Finite Group Databasebeta

← C2×#22570035 #31723385

Subgroups — C2×#22570035 #31723385

Order 17152.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864023C211yesmaximal, characteristic, complemented
2C2×#16863868C211yesmaximal, characteristic
3#22570035C2116yesmaximal, direct product factor
4C2×#16863698C211yesmaximal, characteristic, complemented
5C2×#16863697C211yesmaximal, characteristic, complemented
6C2×#16863696C211yesmaximal, characteristic, complemented
7C2×#16863695C211yesmaximal, characteristic, complemented
8C2×#16863685C211yesmaximal, characteristic, complemented
9C2×#16863674C211yesmaximal, characteristic, complemented
10C2×#16863673C211yesmaximal, characteristic, complemented
11C2×#16863435C211yesmaximal, characteristic, complemented
12C2×#16863431C211yesmaximal, characteristic, complemented
13C2×#16863421C211yesmaximal, characteristic, complemented
14C2×#16863399C211yesmaximal, characteristic
15C2×#102×D67C211yesmaximal, characteristic
16C2×#476×C67C211yesmaximal, characteristic, complemented
17C22×D4×D67C2211yescharacteristic
18C22×#11761611C2211yescharacteristic
19C22×C8×D67C2211yescharacteristic
20#16864023—24no—
21#16864023C2218yescomplemented
22C2×#14524042C2211yescharacteristic, complemented
23C2×#14524041—21no—
24C2×#14524035C2211yescharacteristic, complemented
25C2×#14524034C2211yescharacteristic, complemented
26C2×#14524033—21no—
27C2×#14524021—21no—
28C2×#14524019—21no—
29#16863868—24no—
30#16863868C2218yes—
31C2×C4×D268C2211yescharacteristic
32C2×D4×Dic67C2211yescharacteristic
33C2×#14524005C2211yescharacteristic
34C2×C4×C22⋊D67—21no—
35C2×(C22⋊D67)⋊C4—21no—
36C2×#14524001C2211yescharacteristic
37C2×#14524001C2211yescharacteristic
38C2×#14524000C2211yescharacteristic
39C2×C4⋊C4×D67C2211yescharacteristic
40C22×(C2×D67)⋊C4—21no—
41C2×C22⋊C4×D67—21no—
42#16863698C2218yescomplemented
43#16863697C2218yescomplemented
44#16863696C2218yescomplemented
45#16863695C2218yescomplemented
46#16863685C2218yescomplemented
47#16863674C2218yescomplemented
48#16863673C2218yescomplemented
49#16863435C2218yescomplemented
50#16863431C2218yescomplemented
51C2×#14523977C2211yescharacteristic, complemented
52C2×#14523976C2211yescharacteristic, complemented
53C2×#14523976C2211yescharacteristic, complemented
54C2×#14523976C2211yescharacteristic, complemented
55C2×#14523975C2211yescharacteristic, complemented
56C2×#14523974C2211yescharacteristic, complemented
57#16863421C2218yescomplemented
58C2×C4⋊(C67⋊C8)C2211yescharacteristic, complemented
59C2×Dic67⋊C8C2211yescharacteristic, complemented
60C2×Dic67⋊C8C2211yescharacteristic, complemented
61#16863399C2218yes—
62C2×#14523965C2211yescharacteristic
63C2×#14523965C2211yescharacteristic
64C2×#14523964C2211yescharacteristic
65C2×#14523964C2211yescharacteristic
