Finite Group Databasebeta

← C2×#22569087 #31719989

Subgroups — C2×#22569087 #31719989

Order 17152.

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×#14524064C211yesmaximal, characteristic
2C2×#16863878C211yesmaximal, characteristic, complemented
3C2×#16863875C211yesmaximal, characteristic, complemented
4#22569087C2116yesmaximal, direct product factor
5C2×#16863506C211yesmaximal, characteristic, complemented
6C2×#16863505C211yesmaximal, characteristic, complemented
7C2×#16863501C211yesmaximal, characteristic, complemented
8C2×#16863500C211yesmaximal, characteristic, complemented
9C2×C4×#11761617C211yesmaximal, characteristic, complemented
10C2×SD16×Dic67C211yesmaximal, characteristic, complemented
11C2×#16863483C211yesmaximal, characteristic, complemented
12C2×#106×D67C211yesmaximal, characteristic, complemented
13C2×#16863396C211yesmaximal, characteristic, complemented
14C2×#16863394C211yesmaximal, characteristic, complemented
15C2×#16863350C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×#11761627C2211yescharacteristic
19C2×#14524064C4116yescomplemented
20C2×#14524064C2218yes—
21C22×#11761618C2211yescharacteristic
22C22×#11761617C2211yescharacteristic
23C22×#11761613C2211yescharacteristic
24C22×#11761611C2211yescharacteristic
25C22×C8×D67C2211yescharacteristic
26#16863878—24no—
27#16863878C2218yescomplemented
28#16863875—24no—
29#16863875C2218yescomplemented
30C2×Q8×Dic67C2211yescharacteristic
31C2×C4×Dic134C2211yescharacteristic
32C2×#14524008C2211yescharacteristic
33C2×C4×D268—21no—
34C2×C4×D268C2211yescharacteristic
35C2×D4×Dic67C2211yescharacteristic
36C2×#14524005—21no—
37C2×#14524005C2211yescharacteristic
38C2×C4×C22⋊D67—21no—
39C2×(C22⋊D67)⋊C4—21no—
40C2×#14524000—21no—
41C2×#14524000C2211yescharacteristic
42C2×#14523999—21no—
43C22×Dic67⋊C4—21no—
44C2×C4⋊C4×D67—21no—
45C2×C4⋊C4×D67C2211yescharacteristic
46C2×C4⋊C4×D67C2211yescharacteristic
47#16863506C2218yescomplemented
48#16863505C2218yescomplemented
49#16863501C2218yescomplemented
50#16863500C2218yescomplemented
51C4×#11761617C2218yescomplemented
52SD16×Dic67C2218yescomplemented
53#16863483C2218yescomplemented
54C2×#14523975C2211yescharacteristic
55C2×#14523974C2211yescharacteristic
56C2×#14523974C2211yescharacteristic
57#106×D67C2218yescomplemented
58#16863396C2218yescomplemented
59#16863394C2218yescomplemented
60C2×#14523968C2211yescharacteristic
61C2×#14523967C2211yescharacteristic
62C2×#14523966C2211yescharacteristic
63C2×#14523965C2211yescharacteristic
64C2×#14523964C2211yescharacteristic
65C2×#14523963C2211yescharacteristic
66#16863350C2218yescomplemented
67C2×#14523954C2211yescharacteristic
68C2×#14523953C2211yescharacteristic
69C2×C8×Dic67C2211yescharacteristic
70C22×SD16×C67C2211yescharacteristic
71C2×C4×Q8×C67C2211yescharacteristic
