Finite Group Databasebeta

← C2×#22618809 #33950142

Subgroups — C2×#22618809 #33950142

Order 18688.

2806 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556612C211yesmaximal, characteristic
2C2×#17989069C211yesmaximal, characteristic, complemented
3C2×#17989066C211yesmaximal, characteristic, complemented
4#22618809C2116yesmaximal, direct product factor
5C2×#17988697C211yesmaximal, characteristic, complemented
6C2×#17988696C211yesmaximal, characteristic, complemented
7C2×#17988692C211yesmaximal, characteristic, complemented
8C2×#17988691C211yesmaximal, characteristic, complemented
9C2×C4×#11924017C211yesmaximal, characteristic, complemented
10C2×SD16×Dic73C211yesmaximal, characteristic, complemented
11C2×#17988674C211yesmaximal, characteristic, complemented
12C2×#106×D73C211yesmaximal, characteristic, complemented
13C2×#17988587C211yesmaximal, characteristic, complemented
14C2×#17988585C211yesmaximal, characteristic, complemented
15C2×#17988541C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924027C2211yescharacteristic
19C2×#14556612C4116yescomplemented
20C2×#14556612C2218yes—
21C22×#11924018C2211yescharacteristic
22C22×#11924017C2211yescharacteristic
23C22×#11924013C2211yescharacteristic
24C22×#11924011C2211yescharacteristic
25C22×C8×D73C2211yescharacteristic
26#17989069—24no—
27#17989069C2218yescomplemented
28#17989066—24no—
29#17989066C2218yescomplemented
30C2×Q8×Dic73C2211yescharacteristic
31C2×C4×Dic146C2211yescharacteristic
32C2×#14556556C2211yescharacteristic
33C2×C4×D292—21no—
34C2×C4×D292C2211yescharacteristic
35C2×D4×Dic73C2211yescharacteristic
36C2×#14556553—21no—
37C2×#14556553C2211yescharacteristic
38C2×C4×C22⋊D73—21no—
39C2×#14556551—21no—
40C2×#14556548—21no—
41C2×#14556548C2211yescharacteristic
42C2×#14556547—21no—
43C22×#11924007—21no—
44C2×C4⋊C4×D73—21no—
45C2×C4⋊C4×D73C2211yescharacteristic
46C2×C4⋊C4×D73C2211yescharacteristic
47#17988697C2218yescomplemented
48#17988696C2218yescomplemented
49#17988692C2218yescomplemented
50#17988691C2218yescomplemented
51C4×#11924017C2218yescomplemented
52SD16×Dic73C2218yescomplemented
53#17988674C2218yescomplemented
54C2×#14556523C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57#106×D73C2218yescomplemented
58#17988587C2218yescomplemented
59#17988585C2218yescomplemented
60C2×#14556516C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66#17988541C2218yescomplemented
67C2×#14556502C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C2×C8×Dic73C2211yescharacteristic
70C22×SD16×C73C2211yescharacteristic
71C2×C4×Q8×C73C2211yescharacteristic
72C2×C4×D4×C73C2211yescharacteristic
73C4×SD16×C73C2218yescomplemented
74C2×#106×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×C4×C8×C73C2211yescharacteristic
78C2×#11924029—22no—