66C2×#14523963C2211yescharacteristic
67C2×#14523963C2211yescharacteristic
68#102×D67C2218yes—
69C2×C4⋊Q8×C67C2211yescharacteristic, complemented
70C2×C4×D4×C67C2211yescharacteristic
71#476×C67C2218yescomplemented
72C2×#106×C67C2211yescharacteristic, complemented
73C2×#106×C67C2211yescharacteristic, complemented
74C2×C4⋊C8×C67C2211yescharacteristic, complemented
75C2×#102×C67C2211yescharacteristic
76C2×#102×C67C2211yescharacteristic
77C24×D67—21no—
78C22×Dic134—21no—
79C22×D268C2311yescharacteristic
80C22×C22⋊D67—21no—
81C2×D4×D67—22no—
82C2×D4×D67—24no—
83C2×D4×D67Q818yescomplemented
84C2×D4×D67C2314yes—
85C23×Dic67—21no—
86C22×C4×D67—21no—
87C22×C4×D67—21no—
88C22×C4×D67—21no—
89C22×C4×D67C2311yescharacteristic
90C2×#11761611—24no—
91C2×#11761611C2314yes—
92C22×C67⋊C8C2311yescharacteristic
93C22×C67⋊C8C2311yescharacteristic
94C2×C8×D67—24no—
95C2×C8×D67C2314yes—
96#14524042—22no—
97#14524042C2314yescomplemented
98#14524041—28no—
99#14524035—22no—
100#14524035C2314yescomplemented
101#14524034—22no—
102#14524034C2314yescomplemented
103#14524033—28no—
104#14524021—28no—
105#14524019—28no—
106C4×D268—22no—
107C4×D268C2314yes—
108D4×Dic67—22no—
109D4×Dic67C2314yes—
110#14524005—22no—
111#14524005C2314yes—
112C4×C22⋊D67—28no—
113(C22⋊D67)⋊C4—28no—
114#14524001—22no—
115#14524001—22no—
116#14524001C2314yes—
117#14524001C2314yes—
118#14524000D414yes—
119#14524000C2314yes—
120C2×C4⋊Dic67—21no—
121C2×C4⋊Dic67C2311yescharacteristic
122C2×C4⋊Dic67C2311yescharacteristic
123C2×C4⋊Dic67C2311yescharacteristic
124C2×Dic67⋊C4—21no—
125C2×Dic67⋊C4—21no—
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4D411yescharacteristic
130C2×Dic67⋊C4D411yescharacteristic
131C4⋊C4×D67—22no—
132C4⋊C4×D67C2314yes—
133C2×C22⋊Dic67—21no—
134C2×(C2×D67)⋊C4—21no—
135C2×(C2×D67)⋊C4—21no—
136C2×(C2×D67)⋊C4—21no—
137C2×(C2×D67)⋊C4—28no—
138C2×(C2×D67)⋊C4—21no—
139C2×(C2×D67)⋊C4D411yescharacteristic
140C2×(C2×D67)⋊C4D411yescharacteristic
141C22⋊C4×D67—28no—
142C2×C4×Dic67—21no—
143C2×C4×Dic67—21no—
144C2×C4×Dic67C2311yescharacteristic
145#14523977C2314yescomplemented
146#14523976C2314yescomplemented
147#14523976C2314yescomplemented
148#14523976C2314yescomplemented
149#14523975C2314yescomplemented
150#14523974C2314yescomplemented
151C4⋊(C67⋊C8)C2314yescomplemented
152Dic67⋊C8C2314yescomplemented
153Dic67⋊C8C2314yescomplemented
154#14523965C2314yes—
155#14523965C2314yes—
156#14523964C2314yes—
157#14523964C2314yes—
158#14523963C2314yes—
159#14523963C2314yes—
160C22×Q8×C67—21no—
161C22×D4×C67C2311yescharacteristic
162C23×C4×C67—21no—
163C22×C8×C67C2311yescharacteristic
164C22×C8×C67C2311yescharacteristic
165C4⋊Q8×C67—22no—
166C4⋊Q8×C67C2314yescomplemented
167C4×D4×C67—22no—
168C4×D4×C67C2314yes—
169C2×C4⋊C4×C67—21no—
