Finite Group Databasebeta

← C2×#22573148 #31736352

Subgroups — C2×#22573148 #31736352

Order 17152.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864106C211yesmaximal, characteristic
2#22573148C2116yesmaximal, direct product factor
3C2×#16863806C211yesmaximal, characteristic, complemented
4C2×#16863802C211yesmaximal, characteristic, complemented
5C2×#16863795C211yesmaximal, characteristic, complemented
6C2×#16863703C211yesmaximal, characteristic, complemented
7C2×#16863703C211yesmaximal, characteristic, complemented
8C2×#16863681C211yesmaximal, characteristic, complemented
9C2×#16863693C211yesmaximal, characteristic
10C2×#16863693C211yesmaximal, characteristic
11C2×#16863683C211yesmaximal, characteristic
12C2×#16863527C211yesmaximal, characteristic, complemented
13C2×#16863494C211yesmaximal, characteristic
14C2×#16863494C211yesmaximal, characteristic
15C2×C4×#11761615C211yesmaximal, characteristic
16C2×#557×C67C211yesmaximal, characteristic, complemented
17C22×#11761615C2211yescharacteristic
18#16864106—24no—
19#16864106C2218yes—
20C2×#14524043C2211yescharacteristic
21C2×#14524035C2211yescharacteristic
22C2×#14524035C2211yescharacteristic
23C2×#14524021—21no—
24C2×#14524021—21no—
25C2×#14524019—21no—
26C2×C4×D268C2211yescharacteristic
27C2×C4×D268C2211yescharacteristic
28C2×C4×D268C2211yescharacteristic
29C2×C4⋊C4×D67—21no—
30#16863806C2218yescomplemented
31#16863802C2218yescomplemented
32#16863795C2218yescomplemented
33#16863703C2218yescomplemented
34#16863703C2218yescomplemented
35#16863693C2218yes—
36#16863693C2218yes—
37#16863683C2218yes—
38#16863681C2218yescomplemented
39#16863527C2218yescomplemented
40#16863494C2218yes—
41#16863494C2218yes—
42C4×#11761615C2218yes—
43C2×#14523976C2211yescharacteristic
44C2×#14523976C2211yescharacteristic
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×#14523974C2211yescharacteristic
51C2×#14523974C2211yescharacteristic
52C2×C4⋊(C67⋊C8)C2211yescharacteristic
53C2×C4⋊(C67⋊C8)C2211yescharacteristic
54C2×C4⋊(C67⋊C8)C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
56C2×#14523967C2211yescharacteristic
57C2×#14523967C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×#14523963C2211yescharacteristic
61C2×#14523954C2211yescharacteristic
62C2×#14523954C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64#557×C67—24no—
65#557×C67C2218yescomplemented
66C2×C4⋊Q8×C67—21no—
67C2×C4⋊Q8×C67C2211yescharacteristic
68C2×#125×C67—21no—
69C2×#125×C67—21no—
70C2×#125×C67C2211yescharacteristic
71C2×#125×C67C2211yescharacteristic
72C2×C4×Q8×C67—21no—
73C2×C4×Q8×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic
75C2×C4×Q8×C67C2211yescharacteristic
76C2×C4×Q8×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×D268C2311yescharacteristic
79C22×C4×D67—21no—
80C22×C4×D67—21no—
81C22×C4×D67—21no—
82C2×#11761615Q818yescomplemented
83C2×#11761615C2314yes—
84C22×C67⋊C8C2311yescharacteristic
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2311yescharacteristic
87C22×C67⋊C8C2311yescharacteristic
88#14524043—22no—
89#14524043C2314yes—
90#14524035—22no—
91#14524035—22no—
92#14524035C2314yes—
93#14524035C2314yes—
94#14524021—28no—
95#14524021—28no—
96#14524019—28no—
97C4×D268—22no—
98C4×D268—22no—
99C4×D268—22no—
100C4×D268C2314yes—
101C4×D268C2314yes—
102C4×D268C2314yes—
103C2×C4⋊Dic67—21no—
104C2×C4⋊Dic67C2311yescharacteristic
105C2×C4⋊Dic67C2311yescharacteristic
106C2×C4⋊Dic67C2311yescharacteristic
107C2×Dic67⋊C4—21no—
108C2×Dic67⋊C4—21no—
109C2×Dic67⋊C4—21no—
110C2×Dic67⋊C4—21no—
111C4⋊C4×D67—28no—
112C2×(C2×D67)⋊C4—21no—
113C2×(C2×D67)⋊C4—21no—
114C2×(C2×D67)⋊C4—21no—
115#14523976C2314yes—
116#14523976C2314yes—
117#14523976C2314yes—
118#14523976C2314yes—
119#14523974C2314yes—
120#14523974C2314yes—
121#14523974C2314yes—
122#14523974C2314yes—
123#14523974C2314yes—
124C4⋊(C67⋊C8)C2314yes—
125C4⋊(C67⋊C8)C2314yes—
126C4⋊(C67⋊C8)C2314yes—
127#14523967C2314yes—
128#14523967C2314yes—
129#14523967C2314yes—
130#14523963C2314yes—
131#14523963C2314yes—
132#14523963C2314yes—
133#14523954C2314yes—
134#14523954C2314yes—
135C4×C67⋊C8C2314yes—
136C22×Q8×C67—21no—
137C22×Q8×C67D411yescharacteristic
138C22×Q8×C67C2311yescharacteristic
139C4⋊Q8×C67—28no—
140C4⋊Q8×C67—22no—
141C4⋊Q8×C67C2314yes—
142#125×C67—28no—
143#125×C67—28no—
144#125×C67—22no—
145#125×C67—22no—
146#125×C67C2314yes—
147#125×C67C2314yes—
148C4×Q8×C67—28no—
149C4×Q8×C67—22no—
150C4×Q8×C67—22no—
151C4×Q8×C67—22no—
152C4×Q8×C67D414yes—
153C4×Q8×C67C2314yes—
154C4×Q8×C67C2314yes—
155C4×Q8×C67C2314yes—
156C4×Q8×C67C2314yes—
157C2×C4⋊C4×C67—21no—
158C2×C4⋊C4×C67—21no—
159C2×C4⋊C4×C67—21no—
160C2×C4⋊C4×C67—21no—
161C2×C4⋊C4×C67—21no—
162C2×C4⋊C4×C67—21no—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67D411yescharacteristic
166C2×C4⋊C4×C67D411yescharacteristic
167C2×C4⋊C4×C67D411yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C42×C67—21no—
172C2×C42×C67—21no—
173C2×C42×C67—21no—
174C2×C42×C67C2311yescharacteristic
175C2×C42×C67C2311yescharacteristic
176C2×C42×C67C2311yescharacteristic
177C23×D67—21no—
178C2×Dic134—24no—
179C2×Dic134—82no—
180C2×D268—21no—
181C2×D268—22no—
182C2×D268C2×Q814yes—
183C2×D268C2412yes—
184C22×Dic67—21no—
185C22×Dic67—21no—
186C22×Dic67—21no—
187C2×C4×D67—24no—
188C2×C4×D67—24no—
189C2×C4×D67—24no—
