Finite Group Databasebeta

← C2×#22622686 #33965735

Subgroups — C2×#22622686 #33965735

Order 18688.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989322C211yesmaximal, characteristic, complemented
2C2×#17989297C211yesmaximal, characteristic, complemented
3#22622686C2116yesmaximal, direct product factor
4C2×#17988952C211yesmaximal, characteristic, complemented
5C2×#17988947C211yesmaximal, characteristic, complemented
6C2×#17988942C211yesmaximal, characteristic, complemented
7C2×#17988895C211yesmaximal, characteristic, complemented
8C2×#17988888C211yesmaximal, characteristic, complemented
9C2×#17988868C211yesmaximal, characteristic, complemented
10C2×#17988803C211yesmaximal, characteristic, complemented
11C2×#17988803C211yesmaximal, characteristic, complemented
12C2×#17988783C211yesmaximal, characteristic
13C2×#17988700C211yesmaximal, characteristic, complemented
14C2×#17988689C211yesmaximal, characteristic, complemented
15C2×C4×D584C211yesmaximal, characteristic, complemented
16C2×#446×C73C211yesmaximal, characteristic, complemented
17C22×#11924017C2211yescharacteristic
18C22×D584C2211yescharacteristic
19C22×D584C2211yescharacteristic
20#17989322—24no—
21#17989322C2218yescomplemented
22#17989297—24no—
23#17989297C2218yescomplemented
24C2×#14556591C2211yescharacteristic
25C2×#14556588C2211yescharacteristic
26C2×#14556583C2211yescharacteristic
27C2×#14556583C2211yescharacteristic
28C2×#14556580—21no—
29C2×#14556579C2211yescharacteristic
30C2×#14556579C2211yescharacteristic
31C2×#14556576—21no—
32C2×#14556576—21no—
33C2×#14556569—21no—
34C2×#14556569—21no—
35C2×#14556567—21no—
36C2×C4×Dic146C2211yescharacteristic
37C2×C4×D292C2211yescharacteristic
38C2×C4×D292C2211yescharacteristic
39C2×C4×D292C2211yescharacteristic
40C2×C4×D292C2211yescharacteristic
41C2×C4×D292C2211yescharacteristic
42C2×#14556553—21no—
43C2×C4⋊C4×D73—21no—
44#17988952C2218yescomplemented
45#17988947C2218yescomplemented
46#17988942C2218yescomplemented
47#17988895C2218yescomplemented
48#17988888C2218yescomplemented
49#17988868C2218yescomplemented
50#17988803C2218yescomplemented
51#17988803C2218yescomplemented
52#17988783C2218yes—
53#17988700C2218yescomplemented
54#17988689C2218yescomplemented
55C4×D584C2218yescomplemented
56C2×#14556525C2211yescharacteristic
57C2×#14556525C2211yescharacteristic
58C2×#14556523C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
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×D292—21no—
80C22×D292—21no—
81C22×D292C2311yescharacteristic
82C22×D292C2311yescharacteristic
83C22×D292C2311yescharacteristic
84C22×C4×D73—21no—
85C22×C4×D73—21no—
86C22×C4×D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73—21no—
89C2×#11924017—24no—
90C2×#11924017C2314yes—
91C2×D584—24no—
92C2×D584—24no—
93C2×D584C2314yes—
94C2×D584C2314yes—
95#14556591—22no—
96#14556591C2314yes—
97#14556588—22no—
98#14556588C2314yes—
99#14556583—22no—
100#14556583—22no—
101#14556583C2314yes—
102#14556583C2314yes—
103#14556580—28no—
104#14556579—22no—
105#14556579—22no—
106#14556579C2314yes—
107#14556579C2314yes—
108#14556576—28no—
