Finite Group Databasebeta

← C2×#22572292 #31732359

Subgroups — C2×#22572292 #31732359

Order 17152.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864103C211yesmaximal, characteristic, complemented
2C2×#16864042C211yesmaximal, characteristic
3#22572292C2116yesmaximal, direct product factor
4C2×#16863756C211yesmaximal, characteristic, complemented
5C2×#16863732C211yesmaximal, characteristic, complemented
6C2×#16863710C211yesmaximal, characteristic, complemented
7C2×#16863677C211yesmaximal, characteristic, complemented
8C2×#16863642C211yesmaximal, characteristic, complemented
9C2×#16863637C211yesmaximal, characteristic, complemented
10C2×#16863619C211yesmaximal, characteristic, complemented
11C2×#16863560C211yesmaximal, characteristic, complemented
12C2×#16863549C211yesmaximal, characteristic, complemented
13C2×#16863498C211yesmaximal, characteristic, complemented
14C2×#16863398C211yesmaximal, characteristic, complemented
15C22×#14523965C211yesmaximal, characteristic, complemented
16C2×#435×C67C211yesmaximal, characteristic, complemented
17C22×#11761628C2211yescharacteristic
18C23×D268C2211yescharacteristic
19C22×Dic268C2211yescharacteristic, complemented
20C22×#11761617C2211yescharacteristic
21C22×#11761617C2211yescharacteristic
22#16864103—24no—
23#16864103C2218yescomplemented
24#16864042—24no—
25#16864042C2218yes—
26C2×#14524043C2211yescharacteristic, complemented
27C2×#14524034—21no—
28C2×#14524031C2211yescharacteristic
29C2×#14524028—21no—
30C2×#14524022C2211yescharacteristic
31C2×#14524022C2211yescharacteristic
32C2×#14524022C2211yescharacteristic, complemented
33C2×#14524020—21no—
34C2×#14524020—21no—
35C2×#14524017C2211yescharacteristic
36C2×#14524016—21no—
37C2×#14524011—21no—
38C2×C4×Dic134C2211yescharacteristic, complemented
39C2×C4×D268C2211yescharacteristic
40C2×D4×Dic67—21no—
41C22×C4⋊Dic67C2211yescharacteristic
42C22×C4⋊Dic67C2211yescharacteristic, complemented
43C2×C22⋊C4×D67—21no—
44#16863756C2218yescomplemented
45#16863732C2218yescomplemented
46#16863710C2218yescomplemented
47#16863677C2218yescomplemented
48#16863642C2218yescomplemented
49#16863637C2218yescomplemented
50#16863619C2218yescomplemented
51#16863560C2218yescomplemented
52#16863549C2218yescomplemented
53#16863498C2218yescomplemented
54C2×#14523977C2211yescharacteristic, complemented
55C2×#14523977C2211yescharacteristic, complemented
56C2×#14523977C2211yescharacteristic, complemented
57#16863398C2218yescomplemented
58C2×#14523968C2211yescharacteristic, complemented
59C2×#14523968C2211yescharacteristic, complemented
60C2×#14523968C2211yescharacteristic, complemented