79C2×#11924029—24no—
80C2×#11924029C2×C418yescomplemented
81C2×#11924029C2314yes—
82C2×#11924027—22no—
83C2×#11924027—24no—
84C2×#11924027C2×C418yescomplemented
85C2×#11924027C2314yes—
86C22×Dic146C2311yescharacteristic
87C22×D292—21no—
88C22×D292C2311yescharacteristic
89C22×C22⋊D73—21no—
90C23×Dic73—21no—
91C23×Dic73—21no—
92C22×C4×D73—21no—
93C22×C4×D73—21no—
94C22×C4×D73—21no—
95C22×C4×D73—21no—
96C22×C4×D73—21no—
97C22×C4×D73C2311yescharacteristic
98#14556612C2×C4164yescomplemented
99C2×#11924018C2×C418yescomplemented
100C2×#11924018C2314yes—
101C2×#11924017C2×C418yescomplemented
102C2×#11924017C2314yes—
103C2×#11924013C2×C418yescomplemented
104C2×#11924013C2314yes—
105C2×#11924011—24no—
106C2×#11924011C2314yes—
107C22×#10596831C2311yescharacteristic
108C22×#10596831C2311yescharacteristic
109C2×C8×D73C2×C418yescomplemented
110C2×C8×D73C2314yes—
111Q8×Dic73—22no—
112Q8×Dic73C2314yes—
113C4×Dic146—22no—
114C4×Dic146C2314yes—
115#14556556—22no—
116#14556556C2314yes—
117C4×D292—28no—
118C4×D292—22no—
119C4×D292C2314yes—
120D4×Dic73—22no—
121D4×Dic73C2314yes—
122#14556553—28no—
123#14556553—22no—
124#14556553C2314yes—
125C4×C22⋊D73—28no—
126#14556551—28no—
127#14556548—28no—
128#14556548D414yes—
129#14556548C2314yes—
130#14556547—28no—
131C2×C4⋊Dic73—21no—
132C2×C4⋊Dic73C2311yescharacteristic
133C2×C4⋊Dic73C2311yescharacteristic
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—28no—
138C2×#11924007—21no—
139C2×#11924007D411yescharacteristic
140C2×#11924007D411yescharacteristic
141C4⋊C4×D73—22no—
142C4⋊C4×D73—22no—
143C4⋊C4×D73—28no—
144C4⋊C4×D73C2314yes—
145C4⋊C4×D73C2314yes—
146C2×C22⋊Dic73—21no—
147C2×#11924005—21no—
148C2×#11924005—21no—
149C2×#11924005D411yescharacteristic
150C2×#11924005D411yescharacteristic
151C2×C4×Dic73—21no—
152C2×C4×Dic73—21no—
153C2×C4×Dic73—21no—
154C2×C4×Dic73C2311yescharacteristic
155#14556523C2314yes—
156#14556522C2314yes—
157#14556522C2314yes—
158#14556516C2314yes—
159#14556515C2314yes—
160#14556514C2314yes—
161#14556513C2314yes—
162#14556512C2314yes—
163#14556511C2314yes—
164#14556502C2314yes—
165#14556501C2314yes—
166C8×Dic73C2314yes—
167C22×Q8×C73C2311yescharacteristic
168C22×D4×C73C2311yescharacteristic
169C23×C4×C73—21no—
170C2×SD16×C73C2×C418yescomplemented
171C2×SD16×C73C2314yes—
172C22×C8×C73C2311yescharacteristic
173C22×C8×C73C2311yescharacteristic
174C4×Q8×C73—22no—
175C4×Q8×C73C2314yes—
176C4×D4×C73—22no—
177C4×D4×C73C2314yes—
178C2×C4⋊C4×C73—21no—
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C4⋊C4×C73C2311yescharacteristic
181C2×C22⋊C4×C73—21no—
182C2×C42×C73—21no—
183C2×C42×C73C2311yescharacteristic
184#106×C73C2314yes—
185#103×C73C2314yes—
186#102×C73C2314yes—
187C4×C8×C73C2314yes—
188C23×D73—21no—
189C23×D73C2×D411yescharacteristic
190#11924029—216no—