190C2×C4×D67—44no—
191C2×C4×D67—82no—
192C2×C4×D67—82no—
193#11761615C2×Q8116yescomplemented
194C2×C67⋊C8—22no—
195C2×C67⋊C8—22no—
196C2×C67⋊C8—22no—
197C2×C67⋊C8C2×Q814yes—
198C2×C67⋊C8C2412yes—
199C2×C67⋊C8C2412yes—
200C2×C67⋊C8C2412yes—
201C2×C67⋊C8C2412yes—
202C4⋊Dic67—24no—
203C4⋊Dic67—21no—
204C4⋊Dic67—21no—
205C4⋊Dic67—21no—
206C4⋊Dic67C2412yes—
207C4⋊Dic67C2412yes—
208C4⋊Dic67C2412yes—
209Dic67⋊C4—24no—
210Dic67⋊C4—24no—
211Dic67⋊C4—24no—
212Dic67⋊C4—24no—
213(C2×D67)⋊C4—24no—
214(C2×D67)⋊C4—24no—
215(C2×D67)⋊C4—24no—
216C2×Q8×C67—21no—
217C2×Q8×C67—24no—
218C2×Q8×C67—22no—
219C2×Q8×C67—42no—
220C2×Q8×C67—44no—
221C2×Q8×C67C2×D414yes—
222C2×Q8×C67C2×Q814yes—
223C2×Q8×C67C2412yes—
224C22×C4×C67—21no—
225C22×C4×C67—21no—
226C22×C4×C67—21no—
227C22×C4×C67—21no—
228C22×C4×C67C2×D411yescharacteristic
229C22×C4×C67C2×D411yescharacteristic
230C22×C4×C67C2×D411yescharacteristic
231C22×C4×C67C2×D411yescharacteristic
232C22×C4×C67C2×D411yescharacteristic
233C22×C4×C67C2×D411yescharacteristic
234C22×C4×C67C2411yescharacteristic
235C4⋊C4×C67—24no—
236C4⋊C4×C67—24no—
237C4⋊C4×C67—24no—
238C4⋊C4×C67—24no—
239C4⋊C4×C67—24no—
240C4⋊C4×C67—24no—
241C4⋊C4×C67—24no—
242C4⋊C4×C67—24no—
243C4⋊C4×C67—21no—
244C4⋊C4×C67—21no—
245C4⋊C4×C67—21no—
246C4⋊C4×C67C2×D414yes—
247C4⋊C4×C67C2×D414yes—
248C4⋊C4×C67C2×D414yes—
249C4⋊C4×C67C2412yes—
250C4⋊C4×C67C2412yes—
251C4⋊C4×C67C2412yes—
252C42×C67—24no—
253C42×C67—24no—
254C42×C67—24no—
255C42×C67C2×D412yes—
256C42×C67C2×D412yes—
257C42×C67C2×D412yes—
258C42×C67C2412yes—
259C42×C67C2412yes—
260C42×C67C2412yes—
261C23×C67C22×D411yescharacteristic
262C22×D67—24no—
263C22×D67—22no—
264C22×D67—42no—
265C22×D67—42no—
266Q8×C67—24no—
267Q8×C67—22no—
268Q8×C67—44no—
269Q8×C67—48no—
270Q8×C67C22×Q814yes—
271C2×C4×C67—24no—
272C2×C4×C67—22no—
273C2×C4×C67—22no—
274C2×C4×C67—22no—
275C2×C4×C67—22no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—42no—
283C2×C4×C67—42no—
284C2×C4×C67—42no—
285C2×C4×C67C22×D412yes—
286C2×C4×C67C22×D412yes—
287C2×C4×C67C22×D412yes—
288C2×C4×C67C22×D412yes—
289C2×C4×C67C22×D412yes—
290C2×C4×C67C22×D412yes—
291C2×C4×C67C22×D411yescharacteristic
292C2×C4×C67C22×Q812yes—
293C2×C4×C672−1+412yes—
294C2×C4×C67C2511yescharacteristic
295C2×Dic67—22no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—42no—
299C2×Dic67—42no—
300C2×Dic67—42no—
301D268—24no—
302D268—22no—
303D268C22×Q814yes—
304C4×D67—48no—
305C4×D67—84no—
306C4×D67—84no—
307Dic134—84no—
308C67⋊C8—22no—
309C67⋊C8—22no—
310C67⋊C8—22no—
311C67⋊C8C22×Q814yes—
312C22×C67D4×Q812yes—
313C22×C67#57512yes—
314C22×C67#57712yes—
315C22×C67C23×D411yescharacteristic