61C2×#14523968C2211yescharacteristic, complemented
62C2×#14523965C2211yescharacteristic
63C2×#14523965C2211yescharacteristic
64C2×#14523965C2211yescharacteristic
65C2×#14523965C2211yescharacteristic
66C2×#14523965C2211yescharacteristic
67C2×#14523965C2211yescharacteristic
68C2×#14523965C2218yescomplemented
69C22×M16×C67C2211yescharacteristic, complemented
70C23×C8×C67C2211yescharacteristic
71C2×C4×D4×C67C2211yescharacteristic
72#435×C67C2218yescomplemented
73C2×C4⋊C8×C67C2211yescharacteristic, complemented
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×C22⋊C8×C67C2211yescharacteristic, complemented
76C2×#97×C67C2211yescharacteristic, complemented
77C24×D67—21no—
78C2×#11761628—24no—
79C2×#11761628—22no—
80C2×#11761628—42no—
81C2×#11761628C2314yes—
82C22×Dic134—21no—
83C22×Dic134C2311yescharacteristic
84C22×Dic134C2311yescharacteristic
85C22×D268—24no—
86C22×D268—22no—
87C22×D268—21no—
88C22×D268—42no—
89C22×D268C2311yescharacteristic
90C22×D268C2314yes—
91C22×D268C2311yescharacteristic
92C22×C22⋊D67—21no—
93C22×C22⋊D67—21no—
94C23×Dic67—21no—
95C23×Dic67—21no—
96C22×C4×D67—21no—
97C22×C4×D67—21no—
98C2×Dic268—42no—
99C2×Dic268C2314yescomplemented
100C2×#11761617—24no—
101C2×#11761617—42no—
102C2×#11761617C2314yes—
103C2×#11761617C2314yes—
104#14524043—22no—
105#14524043C2314yescomplemented
106#14524034—28no—
107#14524031—22no—
108#14524031C2314yes—
109#14524028—28no—
110#14524022—22no—
111#14524022—22no—
112#14524022—22no—
113#14524022C2314yes—
114#14524022C2314yes—
115#14524022C2314yescomplemented
116#14524020—28no—
117#14524020—28no—
118#14524017—22no—
119#14524017C2314yes—
120#14524016—28no—
121#14524011—28no—
122C4×Dic134—22no—
123C4×Dic134C2314yescomplemented
124C4×D268—22no—
125C4×D268C2314yes—
126D4×Dic67—28no—
127C2×C4⋊Dic67—22no—
128C2×C4⋊Dic67—21no—
129C2×C4⋊Dic67—22no—
130C2×C4⋊Dic67—21no—
131C2×C4⋊Dic67—21no—
132C2×C4⋊Dic67C2311yescharacteristic
133C2×C4⋊Dic67C2314yes—
134C2×C4⋊Dic67C2311yescharacteristic
135C2×C4⋊Dic67C2311yescharacteristic
136C2×C4⋊Dic67C2311yescharacteristic
137C2×C4⋊Dic67C2314yescomplemented
138C2×Dic67⋊C4—21no—
139C2×Dic67⋊C4—21no—
140C2×Dic67⋊C4—21no—
141C2×Dic67⋊C4—21no—
142C2×C22⋊Dic67—21no—
143C2×C22⋊Dic67—21no—
144C2×C22⋊Dic67—21no—
145C2×(C2×D67)⋊C4—21no—
146C2×(C2×D67)⋊C4—21no—
147C2×(C2×D67)⋊C4—21no—
148C2×(C2×D67)⋊C4—21no—
149C22⋊C4×D67—28no—
150C2×C4×Dic67—21no—
151#14523977C2314yescomplemented
152#14523977C2314yescomplemented
153#14523977C2314yescomplemented
154#14523968C2314yescomplemented
155#14523968C2314yescomplemented
156#14523968C2314yescomplemented
157#14523968C2314yescomplemented