191#11924029—28no—
192#11924029C22×C4116yescomplemented
193#11924027—216no—
194#11924027—28no—
195#11924027C22×C4116yescomplemented
196C2×Dic146—21no—
197C2×Dic146—22no—
198C2×Dic146C22×C414yes—
199C2×Dic146C2412yes—
200C2×D292—28no—
201C2×D292—24no—
202C2×D292—21no—
203C2×D292—22no—
204C2×D292C22×C414yes—
205C2×D292C2412yes—
206C2×C22⋊D73—28no—
207C2×C22⋊D73—24no—
208C22×Dic73—21no—
209C22×Dic73—28no—
210C22×Dic73—24no—
211C22×Dic73—21no—
212C22×Dic73—21no—
213C22×Dic73—24no—
214C22×Dic73—82no—
215C22×Dic73C2×D411yescharacteristic
216C22×Dic73C2×D411yescharacteristic
217C22×Dic73C2×D411yescharacteristic
218C2×C4×D73—28no—
219C2×C4×D73—24no—
220C2×C4×D73—24no—
221C2×C4×D73—24no—
222C2×C4×D73—24no—
223C2×C4×D73—24no—
224C2×C4×D73—82no—
225C2×C4×D73—82no—
226C2×C4×D73—82no—
227C2×C4×D73—82no—
228C2×C4×D73C22×C414yes—
229C2×C4×D73C2×D412yes—
230C2×C4×D73#4114yes—
231C2×C4×D73C2412yes—
232#11924018C22×C4116yescomplemented
233#11924017C22×C4116yescomplemented
234#11924013C22×C4116yescomplemented
235#11924011—28no—
236C2×#10596831—22no—
237C2×#10596831C22×C414yes—
238C2×#10596831C2412yes—
239C2×#10596831C2412yes—
240C8×D73C22×C4116yescomplemented
241C4⋊Dic73—21no—
242C4⋊Dic73—21no—
243C4⋊Dic73—24no—
244C4⋊Dic73C2412yes—
245C4⋊Dic73C2412yes—
246#11924007—24no—
247#11924007—24no—
248#11924007—24no—
249#11924007—24no—
250#11924007C2×D414yes—
251#11924007C2×D414yes—
252C22⋊Dic73—24no—
253#11924005—24no—
254#11924005—24no—
255#11924005C2×D414yes—
256#11924005C2×D414yes—
257C4×Dic73—24no—
258C4×Dic73—24no—
259C4×Dic73—24no—
260C4×Dic73C2×D412yes—
261C4×Dic73C2412yes—
262C24×C73—21no—
263C2×Q8×C73—21no—
264C2×Q8×C73—22no—
265C2×Q8×C73C22×C414yes—
266C2×Q8×C73C2412yes—
267C2×D4×C73—21no—
268C2×D4×C73—22no—
269C2×D4×C73C22×C414yes—
270C2×D4×C73C2412yes—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—24no—
275C22×C4×C73—82no—
276C22×C4×C73C2×D411yescharacteristic
277C22×C4×C73C2×D411yescharacteristic
278C22×C4×C73C2411yescharacteristic
279SD16×C73C22×C4116yescomplemented
280C2×C8×C73—22no—
281C2×C8×C73C22×C414yes—
282C2×C8×C73C2412yes—
283C2×C8×C73C2412yes—
284C4⋊C4×C73—24no—
285C4⋊C4×C73—21no—
286C4⋊C4×C73—21no—
287C4⋊C4×C73C2412yes—
288C4⋊C4×C73C2412yes—
289C22⋊C4×C73—24no—
290C42×C73—24no—
291C42×C73C2×D412yes—
292C42×C73C2412yes—
293C23×C73—24no—
294C23×C73—22no—
295C23×C73—42no—
296C23×C73—42no—
297C23×C73C22×D411yescharacteristic
298C22×D73—22no—
299C22×D73—22no—
300C22×D73—24no—
301C22×D73—22no—
302C22×D73—42no—
303C22×D73—42no—
304C22×D73C4×D414yes—
305C22×D73C22×D412yes—
306Q8×C73—24no—
307Q8×C73—22no—
308Q8×C73C23×C414yes—
309D4×C73—24no—
310D4×C73—22no—
311D4×C73C23×C414yes—
312C2×C4×C73—24no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—22no—
318C2×C4×C73—42no—
319C2×C4×C73—42no—
320C2×C4×C73—84no—