72C2×C4×D4×C67C2211yescharacteristic
73C4×SD16×C67C2218yescomplemented
74C2×#106×C67C2211yescharacteristic
75C2×#103×C67C2211yescharacteristic
76C2×#102×C67C2211yescharacteristic
77C2×C4×C8×C67C2211yescharacteristic
78C2×#11761629—22no—
79C2×#11761629—24no—
80C2×#11761629C2×C418yescomplemented
81C2×#11761629C2314yes—
82C2×#11761627—22no—
83C2×#11761627—24no—
84C2×#11761627C2×C418yescomplemented
85C2×#11761627C2314yes—
86C22×Dic134C2311yescharacteristic
87C22×D268—21no—
88C22×D268C2311yescharacteristic
89C22×C22⋊D67—21no—
90C23×Dic67—21no—
91C23×Dic67—21no—
92C22×C4×D67—21no—
93C22×C4×D67—21no—
94C22×C4×D67—21no—
95C22×C4×D67—21no—
96C22×C4×D67—21no—
97C22×C4×D67C2311yescharacteristic
98#14524064C2×C4164yescomplemented
99C2×#11761618C2×C418yescomplemented
100C2×#11761618C2314yes—
101C2×#11761617C2×C418yescomplemented
102C2×#11761617C2314yes—
103C2×#11761613C2×C418yescomplemented
104C2×#11761613C2314yes—
105C2×#11761611—24no—
106C2×#11761611C2314yes—
107C22×C67⋊C8C2311yescharacteristic
108C22×C67⋊C8C2311yescharacteristic
109C2×C8×D67C2×C418yescomplemented
110C2×C8×D67C2314yes—
111Q8×Dic67—22no—
112Q8×Dic67C2314yes—
113C4×Dic134—22no—
114C4×Dic134C2314yes—
115#14524008—22no—
116#14524008C2314yes—
117C4×D268—28no—
118C4×D268—22no—
119C4×D268C2314yes—
120D4×Dic67—22no—
121D4×Dic67C2314yes—
122#14524005—28no—
123#14524005—22no—
124#14524005C2314yes—
125C4×C22⋊D67—28no—
126(C22⋊D67)⋊C4—28no—
127#14524000—28no—
128#14524000D414yes—
129#14524000C2314yes—
130#14523999—28no—
131C2×C4⋊Dic67—21no—
132C2×C4⋊Dic67C2311yescharacteristic
133C2×C4⋊Dic67C2311yescharacteristic
134C2×Dic67⋊C4—21no—
135C2×Dic67⋊C4—21no—
136C2×Dic67⋊C4—21no—
137C2×Dic67⋊C4—28no—
138C2×Dic67⋊C4—21no—
139C2×Dic67⋊C4D411yescharacteristic
140C2×Dic67⋊C4D411yescharacteristic
141C4⋊C4×D67—22no—
142C4⋊C4×D67—22no—
143C4⋊C4×D67—28no—
144C4⋊C4×D67C2314yes—
145C4⋊C4×D67C2314yes—
146C2×C22⋊Dic67—21no—
147C2×(C2×D67)⋊C4—21no—
148C2×(C2×D67)⋊C4—21no—
149C2×(C2×D67)⋊C4D411yescharacteristic
150C2×(C2×D67)⋊C4D411yescharacteristic
151C2×C4×Dic67—21no—
152C2×C4×Dic67—21no—
153C2×C4×Dic67—21no—
154C2×C4×Dic67C2311yescharacteristic
155#14523975C2314yes—
156#14523974C2314yes—
157#14523974C2314yes—
158#14523968C2314yes—
159#14523967C2314yes—
160#14523966C2314yes—
161#14523965C2314yes—
162#14523964C2314yes—
163#14523963C2314yes—
164#14523954C2314yes—
165#14523953C2314yes—
166C8×Dic67C2314yes—
167C22×Q8×C67C2311yescharacteristic
168C22×D4×C67C2311yescharacteristic
169C23×C4×C67—21no—
170C2×SD16×C67C2×C418yescomplemented
171C2×SD16×C67C2314yes—
172C22×C8×C67C2311yescharacteristic
173C22×C8×C67C2311yescharacteristic
174C4×Q8×C67—22no—
175C4×Q8×C67C2314yes—
176C4×D4×C67—22no—
177C4×D4×C67C2314yes—
178C2×C4⋊C4×C67—21no—
179C2×C4⋊C4×C67C2311yescharacteristic
180C2×C4⋊C4×C67C2311yescharacteristic
181C2×C22⋊C4×C67—21no—