158#14523965C2314yes—
159#14523965C2314yes—
160#14523965C2314yes—
161#14523965C2314yes—
162#14523965C2314yes—
163#14523965C2314yes—
164C22×D4×C67D411yescharacteristic
165C23×C4×C67C2311yescharacteristic
166C23×C4×C67C2311yescharacteristic
167C2×M16×C67—42no—
168C2×M16×C67C2314yescomplemented
169C22×C8×C67—42no—
170C22×C8×C67C2311yescharacteristic
171C22×C8×C67C2311yescharacteristic
172C22×C8×C67C2311yescharacteristic
173C22×C8×C67C2311yescharacteristic
174C22×C8×C67C2314yes—
175C4×D4×C67D414yes—
176C4×D4×C67C2314yes—
177C2×C4⋊C4×C67D411yescharacteristic
178C2×C22⋊C4×C67D411yescharacteristic
179C2×C22⋊C4×C67D411yescharacteristic
180C2×C42×C67C2311yescharacteristic
181C4⋊C8×C67C2314yescomplemented
182C22⋊C8×C67C2314yes—
183C22⋊C8×C67C2314yescomplemented
184#97×C67C2314yescomplemented
185C23×D67—21no—
186C23×D67—21no—
187C23×D67—24no—
188C23×D67—44no—
189C23×D67—44no—
190C23×D67—82no—
191#11761628—28no—
192#11761628—44no—
193#11761628—48no—
194C2×Dic134—22no—
195C2×Dic134—22no—
196C2×Dic134—22no—
197C2×Dic134—22no—
198C2×Dic134—21no—
199C2×Dic134—21no—
200C2×Dic134—24no—
201C2×Dic134—82no—
202C2×Dic134C2412yes—
203C2×Dic134C2412yes—
204C2×D268—21no—
205C2×D268—22no—
206C2×D268—22no—
207C2×D268—22no—
208C2×D268—28no—
209C2×D268—24no—
210C2×D268—21no—
211C2×D268—44no—
212C2×D268—48no—
213C2×D268—44no—
214C2×D268#4114yes—
215C2×D268C2412yes—
216C2×D268C2412yes—
217C2×C22⋊D67—24no—
218C2×C22⋊D67—24no—
219C2×C22⋊D67—44no—
220C2×C22⋊D67—82no—
221C22×Dic67—21no—
222C22×Dic67—21no—
223C22×Dic67—21no—
224C22×Dic67—21no—
225C22×Dic67—21no—
226C22×Dic67—21no—
227C22×Dic67—24no—
228C22×Dic67—24no—
229C22×Dic67—82no—
230C22×Dic67—82no—
231C2×C4×D67—24no—
232C2×C4×D67—24no—
233C2×C4×D67—44no—
234C2×C4×D67—82no—
235Dic268—44no—
236#11761617—28no—
237#11761617—44no—
238C4⋊Dic67—21no—
239C4⋊Dic67—24no—
240C4⋊Dic67—21no—
241C4⋊Dic67—21no—
242C4⋊Dic67—24no—
243C4⋊Dic67—24no—
244C4⋊Dic67—21no—
245C4⋊Dic67C2412yes—
246C4⋊Dic67C2412yes—
247C4⋊Dic67C2412yes—
248C4⋊Dic67C2412yes—
249Dic67⋊C4—24no—
250Dic67⋊C4—24no—
251Dic67⋊C4—24no—
252Dic67⋊C4—24no—
253C22⋊Dic67—24no—
254C22⋊Dic67—24no—
255C22⋊Dic67—24no—
256(C2×D67)⋊C4—24no—
257(C2×D67)⋊C4—24no—
258(C2×D67)⋊C4—24no—
259(C2×D67)⋊C4—24no—
260C4×Dic67—24no—
261C24×C67C2×D411yescharacteristic
262C24×C67C2×D411yescharacteristic
263C2×D4×C67—24no—
264C2×D4×C67C2×D414yes—
265C22×C4×C67—22no—
266C22×C4×C67—22no—
267C22×C4×C67—22no—
268C22×C4×C67—22no—
269C22×C4×C67C2×D411yescharacteristic
270C22×C4×C67C2×D411yescharacteristic
271C22×C4×C67C2×D411yescharacteristic
272C22×C4×C67C2×D411yescharacteristic
273C22×C4×C67C2×D412yes—