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C22⋊C4×C67—21no—
174C2×C42×C67C2311yescharacteristic
175#106×C67C2314yescomplemented
176#106×C67C2314yescomplemented
177C4⋊C8×C67C2314yescomplemented
178#102×C67C2314yes—
179#102×C67C2314yes—
180C23×D67—21no—
181C23×D67—28no—
182C23×D67—24no—
183C23×D67—82no—
184C23×D67—82no—
185C23×D67C2×D411yescharacteristic
186C2×Dic134—24no—
187C2×Dic134—82no—
188C2×D268—21no—
189C2×D268—22no—
190C2×D268C2×Q814yes—
191C2×D268C2412yes—
192C2×C22⋊D67—28no—
193C2×C22⋊D67—24no—
194D4×D67—216no—
195D4×D67—28no—
196D4×D67C2×Q8116yescomplemented
197C22×Dic67—21no—
198C22×Dic67—21no—
199C22×Dic67—21no—
200C22×Dic67—24no—
201C22×Dic67—82no—
202C22×Dic67C2×D411yescharacteristic
203C22×Dic67C2×D411yescharacteristic
204C22×Dic67C2×D411yescharacteristic
205C2×C4×D67—24no—
206C2×C4×D67—24no—
207C2×C4×D67—24no—
208C2×C4×D67—82no—
209C2×C4×D67—82no—
210C2×C4×D67—82no—
211C2×C4×D67C2×D412yes—
212C2×C4×D67C2×Q814yes—
213C2×C4×D67#4114yes—
214C2×C4×D67C2412yes—
215#11761611—28no—
216C2×C67⋊C8—22no—
217C2×C67⋊C8—22no—
218C2×C67⋊C8C2412yes—
219C2×C67⋊C8C2412yes—
220C8×D67—28no—
221C4⋊Dic67—21no—
222C4⋊Dic67—21no—
223C4⋊Dic67—21no—
224C4⋊Dic67—24no—
225C4⋊Dic67C2412yes—
226C4⋊Dic67C2412yes—
227C4⋊Dic67C2412yes—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4—24no—
231Dic67⋊C4—24no—
232Dic67⋊C4—24no—
233Dic67⋊C4C2×D414yes—
234Dic67⋊C4C2×D414yes—
235C22⋊Dic67—24no—
236(C2×D67)⋊C4—24no—
237(C2×D67)⋊C4—24no—
238(C2×D67)⋊C4—24no—
239(C2×D67)⋊C4—24no—
240(C2×D67)⋊C4C2×D414yes—
241(C2×D67)⋊C4C2×D414yes—
242C4×Dic67—24no—
243C4×Dic67—24no—
244C4×Dic67C2×D412yes—
245C4×Dic67C2412yes—
246C24×C67—21no—
247C2×Q8×C67—24no—
248C2×Q8×C67—82no—
249C2×D4×C67—21no—
250C2×D4×C67—22no—
251C2×D4×C67C2×Q814yes—
252C2×D4×C67C2412yes—
253C22×C4×C67—21no—
254C22×C4×C67—21no—
255C22×C4×C67—21no—
256C22×C4×C67—24no—
257C22×C4×C67—82no—
258C22×C4×C67C2×D411yescharacteristic
259C22×C4×C67C2×D411yescharacteristic
260C22×C4×C67C2411yescharacteristic
261C2×C8×C67—22no—
262C2×C8×C67—22no—
263C2×C8×C67C2412yes—
264C2×C8×C67C2412yes—
265C4⋊C4×C67—24no—
266C4⋊C4×C67—21no—
267C4⋊C4×C67—21no—
268C4⋊C4×C67—21no—
269C4⋊C4×C67C2412yes—
270C4⋊C4×C67C2412yes—
271C4⋊C4×C67C2412yes—
272C22⋊C4×C67—24no—
273C42×C67C2×D412yes—
274C42×C67C2412yes—
275C23×C67—24no—
276C23×C67—22no—
277C23×C67—42no—
278C23×C67—42no—
279C23×C67C22×D411yescharacteristic
280C22×D67—22no—
281C22×D67—22no—
282C22×D67—24no—
283C22×D67—22no—
284C22×D67—216no—
285C22×D67—42no—
286C22×D67—42no—
287C22×D67—816no—
288C22×D67—84no—
289C22×D67—84no—
290C22×D67C22⋊Q814yes—
291C22×D67C22×D412yes—
292Q8×C67—84no—
293D4×C67—24no—
294D4×C67—22no—
295D4×C67C22×Q814yes—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—42no—
302C2×C4×C67—42no—