321C2×C4×C73C23×C412yes—
322C2×C4×C73C22×D412yes—
323C2×C4×C73C22×D412yes—
324C2×C4×C73C22×D411yescharacteristic
325C2×C4×C73C2×#4112yes—
326C2×C4×C73C2511yescharacteristic
327C22⋊D73—216no—
328C2×Dic73—24no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—22no—
332C2×Dic73—216no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—42no—
336C2×Dic73—42no—
337C2×Dic73—84no—
338C2×Dic73C4×D414yes—
339C2×Dic73C22×D412yes—
340C2×Dic73C22×D412yes—
341C2×Dic73C22×D412yes—
342D292—216no—
343D292—24no—
344D292—22no—
345D292C23×C414yes—
346C4×D73—216no—
347C4×D73—84no—
348C4×D73—84no—
349C4×D73—84no—
350C4×D73—84no—
351C4×D73C4×D418yes—
352C4×D73C23×C414yes—
353C4×D73C2×#4114yes—
354Dic146—24no—
355Dic146—22no—
356Dic146C23×C414yes—
357C8×C73—22no—
358C8×C73C23×C414yes—
359#10596831—22no—
360#10596831C23×C414yes—
361C22×C73—24no—
362C22×C73—48no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73C2×C4×D412yes—
366C22×C73#57712yes—
367C22×C73#57712yes—
368C22×C73C23×D411yescharacteristic
369C2×D73—28no—
370C2×D73—22no—
371C2×D73—22no—
372C2×D73—24no—
373C2×D73—48no—
374C2×D73—42no—
375C2×D73—42no—
376C2×D73C2×C4×D414yes—
377C4×C73—24no—
378C4×C73—22no—
379C4×C73—22no—
380C4×C73—42no—
381C4×C73—42no—
382C4×C73C2×C4×D412yes—
383C4×C73C24×C411yescharacteristic
384C4×C73C22×#4111yescharacteristic
385Dic73—24no—
386Dic73—22no—
387Dic73—22no—
388Dic73—42no—
389Dic73—42no—
390Dic73C2×C4×D414yes—
391C2×#2952—731nomaximal, Sylow
392C2×C73—44no—
393C2×C73#295214yescomplemented
394C2×C73C22×C4×D411yescharacteristic
395C2×C73C2×#57711yescharacteristic
396C2×C73C2×#57711yescharacteristic
397D73—24no—
398D73—44no—
399C22×#135—731no—
400C2×#520—731no—
401C2×#520—731no—
402#2952—7316no—
403C2×#442—731no—
404C2×#442—731no—
405C2×#441—731no—
406C2×#441—731no—
407C2×C4×SD16—731no—
408C2×C4×SD16—731no—
409C2×C4×SD16—731no—
410C2×C4×SD16D7311yescharacteristic, complemented
411C22×#106—731no—
412C2×#417—731no—
413C2×#417—731no—
414C2×#405—731no—
415C73C2×#295211yescharacteristic, complemented, Sylow
416C22×#41—731no—
417C22×#41—731no—
418C2×#135—7316no—
419C2×#135—738no—
420C22×Q16—731no—
421C22×SD16—731no—
422C22×SD16C2×D7311yescharacteristic
423C22×D8—731no—
424C22×M16—731no—
425C23×C8—731no—
426#520—738no—
427#520—738no—
428#520—1464no—
429#520—1464no—
430C2×C4×Q8—731no—
431C2×C4×Q8—731no—
432C2×C4×Q8—731no—
433C2×C4×Q8C2×D7311yescharacteristic
434C2×C4×D4—731no—
435C2×C4×D4—731no—
436C2×C4×D4—731no—
437C2×C4×D4—1461no—
438C2×C4×D4—1461no—
439C2×C4×D4—1461no—
440C2×C4×D4—1461no—
441C2×C4×D4C2×D7311yescharacteristic
442C2×#117—731no—
443C2×#117—1461no—
444C2×#117—1461no—
445C22×C4⋊C4—731no—
446C22×C4⋊C4—731no—
447C22×C4⋊C4—1461no—
448C22×C4⋊C4—1461no—
449#442—738no—
450#442—738no—
451#441—738no—
452#441—738no—
453C4×SD16—738no—