274C22×C4×C67C2×D412yes—
275C22×C4×C67C2412yes—
276C22×C4×C67C2412yes—
277C22×C4×C67C2411yescharacteristic
278M16×C67—44no—
279C2×C8×C67—22no—
280C2×C8×C67—22no—
281C2×C8×C67—22no—
282C2×C8×C67—22no—
283C2×C8×C67—44no—
284C2×C8×C67C2412yes—
285C2×C8×C67C2412yes—
286C2×C8×C67C2412yes—
287C2×C8×C67C2412yes—
288C4⋊C4×C67C2×D414yes—
289C22⋊C4×C67C2×D414yes—
290C22⋊C4×C67C2×D414yes—
291C42×C67C2×D412yes—
292C42×C67C2412yes—
293C23×C67—22no—
294C23×C67—22no—
295C23×C67—22no—
296C23×C67—22no—
297C23×C67—22no—
298C23×C67#13714yes—
299C23×C67C22×D412yes—
300C23×C67C22×D412yes—
301C23×C67C22×D411yescharacteristic
302C22×D67—24no—
303C22×D67—22no—
304C22×D67—22no—
305C22×D67—48no—
306C22×D67—42no—
307C22×D67—42no—
308C22×D67—42no—
309C22×D67—48no—
310C22×D67—42no—
311C22×D67—42no—
312C22×D67—84no—
313C22×D67—816no—
314D4×C67—28no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—24no—
320C2×C4×C67—24no—
321C2×C4×C67—22no—
322C2×C4×C67—22no—
323C2×C4×C67—22no—
324C2×C4×C67—22no—
325C2×C4×C67C22×D412yes—
326C2×C4×C67C22×D412yes—
327C2×C4×C67C22×D412yes—
328C2×C4×C67C22×D412yes—
329C2×C4×C67C22×D411yescharacteristic
330C2×C4×C67C2×#4112yes—
331C2×C4×C67H(5,𝔽2)12yes—
332C2×C4×C67C2511yescharacteristic
333C22⋊D67—48no—
334C22⋊D67—84no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—22no—
338C2×Dic67—22no—
339C2×Dic67—22no—
340C2×Dic67—22no—
341C2×Dic67—42no—
342C2×Dic67—42no—
343C2×Dic67—42no—
344C2×Dic67—42no—
345C2×Dic67—42no—
346C2×Dic67—42no—
347C2×Dic67—84no—
348C2×Dic67—84no—
349D268—24no—
350D268—22no—
351D268—22no—
352D268—22no—
353D268—48no—
354D268—42no—
355D268C2×#4114yes—
356C4×D67—48no—
357C4×D67—84no—
358Dic134—22no—
359Dic134—22no—
360Dic134—22no—
361Dic134—22no—
362Dic134—42no—
363Dic134—42no—
364Dic134—84no—
365C8×C67—22no—
366C8×C67—22no—
367C8×C67—22no—
368C8×C67—22no—
369C22×C67—22no—
370C22×C67—28no—
371C22×C67—22no—
372C22×C67—22no—
373C22×C67—22no—
374C22×C67—22no—
375C22×C67—44no—
376C22×C67#54612yes—
377C22×C67C2×#13714yes—
378C22×C67C2×#13712yes—
379C22×C67#57612yes—
380C22×C67C23×D411yescharacteristic
381C2×D67—24no—
382C2×D67—48no—
383C2×D67—42no—
384C2×D67—42no—
385C2×D67—42no—
386C2×D67—42no—
387C2×D67—42no—
388C2×D67—816no—
389C2×D67—84no—
390C4×C67—22no—
391C4×C67—22no—
392C4×C67—22no—
393C4×C67—22no—
394C4×C67#54612yes—
395C4×C67C22×#4111yescharacteristic
396C4×C67C2×H(5,𝔽2)11yescharacteristic
397Dic67—42no—
398Dic67—42no—
399Dic67—42no—
400Dic67—42no—
401Dic67—42no—
402Dic67—42no—
403C2×#3314—671nomaximal, Sylow
404C2×C67—24no—
405C2×C67—42no—
406C2×C67#331414yescomplemented
407C2×C67C2×#54611yescharacteristic