303C2×C4×C67—42no—
304C2×C4×C67—84no—
305C2×C4×C67C22×D412yes—
306C2×C4×C67C22×D412yes—
307C2×C4×C67C22×D411yescharacteristic
308C2×C4×C67C22×Q812yes—
309C2×C4×C67C2×#4112yes—
310C2×C4×C67C2511yescharacteristic
311C22⋊D67—216no—
312C2×Dic67—22no—
313C2×Dic67—22no—
314C2×Dic67—22no—
315C2×Dic67—22no—
316C2×Dic67—22no—
317C2×Dic67—42no—
318C2×Dic67—42no—
319C2×Dic67—42no—
320C2×Dic67—84no—
321C2×Dic67C22⋊Q814yes—
322C2×Dic67C22×D412yes—
323C2×Dic67C22×D412yes—
324C2×Dic67C22×D412yes—
325D268—24no—
326D268—22no—
327D268C22×Q814yes—
328C4×D67—84no—
329C4×D67—84no—
330C4×D67—84no—
331C4×D67C22⋊Q818yes—
332C4×D67C22×Q814yes—
333C4×D67C2×#4114yes—
334Dic134—84no—
335C8×C67—22no—
336C8×C67—22no—
337C67⋊C8—22no—
338C67⋊C8—22no—
339C22×C67—24no—
340C22×C67—48no—
341C22×C67—42no—
342C22×C67—42no—
343C22×C67C2×C22⋊Q812yes—
344C22×C67#57612yes—
345C22×C67#57712yes—
346C22×C67C23×D411yescharacteristic
347C2×D67—28no—
348C2×D67—22no—
349C2×D67—22no—
350C2×D67—24no—
351C2×D67—48no—
352C2×D67—42no—
353C2×D67—42no—
354C2×D67—816no—
355C2×D67C2×C22⋊Q814yes—
356C4×C67—22no—
357C4×C67—22no—
358C4×C67—42no—
359C4×C67—42no—
360C4×C67—42no—
361C4×C67C2×C22⋊Q812yes—
362C4×C67C23×Q811yescharacteristic
363C4×C67C22×#4111yescharacteristic
364Dic67—22no—
365Dic67—22no—
366Dic67—42no—
367Dic67—42no—
368Dic67—42no—
369Dic67C2×C22⋊Q814yes—
370C2×#3081—671nomaximal, Sylow
371C2×C67—44no—
372C2×C67#308114yescomplemented
373C2×C67C22×C22⋊Q811yescharacteristic
374C2×C67C2×#57611yescharacteristic
375C2×C67C2×#57711yescharacteristic
376D67—24no—
377D67—44no—
378C2×#544—671no—
379C2×#518—671no—
380#3081—6716no—
381C2×#478—671no—
382C2×#478—671no—
383C2×#478—671no—
384C2×#478—671no—
385C2×#476—671no—
386C2×#476D6711yescharacteristic, complemented
387C2×#474—671no—
388C2×#474—671no—
389C2×#428—671no—
390C2×#427—671no—
391C2×#424—671no—
392C2×#418—671no—
393C22×#102—671no—
394C67C2×#308111yescharacteristic, complemented, Sylow
395C23×D4—671no—
396C22×M16—671no—
397C23×C8—671no—
398#544—678no—
399#544—1344no—
400C2×C4⋊Q8—671no—
401C2×C4⋊Q8—1341no—
402C2×C4⋊Q8C2×D6711yescharacteristic, complemented
403C2×#125—671no—
404C2×#125—671no—
405C2×#125—1341no—
406C2×C22⋊Q8—1341no—
407C2×C22⋊Q8—1341no—
408#518—678no—
409#518—1344no—
410C2×C4×D4—671no—
411C2×C4×D4—671no—
412C2×C4×D4—671no—
413C2×C4×D4—1341no—
414C2×C4×D4—1341no—
415C2×C4×D4C2×D6711yescharacteristic
416C2×#117—671no—
417C2×#117—671no—
418C2×#117—671no—
419C22×C4⋊C4—671no—
420C22×C22⋊C4—1341no—
421C22×C22⋊C4—1341no—
422#478—678no—
423#478—678no—
424#478—678no—
425#478—678no—
426#476—678no—
427#476C2×D6718yescomplemented
428#474—678no—
429#474—678no—
430#428—678no—
431#427—678no—
432C2×#107—671no—
433C2×#107—671no—
434C2×#107—671no—
435C2×#107—671no—
436C2×#106—671no—
437C2×#106—671no—