182C2×C42×C67—21no—
183C2×C42×C67C2311yescharacteristic
184#106×C67C2314yes—
185#103×C67C2314yes—
186#102×C67C2314yes—
187C4×C8×C67C2314yes—
188C23×D67—21no—
189C23×D67C2×D411yescharacteristic
190#11761629—216no—
191#11761629—28no—
192#11761629C22×C4116yescomplemented
193#11761627—216no—
194#11761627—28no—
195#11761627C22×C4116yescomplemented
196C2×Dic134—21no—
197C2×Dic134—22no—
198C2×Dic134C22×C414yes—
199C2×Dic134C2412yes—
200C2×D268—28no—
201C2×D268—24no—
202C2×D268—21no—
203C2×D268—22no—
204C2×D268C22×C414yes—
205C2×D268C2412yes—
206C2×C22⋊D67—28no—
207C2×C22⋊D67—24no—
208C22×Dic67—21no—
209C22×Dic67—28no—
210C22×Dic67—24no—
211C22×Dic67—21no—
212C22×Dic67—21no—
213C22×Dic67—24no—
214C22×Dic67—82no—
215C22×Dic67C2×D411yescharacteristic
216C22×Dic67C2×D411yescharacteristic
217C22×Dic67C2×D411yescharacteristic
218C2×C4×D67—28no—
219C2×C4×D67—24no—
220C2×C4×D67—24no—
221C2×C4×D67—24no—
222C2×C4×D67—24no—
223C2×C4×D67—24no—
224C2×C4×D67—82no—
225C2×C4×D67—82no—
226C2×C4×D67—82no—
227C2×C4×D67—82no—
228C2×C4×D67C22×C414yes—
229C2×C4×D67C2×D412yes—
230C2×C4×D67#4114yes—
231C2×C4×D67C2412yes—
232#11761618C22×C4116yescomplemented
233#11761617C22×C4116yescomplemented
234#11761613C22×C4116yescomplemented
235#11761611—28no—
236C2×C67⋊C8—22no—
237C2×C67⋊C8C22×C414yes—
238C2×C67⋊C8C2412yes—
239C2×C67⋊C8C2412yes—
240C8×D67C22×C4116yescomplemented
241C4⋊Dic67—21no—
242C4⋊Dic67—21no—
243C4⋊Dic67—24no—
244C4⋊Dic67C2412yes—
245C4⋊Dic67C2412yes—
246Dic67⋊C4—24no—
247Dic67⋊C4—24no—
248Dic67⋊C4—24no—
249Dic67⋊C4—24no—
250Dic67⋊C4C2×D414yes—
251Dic67⋊C4C2×D414yes—
252C22⋊Dic67—24no—
253(C2×D67)⋊C4—24no—
254(C2×D67)⋊C4—24no—
255(C2×D67)⋊C4C2×D414yes—
256(C2×D67)⋊C4C2×D414yes—
257C4×Dic67—24no—
258C4×Dic67—24no—
259C4×Dic67—24no—
260C4×Dic67C2×D412yes—
261C4×Dic67C2412yes—
262C24×C67—21no—
263C2×Q8×C67—21no—
264C2×Q8×C67—22no—
265C2×Q8×C67C22×C414yes—
266C2×Q8×C67C2412yes—
267C2×D4×C67—21no—
268C2×D4×C67—22no—
269C2×D4×C67C22×C414yes—
270C2×D4×C67C2412yes—
271C22×C4×C67—21no—
272C22×C4×C67—21no—
273C22×C4×C67—21no—
274C22×C4×C67—24no—
275C22×C4×C67—82no—
276C22×C4×C67C2×D411yescharacteristic
277C22×C4×C67C2×D411yescharacteristic
278C22×C4×C67C2411yescharacteristic
279SD16×C67C22×C4116yescomplemented
280C2×C8×C67—22no—
281C2×C8×C67C22×C414yes—
282C2×C8×C67C2412yes—
283C2×C8×C67C2412yes—
284C4⋊C4×C67—24no—
285C4⋊C4×C67—21no—
286C4⋊C4×C67—21no—
287C4⋊C4×C67C2412yes—
288C4⋊C4×C67C2412yes—
289C22⋊C4×C67—24no—
290C42×C67—24no—
291C42×C67C2×D412yes—
292C42×C67C2412yes—
293C23×C67—24no—
294C23×C67—22no—
295C23×C67—42no—
296C23×C67—42no—
297C23×C67C22×D411yescharacteristic
298C22×D67—22no—
299C22×D67—22no—
300C22×D67—24no—
301C22×D67—22no—
302C22×D67—42no—
303C22×D67—42no—
304C22×D67C4×D414yes—
305C22×D67C22×D412yes—
306Q8×C67—24no—
307Q8×C67—22no—