408C2×C67C22×#13711yescharacteristic
409C2×C67C2×#57611yescharacteristic
410D67—44no—
411D67—82no—
412C2×#554—671no—
413C2×#546—671no—
414#3314—6716no—
415C2×#489—671no—
416C2×#484—671no—
417C2×#480—671no—
418C2×#474—671no—
419C2×#468—671no—
420C2×#467—671no—
421C2×#464—671no—
422C2×#452—671no—
423C2×#450—671no—
424C2×#440—671no—
425C2×#435D6711yescharacteristic, complemented
426C2×#417—671no—
427C22×#102—671no—
428C67C2×#331411yescharacteristic, complemented, Sylow
429C22×#41—671no—
430C23×D4—671no—
431C22×Q16—671no—
432C22×SD16—671no—
433C22×SD16—671no—
434C22×M16C2×D6711yescharacteristic, complemented
435C23×C8C2×D6711yescharacteristic
436#554—678no—
437#554—1344no—
438#546—678no—
439#546—1344no—
440C2×C4⋊Q8—671no—
441C2×#125—1341no—
442C2×#124—671no—
443C2×#123—1341no—
444C2×C22⋊Q8—671no—
445C2×C22⋊Q8—671no—
446C2×C22⋊Q8—671no—
447C2×C22⋊Q8—1341no—
448C2×C22⋊Q8—1341no—
449C2×#121—671no—
450C2×#121—1341no—
451C2×#120—1341no—
452C2×C4×Q8—671no—
453C2×C4×D4—671no—
454C2×C4×D4—1341no—
455C2×C4×D4C2×D6711yescharacteristic
456C22×C4⋊C4—671no—
457C22×C4⋊C4—671no—
458C22×C22⋊C4—1341no—
459#489—678no—
460#484—678no—
461#480—678no—
462#474—678no—
463#468—678no—
464#467—678no—
465#464—678no—
466#452—678no—
467#450—678no—
468#440—678no—
469#435C2×D6718yescomplemented
470C2×#107—671no—
471C2×#107—671no—
472C2×#107—671no—
473C2×C4⋊C8C2×D6711yescharacteristic, complemented
474#417—678no—
475C2×#103—671no—
476C2×#103—671no—
477C2×#103—671no—
478C2×#103—671no—
479C2×#102—671no—
480C2×#102—671no—
481C2×#102—671no—
482C2×#102—671no—
483C2×#102—671no—
484C2×#102—678no—
485C2×#102—671no—
486C2×C22⋊C8C2×D6711yescharacteristic
487C2×C22⋊C8C2×D6711yescharacteristic, complemented
488C2×#97C2×D6711yescharacteristic, complemented
489C25—1341no—
490C2×#41—2682no—
491C2×#41—674no—
492C2×#41—1344no—
493C2×#41—1342no—
494C22×Q8—671no—
495C22×Q8—671no—
496C22×Q8—1341no—
497C22×D4—2682no—
498C22×D4—674no—
499C22×D4—671no—
500C22×D4—671no—
501C22×D4—1344no—
502C22×D4—1341no—
503C22×D4—1341no—
504C22×D4—1341no—
505C22×D4—1342no—
506C22×D4D26811yescharacteristic
507C23×C4—1341no—
508C23×C4—1341no—
509C23×C4—1341no—
510C23×C4—1341no—
511C23×C4C22×D6711yescharacteristic
512C23×C4C22×D6711yescharacteristic
513C2×Q16—2682no—
514C2×Q16—674no—
515C2×SD16—2682no—
516C2×SD16—674no—
517C2×SD16—674no—
518C2×SD16—1344no—
519C2×M16—42no—
520C2×M16C22×D6714yescomplemented
521C22×C8—42no—
522C22×C8C22×D6711yescharacteristic
523C22×C8C22×D6711yescharacteristic
524C22×C8C22×D6711yescharacteristic
525C22×C8C22×D6711yescharacteristic
526C22×C8C22×D6714yes—
527C4⋊Q8—674no—
528C4⋊Q8—1342no—