109#14556576—28no—
110#14556569—28no—
111#14556569—28no—
112#14556567—28no—
113C4×Dic146—22no—
114C4×Dic146C2314yes—
115C4×D292—22no—
116C4×D292—22no—
117C4×D292—22no—
118C4×D292—22no—
119C4×D292—22no—
120C4×D292C2314yes—
121C4×D292C2314yes—
122C4×D292C2314yes—
123C4×D292C2314yes—
124C4×D292C2314yes—
125#14556553—28no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×C4⋊Dic73C2311yescharacteristic
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×#11924005—21no—
146C2×C4×Dic73—21no—
147#14556525C2314yes—
148#14556525C2314yes—
149#14556523C2314yes—
150#14556516C2314yes—
151#14556516C2314yes—
152#14556516C2314yes—
153#14556513C2314yes—
154#14556513C2314yes—
155#14556513C2314yes—
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—
181C23×D73—21no—
182C2×Dic146—22no—
183C2×Dic146—22no—
184C2×Dic146—21no—
185C2×Dic146—24no—
186C2×Dic146—82no—
187C2×Dic146C2412yes—
188C2×D292—21no—
189C2×D292—22no—
190C2×D292—22no—
191C2×D292—22no—
192C2×D292—22no—
193C2×D292—22no—
194C2×D292—24no—
195C2×D292—21no—
196C2×D292—21no—
197C2×D292—24no—
198C2×D292—44no—
199C2×D292—82no—
200C2×D292#4114yes—
201C2×D292C2412yes—
202C2×D292C2412yes—
203C2×D292C2412yes—
204C22×Dic73—21no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C2×C4×D73—24no—
210C2×C4×D73—24no—
211C2×C4×D73—24no—
212C2×C4×D73—24no—
213C2×C4×D73—24no—
214C2×C4×D73—44no—
215C2×C4×D73—82no—
216C2×C4×D73—82no—
217C2×C4×D73—82no—
218C2×C4×D73—82no—
219#11924017—28no—
220D584—28no—
221D584—28no—
222C4⋊Dic73—24no—
223C4⋊Dic73—21no—
224C4⋊Dic73—21no—
225C4⋊Dic73—21no—
226C4⋊Dic73—21no—
227C4⋊Dic73C2412yes—
228C4⋊Dic73C2412yes—
229C4⋊Dic73C2412yes—
230C4⋊Dic73C2412yes—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005—24no—
242#11924005—24no—
243#11924005—24no—
244#11924005—24no—
245C4×Dic73—24no—
246C2×Q8×C73—42no—
247C2×Q8×C73C2×D414yes—
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2411yescharacteristic
255C2×C8×C73—22no—
256C2×C8×C73—22no—
257C2×C8×C73—22no—
258C2×C8×C73—22no—
259C2×C8×C73C2412yes—
260C2×C8×C73C2412yes—
261C2×C8×C73C2412yes—
262C2×C8×C73C2412yes—
263C4⋊C4×C73C2×D414yes—
264C4⋊C4×C73C2×D414yes—
265C4⋊C4×C73C2×D414yes—
266C42×C73C2×D412yes—
267C42×C73C2×D412yes—
268C42×C73C2×D412yes—
269C42×C73C2412yes—
270C42×C73C2412yes—
271C42×C73C2412yes—
272C23×C73C22×D411yescharacteristic
273C22×D73—24no—
274C22×D73—22no—
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—42no—
278C22×D73—42no—
279C22×D73—42no—
280C22×D73—42no—
281C22×D73—42no—
282C22×D73—42no—
283C22×D73—42no—
284C22×D73—42no—
285Q8×C73—44no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73C22×D412yes—
293C2×C4×C73C22×D412yes—
294C2×C4×C73C22×D412yes—
295C2×C4×C73C22×D412yes—
296C2×C4×C73C22×D412yes—
297C2×C4×C73C22×D412yes—
298C2×C4×C73C22×D411yescharacteristic
299C2×C4×C73C2×#4112yes—
300C2×C4×C732−1+412yes—
301C2×C4×C73C2511yescharacteristic
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—42no—
308C2×Dic73—42no—
309C2×Dic73—42no—
310C2×Dic73—42no—
311C2×Dic73—42no—
312D292—24no—
313D292—22no—
314D292—22no—
315D292—22no—
316D292—22no—