438C2×#106C2×D6711yescharacteristic, complemented
439C2×#106C2×D6711yescharacteristic, complemented
440#424—678no—
441C2×C4⋊C8—671no—
442C2×C4⋊C8—671no—
443C2×C4⋊C8—671no—
444C2×C4⋊C8C2×D6711yescharacteristic, complemented
445#418—678no—
446C2×#102—671no—
447C2×#102—671no—
448C2×#102—671no—
449C2×#102—671no—
450C2×#102—671no—
451C2×#102—671no—
452C2×#102—678no—
453C2×#102C2×D6711yescharacteristic
454C2×#102C2×D6711yescharacteristic
455C25—1341no—
456C22×Q8—21no—
457C22×Q8—1341no—
458C22×D4—678no—
459C22×D4—674no—
460C22×D4—671no—
461C22×D4—1342no—
462C22×D4—1344no—
463C22×D4—1341no—
464C22×D4C22×D6711yescharacteristic
465C23×C4—21no—
466C23×C4—671no—
467C23×C4—1341no—
468C23×C4—1341no—
469C23×C4—1341no—
470C23×C4—1341no—
471C2×M16—674no—
472C2×M16—1344no—
473C22×C8—671no—
474C22×C8—671no—
475C22×C8—674no—
476C22×C8—1344no—
477C22×C8C22×D6711yescharacteristic
478C22×C8C22×D6711yescharacteristic
479C4⋊Q8—22no—
480C4⋊Q8—674no—
481C4⋊Q8—1342no—
482C4⋊Q8—1348no—
483C4⋊Q8C22×D6714yescomplemented
484#125—674no—
485#125—674no—
486#125—1342no—
487#125—1348no—
488#125—1342no—
489C22⋊Q8—1348no—
490C22⋊Q8—1348no—
491C4×D4—22no—
492C4×D4—674no—
493C4×D4—674no—
494C4×D4—674no—
495C4×D4—1342no—
496C4×D4—1342no—
497C4×D4—1348no—
498C4×D4—1348no—
499C4×D4—1342no—
500C4×D4C22×D6714yes—
501#117—674no—
502#117—674no—
503#117—674no—
504#117—674no—
505#117—1342no—
506#117—1342no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—671no—
509C2×C4⋊C4—671no—
510C2×C4⋊C4—671no—
511C2×C4⋊C4—671no—
512C2×C4⋊C4—671no—
513C2×C4⋊C4—674no—
514C2×C4⋊C4—1342no—
515C2×C4⋊C4—1341no—
516C2×C4⋊C4—1341no—
517C2×C4⋊C4—1341no—
518C2×C4⋊C4—1341no—
519C2×C4⋊C4—1341no—
520C2×C4⋊C4—1341no—
521C2×C4⋊C4C22×D6711yescharacteristic
522C2×C4⋊C4C22×D6711yescharacteristic
523C2×C4⋊C4C22×D6711yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—671no—
526C2×C22⋊C4—671no—
527C2×C22⋊C4—1348no—
528C2×C22⋊C4—1348no—
529C2×C22⋊C4—1341no—
530C2×C22⋊C4—1341no—
531C2×C22⋊C4—1341no—
532C2×C22⋊C4—1341no—
533C2×C22⋊C4—1341no—
534C2×C42—671no—
535C2×C42—1341no—
536C2×C42—1341no—
537C2×C42C22×D6711yescharacteristic
538#107—674no—
539#107—674no—
540#107—674no—
541#107—674no—
542#106—674no—
543#106—674no—
544#106C22×D6714yescomplemented
545#106C22×D6714yescomplemented
546C4⋊C8—674no—
547C4⋊C8—674no—
548C4⋊C8—674no—
549C4⋊C8C22×D6714yescomplemented
550#102—674no—
551#102—674no—
552#102—674no—
553#102—674no—
554#102—674no—
555#102—674no—
556#102C22×D6714yes—
557#102C22×D6714yes—
558C24—21no—
559C24—5362no—
560C24—5362no—
561C24—671no—
562C24—1344no—
563C24—1348no—
564C24—1341no—
565C2×Q8—24no—
566C2×Q8—82no—
567C2×Q8—5362no—
568C2×Q8—1344no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—6716no—
572C2×D4—674no—
573C2×D4—672no—
574C2×D4—13416no—
575C2×D4—1348no—