308Q8×C67C23×C414yes—
309D4×C67—24no—
310D4×C67—22no—
311D4×C67C23×C414yes—
312C2×C4×C67—24no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—22no—
318C2×C4×C67—42no—
319C2×C4×C67—42no—
320C2×C4×C67—84no—
321C2×C4×C67C23×C412yes—
322C2×C4×C67C22×D412yes—
323C2×C4×C67C22×D412yes—
324C2×C4×C67C22×D411yescharacteristic
325C2×C4×C67C2×#4112yes—
326C2×C4×C67C2511yescharacteristic
327C22⋊D67—216no—
328C2×Dic67—24no—
329C2×Dic67—22no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—216no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—42no—
336C2×Dic67—42no—
337C2×Dic67—84no—
338C2×Dic67C4×D414yes—
339C2×Dic67C22×D412yes—
340C2×Dic67C22×D412yes—
341C2×Dic67C22×D412yes—
342D268—216no—
343D268—24no—
344D268—22no—
345D268C23×C414yes—
346C4×D67—216no—
347C4×D67—84no—
348C4×D67—84no—
349C4×D67—84no—
350C4×D67—84no—
351C4×D67C4×D418yes—
352C4×D67C23×C414yes—
353C4×D67C2×#4114yes—
354Dic134—24no—
355Dic134—22no—
356Dic134C23×C414yes—
357C8×C67—22no—
358C8×C67C23×C414yes—
359C67⋊C8—22no—
360C67⋊C8C23×C414yes—
361C22×C67—24no—
362C22×C67—48no—
363C22×C67—42no—
364C22×C67—42no—
365C22×C67C2×C4×D412yes—
366C22×C67#57712yes—
367C22×C67#57712yes—
368C22×C67C23×D411yescharacteristic
369C2×D67—28no—
370C2×D67—22no—
371C2×D67—22no—
372C2×D67—24no—
373C2×D67—48no—
374C2×D67—42no—
375C2×D67—42no—
376C2×D67C2×C4×D414yes—
377C4×C67—24no—
378C4×C67—22no—
379C4×C67—22no—
380C4×C67—42no—
381C4×C67—42no—
382C4×C67C2×C4×D412yes—
383C4×C67C24×C411yescharacteristic
384C4×C67C22×#4111yescharacteristic
385Dic67—24no—
386Dic67—22no—
387Dic67—22no—
388Dic67—42no—
389Dic67—42no—
390Dic67C2×C4×D414yes—
391C2×#2952—671nomaximal, Sylow
392C2×C67—44no—
393C2×C67#295214yescomplemented
394C2×C67C22×C4×D411yescharacteristic
395C2×C67C2×#57711yescharacteristic
396C2×C67C2×#57711yescharacteristic
397D67—24no—
398D67—44no—
399C22×#135—671no—
400C2×#520—671no—
401C2×#520—671no—
402#2952—6716no—
403C2×#442—671no—
404C2×#442—671no—
405C2×#441—671no—
406C2×#441—671no—
407C2×C4×SD16—671no—
408C2×C4×SD16—671no—
409C2×C4×SD16—671no—
410C2×C4×SD16D6711yescharacteristic, complemented
411C22×#106—671no—
412C2×#417—671no—
413C2×#417—671no—
414C2×#405—671no—
415C67C2×#295211yescharacteristic, complemented, Sylow
416C22×#41—671no—
417C22×#41—671no—
418C2×#135—6716no—
419C2×#135—678no—
420C22×Q16—671no—
421C22×SD16—671no—
422C22×SD16C2×D6711yescharacteristic
423C22×D8—671no—
424C22×M16—671no—
425C23×C8—671no—
426#520—678no—
427#520—678no—
428#520—1344no—
429#520—1344no—
430C2×C4×Q8—671no—
431C2×C4×Q8—671no—
432C2×C4×Q8—671no—
433C2×C4×Q8C2×D6711yescharacteristic
434C2×C4×D4—671no—
435C2×C4×D4—671no—
436C2×C4×D4—671no—
437C2×C4×D4—1341no—
438C2×C4×D4—1341no—
439C2×C4×D4—1341no—
440C2×C4×D4—1341no—
441C2×C4×D4C2×D6711yescharacteristic
442C2×#117—671no—
443C2×#117—1341no—
444C2×#117—1341no—