317D292—22no—
318D292—48no—
319D292—42no—
320D292—42no—
321D292—84no—
322D292C2×#4114yes—
323C4×D73—48no—
324C4×D73—84no—
325C4×D73—84no—
326C4×D73—84no—
327C4×D73—84no—
328Dic146—22no—
329Dic146—22no—
330Dic146—42no—
331Dic146—84no—
332C8×C73—22no—
333C8×C73—22no—
334C8×C73—22no—
335C8×C73—22no—
336C22×C73#54812yes—
337C22×C73#57512yes—
338C22×C73#57612yes—
339C22×C73C23×D411yescharacteristic
340C2×D73—24no—
341C2×D73—48no—
342C2×D73—42no—
343C2×D73—42no—
344C2×D73—42no—
345C2×D73—42no—
346C2×D73—42no—
347C2×D73—42no—
348C2×D73—42no—
349C2×D73—42no—
350C2×D73—84no—
351C2×D73—84no—
352C4×C73—22no—
353C4×C73—22no—
354C4×C73—22no—
355C4×C73—22no—
356C4×C73—22no—
357C4×C73—22no—
358C4×C73#54812yes—
359C4×C73C22×#4111yescharacteristic
360C4×C73C2×2−1+411yescharacteristic
361Dic73—42no—
362Dic73—42no—
363Dic73—42no—
364Dic73—42no—
365Dic73—42no—
366C2×#3370—731nomaximal, Sylow
367C2×C73#337014yescomplemented
368C2×C73C2×#54811yescharacteristic
369C2×C73C2×#57511yescharacteristic
370C2×C73C2×#57611yescharacteristic
371D73—44no—
372D73—82no—
373D73—82no—
374C2×#559—731no—
375C2×#554—731no—
376#3370—7316no—
377C2×#490—731no—
378C2×#489—731no—
379C2×#488—731no—
380C2×#479—731no—
381C2×#478—731no—
382C2×#474—731no—
383C2×#463—731no—
384C2×#463—731no—
385C2×#459—731no—
386C2×#446D7311yescharacteristic, complemented
387C2×#442—731no—
388C2×#440—731no—
389C2×C4×D8—731no—
390C73C2×#337011yescharacteristic, complemented, Sylow
391C22×SD16—731no—
392C22×D8—731no—
393C22×D8—731no—
394#559—738no—
395#559—1464no—
396#554—738no—
397#554—1464no—
398C2×C4⋊Q8—731no—
399C2×#127—731no—
400C2×#125—731no—
401C2×#125—731no—
402C2×#124—731no—
403C2×#124—731no—
404C2×#124—1461no—
405C2×#123—1461no—
406C2×#123—1461no—
407C2×C22⋊Q8—1461no—
408C2×C22⋊Q8—1461no—
409C2×C22⋊Q8—1461no—
410C2×C4×Q8—731no—
411C2×C4×Q8C2×D7311yescharacteristic
412C2×C4×D4—731no—
413C2×C4×D4—731no—
414C2×C4×D4—731no—
415C2×C4×D4—731no—
416C2×C4×D4—731no—
417C2×C4×D4—1461no—
418C22×C4⋊C4—1461no—
419#490—738no—
420#489—738no—
421#488—738no—
422#479—738no—
423#478—738no—
424#474—738no—
425#463—738no—
426#463—738no—
427#459—738no—
428#446C2×D7318yescomplemented
429#442—738no—
430#440—738no—
431C4×D8—738no—
432C2×#107—731no—
433C2×#107—731no—
434C2×#106—731no—
435C2×C4⋊C8C2×D7311yescharacteristic
436C2×C4⋊C8C2×D7311yescharacteristic
437C2×C4⋊C8C2×D7311yescharacteristic
438C2×#103—731no—
439C2×#103—731no—
440C2×#103—731no—
441C2×#102—731no—
442C2×#102—731no—
443C2×#102—731no—
444C2×#102—731no—
445C2×#102—731no—
446C2×#102—731no—
447C2×#102—731no—
448C2×#97C2×D7311yescharacteristic
449C2×#97C2×D7311yescharacteristic
450C2×C4×C8C2×D7311yescharacteristic
451C22×Q8—731no—
452C22×Q8—1461no—
453C22×Q8D29211yescharacteristic
454C22×D4—731no—
455C22×D4—731no—
456C22×D4—731no—
457C22×D4—1461no—
458C22×D4—1461no—
459C23×C4—1461no—
460C23×C4—1461no—
461C23×C4—1461no—
462C23×C4—1461no—
463C23×C4—1461no—
464C2×SD16—734no—
465C2×SD16—1464no—
466C2×D8—734no—
467C2×D8—734no—
468C2×D8—1464no—
469C2×D8—1464no—
470C22×C8C22×D7311yescharacteristic
471C22×C8C22×D7311yescharacteristic