316C2×D67—24no—
317C2×D67—48no—
318C2×D67—42no—
319C2×D67—42no—
320C4×C67—24no—
321C4×C67—22no—
322C4×C67—22no—
323C4×C67—22no—
324C4×C67—22no—
325C4×C67—22no—
326C4×C67—22no—
327C4×C67—42no—
328C4×C67—42no—
329C4×C67—42no—
330C4×C67D4×Q812yes—
331C4×C67C23×Q811yescharacteristic
332C4×C67C2×2−1+411yescharacteristic
333Dic67—42no—
334Dic67—42no—
335Dic67—42no—
336C2×#3388—671nomaximal, Sylow
337C2×C67#338814yescomplemented
338C2×C67C2×D4×Q811yescharacteristic
339C2×C67C2×#57511yescharacteristic
340C2×C67C2×#57711yescharacteristic
341D67—44no—
342C2×#557D6711yescharacteristic, complemented
343C2×#554—671no—
344#3388—6716no—
345C2×#501—671no—
346C2×#501—671no—
347C2×#499—671no—
348C2×#479—671no—
349C2×#479—671no—
350C2×#475—671no—
351C2×#478—671no—
352C2×#478—671no—
353C2×#476—671no—
354C2×#446—671no—
355C2×#440—671no—
356C2×#440—671no—
357C2×C4×SD16—671no—
358C67C2×#338811yescharacteristic, complemented, Sylow
359C22×SD16—671no—
360#557—24no—
361#557C2×D6718yescomplemented
362#554—678no—
363#554—1344no—
364C2×C4⋊Q8—21no—
365C2×C4⋊Q8—671no—
366C2×C4⋊Q8C2×D6711yescharacteristic
367C2×#125—21no—
368C2×#125—21no—
369C2×#125—671no—
370C2×#125—671no—
371C2×#125C2×D6711yescharacteristic
372C2×#125C2×D6711yescharacteristic
373C2×C22⋊Q8—1341no—
374C2×C22⋊Q8—1341no—
375C2×C22⋊Q8—1341no—
376C2×C4×Q8—21no—
377C2×C4×Q8C2×D6711yescharacteristic
378C2×C4×Q8C2×D6711yescharacteristic
379C2×C4×Q8C2×D6711yescharacteristic
380C2×C4×Q8C2×D6711yescharacteristic
381C2×C4×D4—671no—
382C2×C4×D4—671no—
383C2×C4×D4—671no—
384C22×C4⋊C4—1341no—
385#501—678no—
386#501—678no—
387#499—678no—
388#479—678no—
389#479—678no—
390#478—678no—
391#478—678no—
392#476—678no—
393#475—678no—
394#446—678no—
395#440—678no—
396#440—678no—
397C4×SD16—678no—
398C2×#107—671no—
399C2×#107—671no—
400C2×#107—671no—
401C2×#107—671no—
402C2×#106—671no—
403C2×#106—671no—
404C2×#106—671no—
405C2×#106—671no—
406C2×#106—671no—
407C2×C4⋊C8—671no—
408C2×C4⋊C8—671no—
409C2×C4⋊C8—671no—
410C2×#103—671no—
411C2×#103—671no—
412C2×#103—671no—
413C2×#102—671no—
414C2×#102—671no—
415C2×#102—671no—
416C2×#97—671no—
417C2×#97—671no—
418C2×C4×C8—671no—
419C22×Q8—21no—
420C22×Q8—1341no—
421C22×Q8C22⋊D6711yescharacteristic
422C22×Q8C22×D6711yescharacteristic
423C22×D4—671no—
424C23×C4—1341no—
425C23×C4—1341no—
426C23×C4—1341no—
427C2×SD16—678no—
428C2×SD16—674no—
429C22×C8—671no—
430C22×C8—671no—
431C22×C8—671no—
432C22×C8—671no—
433C4⋊Q8—28no—
434C4⋊Q8—22no—
435C4⋊Q8—674no—
436C4⋊Q8—1342no—
437C4⋊Q8C22×D6714yes—
438#125—28no—
439#125—28no—
440#125—22no—
441#125—22no—
442#125—674no—
443#125—674no—
444#125—1342no—
445#125—1342no—