454C4×SD16—738no—
455C4×SD16—738no—
456C4×SD16C2×D7318yescomplemented
457C2×#106—731no—
458C2×#106—731no—
459C2×#106—731no—
460C2×#106—738no—
461C2×#106C2×D7311yescharacteristic
462#417—738no—
463#417—738no—
464C2×#103—731no—
465C2×#103—731no—
466C2×#103—731no—
467C2×#103C2×D7311yescharacteristic
468C2×#102—731no—
469C2×#102—731no—
470C2×#102—731no—
471C2×#102C2×D7311yescharacteristic
472#405—738no—
473C2×#97—731no—
474C2×#97—731no—
475C2×C4×C8—731no—
476C2×C4×C8C2×D7311yescharacteristic
477C2×#41—738no—
478C2×#41—734no—
479C2×#41—738no—
480C2×#41—734no—
481C2×#41—1462no—
482C2×#41—1464no—
483C2×#41—1462no—
484C2×#41—1464no—
485C22×Q8—731no—
486C22×Q8C22×D7311yescharacteristic
487C22×D4—731no—
488C22×D4—1461no—
489C22×D4—1461no—
490C22×D4C22×D7311yescharacteristic
491C23×C4—21no—
492C23×C4—731no—
493C23×C4—1461no—
494C23×C4—1461no—
495C23×C4—1461no—
496C23×C4—1461no—
497C23×C4—1461no—
498C23×C4—1461no—
499C23×C4—1461no—
500#135—7364no—
501C2×Q16—738no—
502C2×Q16—734no—
503C2×SD16—738no—
504C2×SD16—734no—
505C2×SD16C4×D7318yescomplemented
506C2×SD16C22×D7314yes—
507C2×D8—738no—
508C2×D8—734no—
509C2×M16—734no—
510C2×M16—1464no—
511C22×C8—731no—
512C22×C8—738no—
513C22×C8—734no—
514C22×C8—731no—
515C22×C8C22×D7311yescharacteristic
516C22×C8C22×D7311yescharacteristic
517C4×Q8—22no—
518C4×Q8—734no—
519C4×Q8—734no—
520C4×Q8—734no—
521C4×Q8—1462no—
522C4×Q8—1462no—
523C4×Q8—1462no—
524C4×Q8C22×D7314yes—
525C4×D4—22no—
526C4×D4—734no—
527C4×D4—734no—
528C4×D4—734no—
529C4×D4—1468no—
530C4×D4—1462no—
531C4×D4—1462no—
532C4×D4—1468no—
533C4×D4—1468no—
534C4×D4—1468no—
535C4×D4—1462no—
536C4×D4C22×D7314yes—
537#117—734no—
538#117—734no—
539#117—1468no—
540#117—1468no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—731no—
543C2×C4⋊C4—731no—
544C2×C4⋊C4—731no—
545C2×C4⋊C4—731no—
546C2×C4⋊C4—734no—
547C2×C4⋊C4—734no—
548C2×C4⋊C4—1468no—
549C2×C4⋊C4—1462no—
550C2×C4⋊C4—1462no—
551C2×C4⋊C4—1468no—
552C2×C4⋊C4—1461no—
553C2×C4⋊C4—1461no—
554C2×C4⋊C4—1461no—
555C2×C4⋊C4—1461no—
556C2×C4⋊C4—1461no—
557C2×C4⋊C4C22×D7311yescharacteristic
558C2×C4⋊C4C22×D7311yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—731no—
561C2×C22⋊C4—731no—
562C2×C22⋊C4—1461no—
563C2×C22⋊C4—1461no—
564C2×C22⋊C4—1461no—
565C2×C42—21no—
566C2×C42—731no—
567C2×C42—1461no—
568C2×C42—1461no—
569C2×C42—1461no—
570C2×C42C22×D7311yescharacteristic
571#106—734no—
572#106—734no—
573#106—734no—
574#106C22×D7314yes—
575#103—734no—
576#103—734no—
577#103—734no—
578#103C22×D7314yes—
579#102—734no—
580#102—734no—
581#102—734no—
582#102C22×D7314yes—
583#97—734no—
584#97—734no—
585C4×C8—734no—
586C4×C8C22×D7314yes—
587C24—21no—
588C24—731no—
589C24—1461no—
590#41—7316no—
591#41—7316no—
592#41—1468no—
593#41—14616no—
594#41—1468no—
