—734no—
497C4×D4—1462no—
498C4×D4—1462no—
499C4×D4—1462no—
500C4×D4—1462no—
501#117—1468no—
502C2×C4⋊C4—21no—
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⋊C4C22×D7311yescharacteristic
515C2×C4⋊C4C22×D7311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—1461no—
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⋊C8—734no—
535#103—734no—
536#103—734no—
537#103—734no—
538#103—734no—
539#103C22×D7314yes—
540#103C22×D7314yes—
541#102—734no—
542#102—734no—
543#102C22×D7314yes—
544#102C22×D7314yes—
545#97—734no—
546#97C22×D7314yes—
547C4×C8—734no—
548C24—21no—
549C24—1461no—
550C2×Q8—21no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—44no—
555C2×Q8—2924no—
556C2×Q8—2924no—
557C2×Q8—29232no—
558C2×Q8—734no—
559C2×Q8—732no—
560C2×Q8—1464no—
561C2×Q8—1464no—
562C2×Q8—1464no—
563C2×Q8—1462no—
564C2×Q8—1462no—
565C2×Q8—1461no—
566C2×Q8C23×D7312yes—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—734no—
571C2×D4—732no—
572C2×D4—1461no—
573C2×D4—1462no—
574C2×D4C23×D7312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—2924no—
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—1464no—
593C22×C4D4×D7311yescharacteristic
594C22×C4D4×D7311yescharacteristic
595C22×C4C23×D7311yescharacteristic
596SD16—1468no—
597SD16—1468no—
598D8—1468no—
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—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—734no—
611C4⋊C4—734no—
612C4⋊C4—734no—
613C4⋊C4—732no—
614C4⋊C4—732no—
615C4⋊C4—1464no—
616C4⋊C4—1464no—
617C4⋊C4—1464no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1464no—
621C4⋊C4—1461no—
622C4⋊C4—1461no—
623C4⋊C4C23×D7312yes—
624C4⋊C4C23×D7312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—1464no—
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—42no—
643C23—42no—
644C23—42no—
645C23—2922no—
646C23—2922no—
647C23—1462no—
648C23—1464no—
649C23C2×D4×D7311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—48no—
653Q8—42no—
654Q8—2928no—
655Q8—2928no—
656Q8—2922no—
657Q8—1468no—
658Q8—1462no—
659Q8—1462no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—734no—
664D4—1462no—
665D4—1464no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—2928no—
675C2×C4—2928no—
676C2×C4—2928no—
677C2×C4—2922no—
678C2×C4—2922no—
679C2×C4—2922no—
680C2×C4—2928no—
681C2×C4—732no—
682C2×C4—734no—
683C2×C4—732no—
684C2×C4—732no—
685C2×C4—732no—
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×C4#41×D7312yes—
696C2×C4#1455663812yes—
697C2×C4C24×D7311yescharacteristic
698C8—22no—
699C8—22no—
700C8—1462no—
701C8—1462no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—2922no—
707C22—2928no—
708C22—2922no—
709C22—1464no—
710C22#1798924512yes—
711C22AGL(1,ℤ/8)×D7312yes—
712C22#1798940312yes—
713C22C22×D4×D7311yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—2922no—
720C4—2922no—
721C4—2922no—
722C4—734no—
723C4—1462no—
724C4—1462no—
725C4—1462no—
726C4#1798924512yes—
727C4C2×#41×D7311yescharacteristic
728C4C2×#1455663811yescharacteristic
729C2—82no—
730C2—2924no—
731C2#2262264614yesdirect product factor
732C2C2×#1798924511yescharacteristic
733C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
734C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#489×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924013C22
hypercenterC2×#489D73
hypocenterC73C2×#3367
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#17989306C2semidirect
2. C2×#17989252C2semidirect
3. #22622646C2direct (N × H)
4. C2×#17988945C2semidirect
5. C2×#17988936C2semidirect
6. C2×#17988880C2semidirect
7. C2×#17988879C2semidirect
8. C2×#17988865C2semidirect
11. C2×#17988791C2semidirect
12. C2×#17988715C2semidirect
13. C2×#17988690C2semidirect
14. C2×#17988689C2semidirect
16. C2×#489×C73C2semidirect
22. #17989306C22semidirect
24. #17989252C22semidirect
43. #17988945C22semidirect
44. #17988936C22semidirect
45. #17988880C22semidirect
46. #17988879C22semidirect
47. #17988865C22semidirect
50. #17988791C22semidirect
51. #17988715C22semidirect
52. #17988690C22semidirect
53. #17988689C22semidirect
71. #489×C73C22semidirect
363. C2×C73#3367semidirect
372. C2×#489D73semidirect
384. C73C2×#3367semidirect
414. #489C2×D73semidirect
731. C2#22622646direct (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×#179892522
#226226462
C2×#179889452
C2×#179889362
C2×#179888802
C2×#179888792
C2×#179888652
C2×#179888012
C2×#179887992
C2×#179887912
C2×#179887152
C2×#179886902
C2×#179886892
C2×#179886672
C2×#489×C732
C2×#336773