445C22×C4⋊C4—671no—
446C22×C4⋊C4—671no—
447C22×C4⋊C4—1341no—
448C22×C4⋊C4—1341no—
449#442—678no—
450#442—678no—
451#441—678no—
452#441—678no—
453C4×SD16—678no—
454C4×SD16—678no—
455C4×SD16—678no—
456C4×SD16C2×D6718yescomplemented
457C2×#106—671no—
458C2×#106—671no—
459C2×#106—671no—
460C2×#106—678no—
461C2×#106C2×D6711yescharacteristic
462#417—678no—
463#417—678no—
464C2×#103—671no—
465C2×#103—671no—
466C2×#103—671no—
467C2×#103C2×D6711yescharacteristic
468C2×#102—671no—
469C2×#102—671no—
470C2×#102—671no—
471C2×#102C2×D6711yescharacteristic
472#405—678no—
473C2×#97—671no—
474C2×#97—671no—
475C2×C4×C8—671no—
476C2×C4×C8C2×D6711yescharacteristic
477C2×#41—678no—
478C2×#41—674no—
479C2×#41—678no—
480C2×#41—674no—
481C2×#41—1342no—
482C2×#41—1344no—
483C2×#41—1342no—
484C2×#41—1344no—
485C22×Q8—671no—
486C22×Q8C22×D6711yescharacteristic
487C22×D4—671no—
488C22×D4—1341no—
489C22×D4—1341no—
490C22×D4C22×D6711yescharacteristic
491C23×C4—21no—
492C23×C4—671no—
493C23×C4—1341no—
494C23×C4—1341no—
495C23×C4—1341no—
496C23×C4—1341no—
497C23×C4—1341no—
498C23×C4—1341no—
499C23×C4—1341no—
500#135—6764no—
501C2×Q16—678no—
502C2×Q16—674no—
503C2×SD16—678no—
504C2×SD16—674no—
505C2×SD16C4×D6718yescomplemented
506C2×SD16C22×D6714yes—
507C2×D8—678no—
508C2×D8—674no—
509C2×M16—674no—
510C2×M16—1344no—
511C22×C8—671no—
512C22×C8—678no—
513C22×C8—674no—
514C22×C8—671no—
515C22×C8C22×D6711yescharacteristic
516C22×C8C22×D6711yescharacteristic
517C4×Q8—22no—
518C4×Q8—674no—
519C4×Q8—674no—
520C4×Q8—674no—
521C4×Q8—1342no—
522C4×Q8—1342no—
523C4×Q8—1342no—
524C4×Q8C22×D6714yes—
525C4×D4—22no—
526C4×D4—674no—
527C4×D4—674no—
528C4×D4—674no—
529C4×D4—1348no—
530C4×D4—1342no—
531C4×D4—1342no—
532C4×D4—1348no—
533C4×D4—1348no—
534C4×D4—1348no—
535C4×D4—1342no—
536C4×D4C22×D6714yes—
537#117—674no—
538#117—674no—
539#117—1348no—
540#117—1348no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—671no—
543C2×C4⋊C4—671no—
544C2×C4⋊C4—671no—
545C2×C4⋊C4—671no—
546C2×C4⋊C4—674no—
547C2×C4⋊C4—674no—
548C2×C4⋊C4—1348no—
549C2×C4⋊C4—1342no—
550C2×C4⋊C4—1342no—
551C2×C4⋊C4—1348no—
552C2×C4⋊C4—1341no—
553C2×C4⋊C4—1341no—
554C2×C4⋊C4—1341no—
555C2×C4⋊C4—1341no—
556C2×C4⋊C4—1341no—
557C2×C4⋊C4C22×D6711yescharacteristic
558C2×C4⋊C4C22×D6711yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—671no—
561C2×C22⋊C4—671no—
562C2×C22⋊C4—1341no—
563C2×C22⋊C4—1341no—
564C2×C22⋊C4—1341no—
565C2×C42—21no—
566C2×C42—671no—
567C2×C42—1341no—
568C2×C42—1341no—
569C2×C42—1341no—
570C2×C42C22×D6711yescharacteristic
571#106—674no—
572#106—674no—
573#106—674no—
574#106C22×D6714yes—
575#103—674no—
576#103—674no—
577#103—674no—
578#103C22×D6714yes—
579#102—674no—
580#102—674no—
581#102—674no—
582#102C22×D6714yes—
583#97—674no—
584#97—674no—
585C4×C8—674no—
586C4×C8C22×D6714yes—
587C24—21no—