472C22×C8C22×D7311yescharacteristic
473C22×C8C22×D7311yescharacteristic
474C4⋊Q8—734no—
475C4⋊Q8—1462no—
476#127—734no—
477#127—1462no—
478#125—734no—
479#125—734no—
480#125—1462no—
481#125—1462no—
482#124—734no—
483#124—734no—
484#124—1468no—
485#124—1462no—
486#124—1462no—
487#123—1468no—
488#123—1468no—
489C22⋊Q8—1468no—
490C22⋊Q8—1468no—
491C22⋊Q8—1468no—
492C4×Q8—734no—
493C4×Q8—1462no—
494C4×Q8D29214yes—
495C4×Q8C22×D7314yes—
496C4×D4—734no—
497C4×D4—734no—
498C4×D4—734no—
499C4×D4—734no—
500C4×D4—734no—
501C4×D4—1468no—
502C4×D4—1462no—
503C4×D4—1462no—
504C4×D4—1462no—
505C4×D4—1462no—
506C4×D4—1462no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—731no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1468no—
518C2×C4⋊C4D29211yescharacteristic
519C2×C4⋊C4D29211yescharacteristic
520C2×C4⋊C4D29211yescharacteristic
521C2×C22⋊C4—1461no—
522C2×C22⋊C4—1461no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C22⋊C4—1461no—
529C2×C22⋊C4—1461no—
530C2×C42—1461no—
531C2×C42C22×D7311yescharacteristic
532C2×C42C22×D7311yescharacteristic
533C2×C42C22×D7311yescharacteristic
534#107—734no—
535#107—734no—
536#106—734no—
537C4⋊C8C22×D7314yes—
538C4⋊C8C22×D7314yes—
539C4⋊C8C22×D7314yes—
540#103—734no—
541#103—734no—
542#103—734no—
543#102—734no—
544#102—734no—
545#102—734no—
546#102—734no—
547#102—734no—
548#102—734no—
549#102—734no—
550#97C22×D7314yes—
551#97C22×D7314yes—
552C4×C8C22×D7314yes—
553C24—1461no—
554C24—1461no—
555C24—1461no—
556C2×Q8—42no—
557C2×Q8—5842no—
558C2×Q8—732no—
559C2×Q8—1462no—
560C2×Q8—1462no—
561C2×Q8—1461no—
562C2×Q8—1464no—
563C2×Q8C2×D29214yes—
564C2×D4—2924no—
565C2×D4—5842no—
566C2×D4—734no—
567C2×D4—732no—
568C2×D4—732no—
569C2×D4—732no—
570C2×D4—1464no—
571C2×D4—1461no—
572C2×D4—1461no—
573C2×D4—1464no—
574C2×D4—1461no—
575C2×D4—1462no—
576C2×D4—1462no—
577C2×D4—1462no—
578C2×D4—1462no—
579C2×D4—1462no—
580C22×C4—2924no—
581C22×C4—5842no—
582C22×C4—5842no—
583C22×C4—5842no—
584C22×C4—5842no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1464no—
591C22×C4—1464no—
592C22×C4—1464no—
593C22×C4—1464no—
594C22×C4—1464no—
595C22×C4C2×D29211yescharacteristic
596C22×C4C2×D29211yescharacteristic
597C22×C4C2×D29211yescharacteristic
598C22×C4C2×D29211yescharacteristic
599C22×C4C2×D29211yescharacteristic
600C22×C4C2×D29211yescharacteristic
601C22×C4C23×D7311yescharacteristic
602SD16—1468no—
603D8—1468no—
604D8—1468no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8C23×D7312yes—
610C2×C8C23×D7312yes—
611C2×C8C23×D7312yes—
612C2×C8C23×D7312yes—
613C4⋊C4—732no—
614C4⋊C4—732no—
615C4⋊C4—732no—
616C4⋊C4—732no—
617C4⋊C4—1464no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1464no—
621C4⋊C4—1464no—
622C4⋊C4—1461no—
623C4⋊C4—1461no—
624C4⋊C4—1461no—
625C4⋊C4—1461no—
626C4⋊C4—1464no—
627C4⋊C4C2×D29214yes—
628C4⋊C4C2×D29214yes—
629C4⋊C4C2×D29214yes—
630C22⋊C4—1464no—
631C22⋊C4—1464no—
632C22⋊C4—1464no—
633C22⋊C4—1464no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C42—1464no—
640C42C2×D29212yes—
641C42C2×D29212yes—
642C42C2×D29212yes—
643C42C23×D7312yes—
644C42C23×D7312yes—