576C2×D4—1344no—
577C2×D4—1348no—
578C2×D4—1341no—
579C2×D4—1342no—
580C2×D4Q8×D6714yes—
581C2×D4C23×D6712yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—5362no—
588C22×C4—5362no—
589C22×C4—5362no—
590C22×C4—5362no—
591C22×C4—671no—
592C22×C4—672no—
593C22×C4—674no—
594C22×C4—674no—
595C22×C4—672no—
596C22×C4—671no—
597C22×C4—671no—
598C22×C4—1344no—
599C22×C4—1344no—
600C22×C4—1341no—
601C22×C4—1341no—
602C22×C4—1341no—
603C22×C4—1344no—
604C22×C4—1344no—
605C22×C4D4×D6711yescharacteristic
606C22×C4D4×D6711yescharacteristic
607C22×C4C23×D6711yescharacteristic
608M16—1348no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—672no—
612C2×C8—672no—
613C2×C8—1348no—
614C2×C8—1342no—
615C2×C8—1342no—
616C2×C8C23×D6712yes—
617C2×C8C23×D6712yes—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—674no—
623C4⋊C4—674no—
624C4⋊C4—672no—
625C4⋊C4—672no—
626C4⋊C4—672no—
627C4⋊C4—1344no—
628C4⋊C4—1344no—
629C4⋊C4—1344no—
630C4⋊C4—1344no—
631C4⋊C4—1341no—
632C4⋊C4—1341no—
633C4⋊C4—1341no—
634C4⋊C4—1344no—
635C4⋊C4—1344no—
636C4⋊C4C23×D6712yes—
637C4⋊C4C23×D6712yes—
638C4⋊C4C23×D6712yes—
639C22⋊C4—24no—
640C22⋊C4—674no—
641C22⋊C4—674no—
642C22⋊C4—1344no—
643C22⋊C4—1344no—
644C22⋊C4—1344no—
645C22⋊C4—1344no—
646C22⋊C4—1344no—
647C42—672no—
648C42—672no—
649C42—1344no—
650C42—1344no—
651C42D4×D6712yes—
652C42C23×D6712yes—
653C23—24no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—2682no—
658C23—2682no—
659C23—53616no—
660C23—5364no—
661C23—5364no—
662C23—674no—
663C23—672no—
664C23—13416no—
665C23—1344no—
666C23—1342no—
667C23—1342no—
668C23—1342no—
669C23C2×D4×D6711yescharacteristic
670Q8—84no—
671Q8—5364no—
672D4—24no—
673D4—22no—
674D4—674no—
675D4—13416no—
676D4—1344no—
677D4—1342no—
678D4C2×Q8×D6714yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—2682no—
689C2×C4—2682no—
690C2×C4—2682no—
691C2×C4—5364no—
692C2×C4—5364no—
693C2×C4—5364no—
694C2×C4—5364no—
695C2×C4—674no—
696C2×C4—672no—
697C2×C4—678no—
698C2×C4—674no—
699C2×C4—674no—
700C2×C4—672no—
701C2×C4—672no—
702C2×C4—1342no—
703C2×C4—1342no—
704C2×C4—1342no—
705C2×C4—1342no—
706C2×C4—1342no—
707C2×C4C2×D4×D6712yes—
708C2×C4C2×D4×D6712yes—
709C2×C4C2×D4×D6711yescharacteristic
710C2×C4C2×Q8×D6712yes—
711C2×C4#41×D6712yes—
712C2×C4C24×D6711yescharacteristic
713C8—22no—
714C8—22no—
715C8—1342no—
716C8—1342no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—2688no—
722C22—2682no—
723C22—2682no—
724C22—53616no—
725C22—674no—
726C22—1344no—
727C22—1348no—
728C22—1342no—
729C22—1342no—
730C22C22⋊Q8×D6712yes—
731C22#1686420012yes—
732C22#1686420212yes—
733C22C22×D4×D6711yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—2682no—
740C4—2682no—
741C4—2682no—
742C4—674no—
743C4—1342no—
744C4—1342no—
745C4C22⋊Q8×D6712yes—