529#125—1348no—
530#124—674no—
531#124—1342no—
532#123—1348no—
533C22⋊Q8—674no—
534C22⋊Q8—674no—
535C22⋊Q8—674no—
536C22⋊Q8—1342no—
537C22⋊Q8—1342no—
538C22⋊Q8—1342no—
539C22⋊Q8—1348no—
540C22⋊Q8—1348no—
541#121—674no—
542#121—1342no—
543#121—1348no—
544#120—1348no—
545C4×Q8—674no—
546C4×Q8—1342no—
547C4×D4—674no—
548C4×D4—1348no—
549C4×D4—1342no—
550C4×D4D26814yes—
551C4×D4C22×D6714yes—
552C2×C4⋊C4—671no—
553C2×C4⋊C4—671no—
554C2×C4⋊C4—671no—
555C2×C4⋊C4—674no—
556C2×C4⋊C4—674no—
557C2×C4⋊C4—671no—
558C2×C4⋊C4—1341no—
559C2×C4⋊C4—1341no—
560C2×C4⋊C4—1342no—
561C2×C4⋊C4—1342no—
562C2×C4⋊C4—1341no—
563C2×C4⋊C4—1341no—
564C2×C4⋊C4—1341no—
565C2×C4⋊C4—1341no—
566C2×C4⋊C4—1341no—
567C2×C4⋊C4D26811yescharacteristic
568C2×C22⋊C4—1341no—
569C2×C22⋊C4—1341no—
570C2×C22⋊C4—1341no—
571C2×C22⋊C4—1341no—
572C2×C22⋊C4—1341no—
573C2×C22⋊C4—1341no—
574C2×C22⋊C4—1341no—
575C2×C22⋊C4—1348no—
576C2×C22⋊C4D26811yescharacteristic
577C2×C22⋊C4D26811yescharacteristic
578C2×C42—1341no—
579C2×C42C22×D6711yescharacteristic
580#107—674no—
581#107—674no—
582#107—674no—
583C4⋊C8C22×D6714yescomplemented
584#103—674no—
585#103—674no—
586#103—674no—
587#103—674no—
588#102—674no—
589#102—674no—
590#102—674no—
591#102—674no—
592#102—674no—
593#102—674no—
594C22⋊C8C22×D6714yes—
595C22⋊C8C22×D6714yescomplemented
596#97C22×D6714yescomplemented
597C24—2684no—
598C24—2684no—
599C24—5362no—
600C24—1341no—
601C24—1344no—
602C24—1341no—
603C24C2×D26811yescharacteristic
604C24C2×D26811yescharacteristic
605#41—2688no—
606#41—2684no—
607#41—1348no—
608C2×Q8—5362no—
609C2×Q8—672no—
610C2×Q8—672no—
611C2×Q8—1342no—
612C2×Q8—1342no—
613C2×Q8—1342no—
614C2×Q8—1342no—
615C2×Q8—1341no—
616C2×Q8—1341no—
617C2×Q8—1344no—
618C2×D4—24no—
619C2×D4—2684no—
620C2×D4—2688no—
621C2×D4—2684no—
622C2×D4—2684no—
623C2×D4—5362no—
624C2×D4—674no—
625C2×D4—672no—
626C2×D4—672no—
627C2×D4—1348no—
628C2×D4—1344no—
629C2×D4—1344no—
630C2×D4—1344no—
631C2×D4—1341no—
632C2×D4—1341no—
633C2×D4—1342no—
634C2×D4—1342no—
635C2×D4—1342no—
636C2×D4C2×D26814yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—2684no—
642C22×C4—5362no—
643C22×C4—5362no—
644C22×C4—5362no—
645C22×C4—1341no—
646C22×C4—1341no—
647C22×C4—1341no—
648C22×C4—1341no—
649C22×C4—1341no—
650C22×C4—1341no—
651C22×C4—1344no—
652C22×C4—1344no—
653C22×C4—1344no—
654C22×C4—1344no—
655C22×C4C2×D26812yes—
656C22×C4C2×D26812yes—
657C22×C4C2×D26811yescharacteristic
658C22×C4C2×D26811yescharacteristic
659C22×C4C2×D26811yescharacteristic
660C22×C4C2×D26811yescharacteristic
661C22×C4C23×D6712yes—
662C22×C4C23×D6712yes—
663C22×C4C23×D6711yescharacteristic