446#125C22×D6714yes—
447#125C22×D6714yes—
448C22⋊Q8—1348no—
449C22⋊Q8—1348no—
450C22⋊Q8—1348no—
451C4×Q8—28no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8C22⋊D6714yes—
456C4×Q8C22×D6714yes—
457C4×Q8C22×D6714yes—
458C4×Q8C22×D6714yes—
459C4×Q8C22×D6714yes—
460C4×D4—674no—
461C4×D4—674no—
462C4×D4—674no—
463C4×D4—1342no—
464C4×D4—1342no—
465C4×D4—1342no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—671no—
475C2×C4⋊C4—671no—
476C2×C4⋊C4—671no—
477C2×C4⋊C4—1341no—
478C2×C4⋊C4—1341no—
479C2×C4⋊C4—1341no—
480C2×C4⋊C4—1341no—
481C2×C4⋊C4—1341no—
482C2×C4⋊C4—1348no—
483C2×C4⋊C4C22⋊D6711yescharacteristic
484C2×C4⋊C4C22⋊D6711yescharacteristic
485C2×C4⋊C4C22⋊D6711yescharacteristic
486C2×C4⋊C4C22×D6711yescharacteristic
487C2×C4⋊C4C22×D6711yescharacteristic
488C2×C4⋊C4C22×D6711yescharacteristic
489C2×C22⋊C4—1341no—
490C2×C22⋊C4—1341no—
491C2×C22⋊C4—1341no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42C22×D6711yescharacteristic
496C2×C42C22×D6711yescharacteristic
497C2×C42C22×D6711yescharacteristic
498#107—674no—
499#107—674no—
500#107—674no—
501#107—674no—
502#106—674no—
503#106—674no—
504#106—674no—
505#106—674no—
506#106—674no—
507C4⋊C8—674no—
508C4⋊C8—674no—
509C4⋊C8—674no—
510#103—674no—
511#103—674no—
512#103—674no—
513#102—674no—
514#102—674no—
515#102—674no—
516#97—674no—
517#97—674no—
518C4×C8—674no—
519C24—1341no—
520C2×Q8—21no—
521C2×Q8—24no—
522C2×Q8—22no—
523C2×Q8—42no—
524C2×Q8—44no—
525C2×Q8—5362no—
526C2×Q8—1344no—
527C2×Q8C2×C22⋊D6714yes—
528C2×Q8Q8×D6714yes—
529C2×Q8C23×D6712yes—
530C2×D4—674no—
531C2×D4—672no—
532C2×D4—1341no—
533C2×D4—1342no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—2684no—
539C22×C4—5362no—
540C22×C4—5362no—
541C22×C4—1341no—
542C22×C4—1341no—
543C22×C4—1341no—
544C22×C4—1344no—
545C22×C4—1344no—
546C22×C4—1344no—
547C22×C4C2×C22⋊D6711yescharacteristic
548C22×C4C2×C22⋊D6711yescharacteristic
549C22×C4C2×C22⋊D6711yescharacteristic
550C22×C4C2×C22⋊D6711yescharacteristic
551C22×C4C2×C22⋊D6711yescharacteristic
552C22×C4C2×C22⋊D6711yescharacteristic
553C22×C4C23×D6711yescharacteristic
554SD16—6716no—
555C2×C8—674no—
556C2×C8—672no—
557C2×C8—672no—
558C2×C8—672no—
559C2×C8—672no—
560C2×C8—1342no—
561C2×C8—1342no—
562C2×C8—1342no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—672no—
575C4⋊C4—672no—
576C4⋊C4—672no—
577C4⋊C4—1341no—
578C4⋊C4—1341no—
579C4⋊C4—1341no—
580C4⋊C4—1344no—
581C4⋊C4—1344no—
582C4⋊C4—1344no—
583C4⋊C4—1344no—
584C4⋊C4—1344no—
585C4⋊C4C2×C22⋊D6714yes—
586C4⋊C4C2×C22⋊D6714yes—
587C4⋊C4C2×C22⋊D6714yes—
588C4⋊C4C23×D6712yes—
589C4⋊C4C23×D6712yes—
590C4⋊C4C23×D6712yes—
591C22⋊C4—1344no—