746C4C22×Q8×D6711yescharacteristic
747C4C2×#41×D6711yescharacteristic
748C2—44no—
749C2—2684no—
750C2—1344no—
751C2#2257003514yesdirect product factor
752C2C2×C22⋊Q8×D6711yescharacteristic
753C2C2×#1686420011yescharacteristic
754C2C2×#1686420211yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#476×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×D67C22
hypercenterC2×#476D67
hypocenterC67C2×#3081
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16864023C2semidirect
3. #22570035C2direct (N × H)
4. C2×#16863698C2semidirect
5. C2×#16863697C2semidirect
6. C2×#16863696C2semidirect
7. C2×#16863695C2semidirect
8. C2×#16863685C2semidirect
9. C2×#16863674C2semidirect
10. C2×#16863673C2semidirect
11. C2×#16863435C2semidirect
12. C2×#16863431C2semidirect
13. C2×#16863421C2semidirect
16. C2×#476×C67C2semidirect
21. #16864023C22semidirect
22. C2×#14524042C22semidirect
24. C2×#14524035C22semidirect
25. C2×#14524034C22semidirect
42. #16863698C22semidirect
43. #16863697C22semidirect
44. #16863696C22semidirect
45. #16863695C22semidirect
46. #16863685C22semidirect
47. #16863674C22semidirect
48. #16863673C22semidirect
49. #16863435C22semidirect
50. #16863431C22semidirect
51. C2×#14523977C22semidirect
52. C2×#14523976C22semidirect
53. C2×#14523976C22semidirect
54. C2×#14523976C22semidirect
55. C2×#14523975C22semidirect
56. C2×#14523974C22semidirect
57. #16863421C22semidirect
58. C2×C4⋊(C67⋊C8)C22semidirect
59. C2×Dic67⋊C8C22semidirect
60. C2×Dic67⋊C8C22semidirect
69. C2×C4⋊Q8×C67C22semidirect
71. #476×C67C22semidirect
72. C2×#106×C67C22semidirect
73. C2×#106×C67C22semidirect
74. C2×C4⋊C8×C67C22semidirect
83. C2×D4×D67Q8semidirect
97. #14524042C23semidirect
100. #14524035C23semidirect
102. #14524034C23semidirect
145. #14523977C23semidirect
146. #14523976C23semidirect
147. #14523976C23semidirect
148. #14523976C23semidirect
149. #14523975C23semidirect
150. #14523974C23semidirect
151. C4⋊(C67⋊C8)C23semidirect
152. Dic67⋊C8C23semidirect
153. Dic67⋊C8C23semidirect
166. C4⋊Q8×C67C23semidirect
175. #106×C67C23semidirect
176. #106×C67C23semidirect
177. C4⋊C8×C67C23semidirect
196. D4×D67C2×Q8semidirect
372. C2×C67#3081semidirect
386. C2×#476D67semidirect
394. C67C2×#3081semidirect
402. C2×C4⋊Q8C2×D67semidirect
427. #476C2×D67semidirect
438. C2×#106C2×D67semidirect
439. C2×#106C2×D67semidirect
444. C2×C4⋊C8C2×D67semidirect
483. C4⋊Q8C22×D67semidirect
544. #106C22×D67semidirect
545. #106C22×D67semidirect
549. C4⋊C8C22×D67semidirect
751. C2#22570035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640232
C2×#168638682
#225700352
C2×#168636982
C2×#168636972
C2×#168636962
C2×#168636952
C2×#168636852
C2×#168636742
C2×#168636732
C2×#168634352
C2×#168634312
C2×#168634212
C2×#168633992
C2×#102×D672
C2×#476×C672
C2×#308167