588C24—671no—
589C24—1341no—
590#41—6716no—
591#41—6716no—
592#41—13416no—
593#41—1348no—
594#41—13416no—
595#41—1348no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—674no—
599C2×Q8—672no—
600C2×Q8—1341no—
601C2×Q8—1342no—
602C2×Q8C2×C4×D6714yes—
603C2×Q8C23×D6712yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—674no—
607C2×D4—672no—
608C2×D4—1344no—
609C2×D4—1348no—
610C2×D4—1344no—
611C2×D4—1348no—
612C2×D4—1341no—
613C2×D4—1342no—
614C2×D4C2×C4×D6714yes—
615C2×D4C23×D6712yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—5362no—
622C22×C4—5362no—
623C22×C4—5362no—
624C22×C4—5362no—
625C22×C4—5362no—
626C22×C4—671no—
627C22×C4—674no—
628C22×C4—672no—
629C22×C4—674no—
630C22×C4—672no—
631C22×C4—671no—
632C22×C4—671no—
633C22×C4—1344no—
634C22×C4—1344no—
635C22×C4—1344no—
636C22×C4—1344no—
637C22×C4—1348no—
638C22×C4—1341no—
639C22×C4—1341no—
640C22×C4—1344no—
641C22×C4—1344no—
642C22×C4—1344no—
643C22×C4—1348no—
644C22×C4—1341no—
645C22×C4D4×D6711yescharacteristic
646C22×C4D4×D6711yescharacteristic
647C22×C4C23×D6711yescharacteristic
648Q16—6716no—
649SD16—6716no—
650SD16C2×C4×D67116yescomplemented
651D8—6716no—
652M16—1348no—
653C2×C8—22no—
654C2×C8—674no—
655C2×C8—672no—
656C2×C8—6716no—
657C2×C8—672no—
658C2×C8—1342no—
659C2×C8C2×C4×D6714yes—
660C2×C8C23×D6712yes—
661C2×C8C23×D6712yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—674no—
666C4⋊C4—674no—
667C4⋊C4—672no—
668C4⋊C4—672no—
669C4⋊C4—1344no—
670C4⋊C4—1344no—
671C4⋊C4—1344no—
672C4⋊C4—1344no—
673C4⋊C4—1341no—
674C4⋊C4—1341no—
675C4⋊C4—1344no—
676C4⋊C4C23×D6712yes—
677C4⋊C4C23×D6712yes—
678C22⋊C4—24no—
679C22⋊C4—674no—
680C22⋊C4—674no—
681C22⋊C4—1344no—
682C22⋊C4—1344no—
683C22⋊C4—1344no—
684C42—24no—
685C42—672no—
686C42—672no—
687C42—1344no—
688C42—1344no—
689C42—1344no—
690C42D4×D6712yes—
691C42C23×D6712yes—
692C23—24no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—2682no—
697C23—2682no—
698C23—674no—
699C23—672no—
700C23—1344no—
701C23—1342no—
702C23—1342no—
703C23—1342no—
704C23C2×D4×D6711yescharacteristic
705Q8—24no—
706Q8—22no—
707Q8—674no—
708Q8—1344no—
709Q8—1342no—
710Q8C22×C4×D6714yes—
711D4—24no—
712D4—22no—
713D4—674no—
714D4—13416no—
715D4—13416no—
716D4—1344no—
717D4—1342no—
718D4C22×C4×D6714yes—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—2682no—
729C2×C4—2682no—
730C2×C4—5364no—
731C2×C4—5364no—
732C2×C4—5364no—
733C2×C4—5364no—
734C2×C4—5364no—
735C2×C4—674no—
736C2×C4—672no—
737C2×C4—678no—
738C2×C4—674no—
739C2×C4—674no—
740C2×C4—672no—
741C2×C4—672no—
742C2×C4—13416no—
743C2×C4—1342no—
744C2×C4—1342no—
745C2×C4—13416no—
746C2×C4—1344no—
747C2×C4—1342no—
748C2×C4—1342no—
749C2×C4—1342no—
750C2×C4C22×C4×D6712yes—
751C2×C4C2×D4×D6712yes—
752C2×C4C2×D4×D6712yes—
753C2×C4C2×D4×D6711yescharacteristic
754C2×C4#41×D6712yes—