595#41—14616no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—734no—
599C2×Q8—732no—
600C2×Q8—1461no—
601C2×Q8—1462no—
602C2×Q8C2×C4×D7314yes—
603C2×Q8C23×D7312yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—734no—
607C2×D4—732no—
608C2×D4—1464no—
609C2×D4—1468no—
610C2×D4—1464no—
611C2×D4—1468no—
612C2×D4—1461no—
613C2×D4—1462no—
614C2×D4C2×C4×D7314yes—
615C2×D4C23×D7312yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—5842no—
622C22×C4—5842no—
623C22×C4—5842no—
624C22×C4—5842no—
625C22×C4—5842no—
626C22×C4—731no—
627C22×C4—734no—
628C22×C4—732no—
629C22×C4—734no—
630C22×C4—732no—
631C22×C4—731no—
632C22×C4—731no—
633C22×C4—1464no—
634C22×C4—1464no—
635C22×C4—1464no—
636C22×C4—1464no—
637C22×C4—1468no—
638C22×C4—1461no—
639C22×C4—1461no—
640C22×C4—1464no—
641C22×C4—1464no—
642C22×C4—1464no—
643C22×C4—1468no—
644C22×C4—1461no—
645C22×C4D4×D7311yescharacteristic
646C22×C4D4×D7311yescharacteristic
647C22×C4C23×D7311yescharacteristic
648Q16—7316no—
649SD16—7316no—
650SD16C2×C4×D73116yescomplemented
651D8—7316no—
652M16—1468no—
653C2×C8—22no—
654C2×C8—734no—
655C2×C8—732no—
656C2×C8—7316no—
657C2×C8—732no—
658C2×C8—1462no—
659C2×C8C2×C4×D7314yes—
660C2×C8C23×D7312yes—
661C2×C8C23×D7312yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—734no—
666C4⋊C4—734no—
667C4⋊C4—732no—
668C4⋊C4—732no—
669C4⋊C4—1464no—
670C4⋊C4—1464no—
671C4⋊C4—1464no—
672C4⋊C4—1464no—
673C4⋊C4—1464no—
674C4⋊C4—1461no—
675C4⋊C4—1461no—
676C4⋊C4C23×D7312yes—
677C4⋊C4C23×D7312yes—
678C22⋊C4—24no—
679C22⋊C4—734no—
680C22⋊C4—734no—
681C22⋊C4—1464no—
682C22⋊C4—1464no—
683C22⋊C4—1464no—
684C42—24no—
685C42—732no—
686C42—732no—
687C42—1464no—
688C42—1464no—
689C42—1464no—
690C42D4×D7312yes—
691C42C23×D7312yes—
692C23—22no—
693C23—24no—
694C23—42no—
695C23—42no—
696C23—2922no—
697C23—2922no—
698C23—732no—
699C23—734no—
700C23—1462no—
701C23—1464no—
702C23—1462no—
703C23—1462no—
704C23C2×D4×D7311yescharacteristic
705Q8—22no—
706Q8—24no—
707Q8—734no—
708Q8—1462no—
709Q8—1464no—
710Q8C22×C4×D7314yes—
711D4—22no—
712D4—24no—
713D4—734no—
714D4—14616no—
715D4—14616no—
716D4—1462no—
717D4—1464no—
718D4C22×C4×D7314yes—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—2922no—
729C2×C4—2922no—
730C2×C4—5844no—
731C2×C4—5844no—
732C2×C4—5844no—
733C2×C4—5844no—
734C2×C4—5844no—
735C2×C4—732no—
736C2×C4—734no—
737C2×C4—734no—
738C2×C4—734no—
739C2×C4—738no—
740C2×C4—732no—
741C2×C4—732no—
742C2×C4—14616no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—14616no—
746C2×C4—1462no—
747C2×C4—1462no—
748C2×C4—1462no—
749C2×C4—1464no—
750C2×C4C22×C4×D7312yes—
751C2×C4C2×D4×D7312yes—
752C2×C4C2×D4×D7312yes—
753C2×C4C2×D4×D7311yescharacteristic
754C2×C4#41×D7312yes—
755C2×C4C24×D7311yescharacteristic
756C8—22no—
757C8—734no—
758C8—1462no—