592C22⋊C4—1344no—
593C22⋊C4—1344no—
594C42—24no—
595C42—24no—
596C42—24no—
597C42C2×C22⋊D6712yes—
598C42C2×C22⋊D6712yes—
599C42C2×C22⋊D6712yes—
600C42C23×D6712yes—
601C42C23×D6712yes—
602C42C23×D6712yes—
603C23—2682no—
604C23—2682no—
605C23—1344no—
606C23—1342no—
607C23C22×C22⋊D6711yescharacteristic
608Q8—24no—
609Q8—22no—
610Q8—44no—
611Q8—48no—
612Q8—5364no—
613Q8C2×Q8×D6714yes—
614D4—674no—
615D4—1344no—
616D4—1342no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—2688no—
632C2×C4—2682no—
633C2×C4—2682no—
634C2×C4—2682no—
635C2×C4—5364no—
636C2×C4—5364no—
637C2×C4—1342no—
638C2×C4—1342no—
639C2×C4—1342no—
640C2×C4C22×C22⋊D6712yes—
641C2×C4C22×C22⋊D6712yes—
642C2×C4C22×C22⋊D6712yes—
643C2×C4C22×C22⋊D6712yes—
644C2×C4C22×C22⋊D6712yes—
645C2×C4C22×C22⋊D6712yes—
646C2×C4C22×C22⋊D6711yescharacteristic
647C2×C4C2×Q8×D6712yes—
648C2×C4#1452409112yes—
649C2×C4C24×D6711yescharacteristic
650C8—674no—
651C8—1342no—
652C8—1342no—
653C8—1342no—
654C22—2688no—
655C22—2682no—
656C22—2682no—
657C22—1344no—
658C22Q8×C22⋊D6712yes—
659C22#1686419412yes—
660C22#1686420412yes—
661C22C23×C22⋊D6711yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—24no—
666C4—22no—
667C4—22no—
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—2682no—
673C4—2682no—
674C4—2682no—
675C4Q8×C22⋊D6712yes—
676C4C22×Q8×D6711yescharacteristic
677C4C2×#1452409111yescharacteristic
678C2—2684no—
679C2#2257314814yesdirect product factor
680C2C2×Q8×C22⋊D6711yescharacteristic
681C2C2×#1686419411yescharacteristic
682C2C2×#1686420411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#557×C67C2
socleC23×C67C22×D4
prime radicalC22×D268C23
hypercenterC2×#557D67
hypocenterC67C2×#3388
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #22573148C2direct (N × H)
3. C2×#16863806C2semidirect
4. C2×#16863802C2semidirect
5. C2×#16863795C2semidirect
6. C2×#16863703C2semidirect
7. C2×#16863703C2semidirect
8. C2×#16863681C2semidirect
12. C2×#16863527C2semidirect
16. C2×#557×C67C2semidirect
30. #16863806C22semidirect
31. #16863802C22semidirect
32. #16863795C22semidirect
33. #16863703C22semidirect
34. #16863703C22semidirect
38. #16863681C22semidirect
39. #16863527C22semidirect
65. #557×C67C22semidirect
82. C2×#11761615Q8semidirect
193. #11761615C2×Q8semidirect
337. C2×C67#3388semidirect
342. C2×#557D67semidirect
358. C67C2×#3388semidirect
361. #557C2×D67semidirect
679. C2#22573148direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641062
#225731482
C2×#168638062
C2×#168638022
C2×#168637952
C2×#168637032
C2×#168636812
C2×#168636932
C2×#168636832
C2×#168635272
C2×#168634942
C2×C4×#117616152
C2×#557×C672
C2×#338867