755C2×C4C24×D6711yescharacteristic
756C8—22no—
757C8—674no—
758C8—1342no—
759C8C22×C4×D6714yes—
760C22—24no—
761C22—42no—
762C22—42no—
763C22—48no—
764C22—2682no—
765C22—2682no—
766C22—2688no—
767C22—674no—
768C22—1344no—
769C22—1342no—
770C22—1342no—
771C22—1348no—
772C22C4×D4×D6712yes—
773C22#1686420212yes—
774C22#1686420312yes—
775C22C22×D4×D6711yescharacteristic
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—2682no—
782C4—2682no—
783C4—674no—
784C4—1344no—
785C4—1342no—
786C4—1342no—
787C4C4×D4×D6712yes—
788C4C23×C4×D6711yescharacteristic
789C4C2×#41×D6711yescharacteristic
790C2—44no—
791C2—2684no—
792C2—1344no—
793C2#2256908714yesdirect product factor
794C2C2×C4×D4×D6711yescharacteristic
795C2C2×#1686420211yescharacteristic
796C2C2×#1686420311yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×C4×SD16×C67C2
socleC23×C67C22×D4
prime radicalC22×#14524064C2
cosocleC2×C4×C67C25
hypercenterC2×C4×SD16D67
hypocenterC67C2×#2952
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#16863878C2semidirect
3. C2×#16863875C2semidirect
4. #22569087C2direct (N × H)
5. C2×#16863506C2semidirect
6. C2×#16863505C2semidirect
7. C2×#16863501C2semidirect
8. C2×#16863500C2semidirect
9. C2×C4×#11761617C2semidirect
10. C2×SD16×Dic67C2semidirect
11. C2×#16863483C2semidirect
12. C2×#106×D67C2semidirect
13. C2×#16863396C2semidirect
14. C2×#16863394C2semidirect
15. C2×#16863350C2semidirect
16. C2×C4×SD16×C67C2semidirect
19. C2×#14524064C4semidirect
27. #16863878C22semidirect
29. #16863875C22semidirect
47. #16863506C22semidirect
48. #16863505C22semidirect
49. #16863501C22semidirect
50. #16863500C22semidirect
51. C4×#11761617C22semidirect
52. SD16×Dic67C22semidirect
53. #16863483C22semidirect
57. #106×D67C22semidirect
58. #16863396C22semidirect
59. #16863394C22semidirect
66. #16863350C22semidirect
73. C4×SD16×C67C22semidirect
80. C2×#11761629C2×C4semidirect
84. C2×#11761627C2×C4semidirect
98. #14524064C2×C4semidirect
99. C2×#11761618C2×C4semidirect
101. C2×#11761617C2×C4semidirect
103. C2×#11761613C2×C4semidirect
109. C2×C8×D67C2×C4semidirect
170. C2×SD16×C67C2×C4semidirect
192. #11761629C22×C4semidirect
195. #11761627C22×C4semidirect
232. #11761618C22×C4semidirect
233. #11761617C22×C4semidirect
234. #11761613C22×C4semidirect
240. C8×D67C22×C4semidirect
279. SD16×C67C22×C4semidirect
393. C2×C67#2952semidirect
410. C2×C4×SD16D67semidirect
415. C67C2×#2952semidirect
456. C4×SD16C2×D67semidirect
505. C2×SD16C4×D67semidirect
650. SD16C2×C4×D67semidirect
793. C2#22569087direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240642
C2×#168638782
C2×#168638752
#225690872
C2×#168635062
C2×#168635052
C2×#168635012
C2×#168635002
C2×C4×#117616172
C2×SD16×Dic672
C2×#168634832
C2×#106×D672
C2×#168633962
C2×#168633942
C2×#168633502
C2×C4×SD16×C672
C2×#295267