759C8C22×C4×D7314yes—
760C22—24no—
761C22—42no—
762C22—42no—
763C22—48no—
764C22—2922no—
765C22—2922no—
766C22—2928no—
767C22—734no—
768C22—1464no—
769C22—1462no—
770C22—1462no—
771C22—1468no—
772C22C4×D4×D7312yes—
773C22#1798939312yes—
774C22#1798939412yes—
775C22C22×D4×D7311yescharacteristic
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—2922no—
782C4—2922no—
783C4—734no—
784C4—1464no—
785C4—1462no—
786C4—1462no—
787C4C4×D4×D7312yes—
788C4C23×C4×D7311yescharacteristic
789C4C2×#41×D7311yescharacteristic
790C2—44no—
791C2—2924no—
792C2—1464no—
793C2#2261880914yesdirect product factor
794C2C2×C4×D4×D7311yescharacteristic
795C2C2×#1798939311yescharacteristic
796C2C2×#1798939411yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC4×C73C24×C4
FrattiniC2×C4C24×D73
FittingC2×C4×SD16×C73C2
socleC23×C73C22×D4
prime radicalC22×#14556612C2
cosocleC2×C4×C73C25
hypercenterC2×C4×SD16D73
hypocenterC73C2×#2952
LCSG ▷ 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
2. C2×#17989069C2semidirect
3. C2×#17989066C2semidirect
4. #22618809C2direct (N × H)
5. C2×#17988697C2semidirect
6. C2×#17988696C2semidirect
7. C2×#17988692C2semidirect
8. C2×#17988691C2semidirect
9. C2×C4×#11924017C2semidirect
10. C2×SD16×Dic73C2semidirect
11. C2×#17988674C2semidirect
12. C2×#106×D73C2semidirect
13. C2×#17988587C2semidirect
14. C2×#17988585C2semidirect
15. C2×#17988541C2semidirect
16. C2×C4×SD16×C73C2semidirect
19. C2×#14556612C4semidirect
27. #17989069C22semidirect
29. #17989066C22semidirect
47. #17988697C22semidirect
48. #17988696C22semidirect
49. #17988692C22semidirect
50. #17988691C22semidirect
51. C4×#11924017C22semidirect
52. SD16×Dic73C22semidirect
53. #17988674C22semidirect
57. #106×D73C22semidirect
58. #17988587C22semidirect
59. #17988585C22semidirect
66. #17988541C22semidirect
73. C4×SD16×C73C22semidirect
80. C2×#11924029C2×C4semidirect
84. C2×#11924027C2×C4semidirect
98. #14556612C2×C4semidirect
99. C2×#11924018C2×C4semidirect
101. C2×#11924017C2×C4semidirect
103. C2×#11924013C2×C4semidirect
109. C2×C8×D73C2×C4semidirect
170. C2×SD16×C73C2×C4semidirect
192. #11924029C22×C4semidirect
195. #11924027C22×C4semidirect
232. #11924018C22×C4semidirect
233. #11924017C22×C4semidirect
234. #11924013C22×C4semidirect
240. C8×D73C22×C4semidirect
279. SD16×C73C22×C4semidirect
393. C2×C73#2952semidirect
410. C2×C4×SD16D73semidirect
415. C73C2×#2952semidirect
456. C4×SD16C2×D73semidirect
505. C2×SD16C4×D73semidirect
650. SD16C2×C4×D73semidirect
793. C2#22618809direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566122
C2×#179890692
C2×#179890662
#226188092
C2×#179886972
C2×#179886962
C2×#179886922
C2×#179886912
C2×C4×#119240172
C2×SD16×Dic732
C2×#179886742
C2×#106×D732
C2×#179885872
C2×#179885852
C2×#179885412
C2×C4×SD16×C732
C2×#295273