664Q16—2684no—
665SD16—2684no—
666SD16—1348no—
667M16—44no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—44no—
673C2×C8C23×D6712yes—
674C2×C8C23×D6712yes—
675C2×C8C23×D6712yes—
676C2×C8C23×D6712yes—
677C4⋊C4—672no—
678C4⋊C4—672no—
679C4⋊C4—672no—
680C4⋊C4—672no—
681C4⋊C4—1341no—
682C4⋊C4—1344no—
683C4⋊C4—1344no—
684C4⋊C4—1341no—
685C4⋊C4—1341no—
686C4⋊C4—1341no—
687C4⋊C4—1344no—
688C4⋊C4—1344no—
689C4⋊C4—1344no—
690C4⋊C4—1344no—
691C4⋊C4—1344no—
692C4⋊C4C2×D26814yes—
693C22⋊C4—1344no—
694C22⋊C4—1344no—
695C22⋊C4—1344no—
696C22⋊C4—1344no—
697C22⋊C4—1344no—
698C22⋊C4—1344no—
699C22⋊C4—1344no—
700C22⋊C4C2×D26814yes—
701C22⋊C4C2×D26814yes—
702C42—1344no—
703C42C2×D26812yes—
704C42C23×D6712yes—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—2688no—
711C23—2682no—
712C23—2682no—
713C23—2682no—
714C23—2688no—
715C23—2682no—
716C23—2682no—
717C23—5364no—
718C23—53616no—
719C23—1342no—
720C23—1344no—
721C23—1342no—
722C23#1452407614yes—
723C23C22×D26812yes—
724C23C22×D26812yes—
725C23C22×D26811yescharacteristic
726Q8—2682no—
727Q8—2682no—
728Q8—5364no—
729Q8—1342no—
730Q8—1342no—
731Q8—1342no—
732Q8—1342no—
733D4—28no—
734D4—2688no—
735D4—2688no—
736D4—2682no—
737D4—5364no—
738D4—674no—
739D4—1344no—
740D4—1342no—
741D4—1342no—
742D4—1342no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—2688no—
754C2×C4—2682no—
755C2×C4—2682no—
756C2×C4—2682no—
757C2×C4—2682no—
758C2×C4—2682no—
759C2×C4—2682no—
760C2×C4—5364no—
761C2×C4—5364no—
762C2×C4—5364no—
763C2×C4—1342no—
764C2×C4—1342no—
765C2×C4—1342no—
766C2×C4—1342no—
767C2×C4—1342no—
768C2×C4—1342no—
769C2×C4C22×D26812yes—
770C2×C4C22×D26812yes—
771C2×C4C22×D26812yes—
772C2×C4C22×D26812yes—
773C2×C4C22×D26811yescharacteristic
774C2×C4#41×D6712yes—
775C2×C4#1452408812yes—
776C2×C4C24×D6711yescharacteristic
777C8—22no—
778C8—22no—
779C8—22no—
780C8—22no—
781C22—28no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—44no—
788C22—2688no—
789C22—2682no—
790C22—2682no—
791C22—2682no—
792C22—2682no—
793C22—2682no—
794C22—53616no—
795C22—5364no—
796C22—1344no—
797C22#1686404112yes—
798C22C2×#1452407614yes—
799C22C2×#1452407612yes—
800C22#1686420112yes—
801C22C23×D26811yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—2682no—
807C4—2682no—
808C4—2682no—
809C4—2682no—
810C4—2682no—
811C4—2682no—
812C4#1686404112yes—
813C4C2×#41×D6711yescharacteristic
814C4C2×#1452408811yescharacteristic
815C2—24no—
816C2—42no—
817C2—2684no—
818C2—5362no—
819C2#2257229214yesdirect product factor
820C2C2×#1686404111yescharacteristic
821C2C22×#1452407611yescharacteristic
822C2C2×#1686420111yescharacteristic