645C42C23×D7312yes—
646C23—2922no—
647C23—2922no—
648C23—2922no—
649C23—2922no—
650C23—2922no—
651C23—2922no—
652C23—2922no—
653C23—2922no—
654C23—1462no—
655C23—1462no—
656C23—1462no—
657C23—1464no—
658C23C22×D29211yescharacteristic
659Q8—44no—
660Q8—2922no—
661Q8—5844no—
662Q8—1462no—
663Q8—1462no—
664D4—2928no—
665D4—2922no—
666D4—2922no—
667D4—5844no—
668D4—734no—
669D4—1462no—
670D4—1462no—
671D4—1462no—
672D4—1462no—
673D4—1462no—
674D4—1464no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—2928no—
682C2×C4—2922no—
683C2×C4—2922no—
684C2×C4—2922no—
685C2×C4—2922no—
686C2×C4—2922no—
687C2×C4—5844no—
688C2×C4—5844no—
689C2×C4—5844no—
690C2×C4—5844no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4C22×D29212yes—
697C2×C4C22×D29212yes—
698C2×C4C22×D29212yes—
699C2×C4C22×D29212yes—
700C2×C4C22×D29212yes—
701C2×C4C22×D29212yes—
702C2×C4C22×D29211yescharacteristic
703C2×C4#41×D7312yes—
704C2×C4#1455663912yes—
705C2×C4C24×D7311yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—2922no—
711C22—2922no—
712C22—2928no—
713C22—2922no—
714C22—2922no—
715C22—2922no—
716C22—2922no—
717C22—2922no—
718C22—2922no—
719C22—5844no—
720C22—5844no—
721C22—1464no—
722C22#1798924912yes—
723C22#1798938712yes—
724C22#1798939212yes—
725C22C23×D29211yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—2922no—
733C4—2922no—
734C4—2922no—
735C4—2922no—
736C4—2922no—
737C4#1798924912yes—
738C4C2×#41×D7311yescharacteristic
739C4C2×#1455663911yescharacteristic
740C2—2924no—
741C2—5842no—
742C2—5842no—
743C2#2262268614yesdirect product factor
744C2C2×#1798924911yescharacteristic
745C2C2×#1798938711yescharacteristic
746C2C2×#1798939211yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#446×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988783C2
hypercenterC2×#446D73
hypocenterC73C2×#3370
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×#17989322C2semidirect
2. C2×#17989297C2semidirect
3. #22622686C2direct (N × H)
4. C2×#17988952C2semidirect
5. C2×#17988947C2semidirect
6. C2×#17988942C2semidirect
7. C2×#17988895C2semidirect
8. C2×#17988888C2semidirect
9. C2×#17988868C2semidirect
10. C2×#17988803C2semidirect
11. C2×#17988803C2semidirect
13. C2×#17988700C2semidirect
14. C2×#17988689C2semidirect
15. C2×C4×D584C2semidirect
16. C2×#446×C73C2semidirect
21. #17989322C22semidirect
23. #17989297C22semidirect
44. #17988952C22semidirect
45. #17988947C22semidirect
46. #17988942C22semidirect
47. #17988895C22semidirect
48. #17988888C22semidirect
49. #17988868C22semidirect
50. #17988803C22semidirect
51. #17988803C22semidirect
53. #17988700C22semidirect
54. #17988689C22semidirect
55. C4×D584C22semidirect
70. #446×C73C22semidirect
367. C2×C73#3370semidirect
386. C2×#446D73semidirect
390. C73C2×#3370semidirect
428. #446C2×D73semidirect
743. C2#22622686direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893222
C2×#179892972
#226226862
C2×#179889522
C2×#179889472
C2×#179889422
C2×#179888952
C2×#179888882
C2×#179888682
C2×#179888032
C2×#179887832
C2×#179887002
C2×#179886892
C2×C4×D5842
C2×#446×C732
C2×#337073