subgroupG/H
centerC23C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#435×C67C2
socleC23×C67C22×D4
prime radicalC2×#16864042C2
hypercenterC2×#435D67
hypocenterC67C2×#3314
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16864103C2semidirect
3. #22572292C2direct (N × H)
4. C2×#16863756C2semidirect
5. C2×#16863732C2semidirect
6. C2×#16863710C2semidirect
7. C2×#16863677C2semidirect
8. C2×#16863642C2semidirect
9. C2×#16863637C2semidirect
10. C2×#16863619C2semidirect
11. C2×#16863560C2semidirect
12. C2×#16863549C2semidirect
13. C2×#16863498C2semidirect
14. C2×#16863398C2semidirect
15. C22×#14523965C2semidirect
16. C2×#435×C67C2semidirect
19. C22×Dic268C22semidirect
23. #16864103C22semidirect
26. C2×#14524043C22semidirect
32. C2×#14524022C22semidirect
38. C2×C4×Dic134C22semidirect
42. C22×C4⋊Dic67C22semidirect
44. #16863756C22semidirect
45. #16863732C22semidirect
46. #16863710C22semidirect
47. #16863677C22semidirect
48. #16863642C22semidirect
49. #16863637C22semidirect
50. #16863619C22semidirect
51. #16863560C22semidirect
52. #16863549C22semidirect
53. #16863498C22semidirect
54. C2×#14523977C22semidirect
55. C2×#14523977C22semidirect
56. C2×#14523977C22semidirect
57. #16863398C22semidirect
58. C2×#14523968C22semidirect
59. C2×#14523968C22semidirect
60. C2×#14523968C22semidirect
61. C2×#14523968C22semidirect
68. C2×#14523965C22semidirect
69. C22×M16×C67C22semidirect
72. #435×C67C22semidirect
73. C2×C4⋊C8×C67C22semidirect
75. C2×C22⋊C8×C67C22semidirect
76. C2×#97×C67C22semidirect
99. C2×Dic268C23semidirect
105. #14524043C23semidirect
115. #14524022C23semidirect
123. C4×Dic134C23semidirect
137. C2×C4⋊Dic67C23semidirect
151. #14523977C23semidirect
152. #14523977C23semidirect
153. #14523977C23semidirect
154. #14523968C23semidirect
155. #14523968C23semidirect
156. #14523968C23semidirect
157. #14523968C23semidirect
168. C2×M16×C67C23semidirect
181. C4⋊C8×C67C23semidirect
183. C22⋊C8×C67C23semidirect
184. #97×C67C23semidirect
406. C2×C67#3314semidirect
425. C2×#435D67semidirect
428. C67C2×#3314semidirect
434. C22×M16C2×D67semidirect
469. #435C2×D67semidirect
473. C2×C4⋊C8C2×D67semidirect
487. C2×C22⋊C8C2×D67semidirect
488. C2×#97C2×D67semidirect
520. C2×M16C22×D67semidirect
583. C4⋊C8C22×D67semidirect
595. C22⋊C8C22×D67semidirect
596. #97C22×D67semidirect
819. C2#22572292direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641032
C2×#168640422
#225722922
C2×#168637562
C2×#168637322
C2×#168637102
C2×#168636772
C2×#168636422
C2×#168636372
C2×#168636192
C2×#168635602
C2×#168635492
C2×#168634982
C2×#168633982
C22×#145239652
C2×#435×C672
C2×#331467