Finite Group Databasebeta

← #30873202

Subgroups — #30873202

Order 17152.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22568867C211yesmaximal, characteristic, complemented
2#22568658C211yesmaximal, characteristic
3#22560922C211yesmaximal, characteristic, complemented
4#22560915C211yesmaximal, characteristic, complemented
5#22560859C211yesmaximal, characteristic, complemented
6#22560859C211yesmaximal, characteristic, complemented
7#22560486C211yesmaximal, characteristic, complemented
8#22560486C211yesmaximal, characteristic, complemented
9#22560308C211yesmaximal, characteristic, complemented
10#22560251C211yesmaximal, characteristic, complemented
11#22560153C211yesmaximal, characteristic
12#22560056C211yesmaximal, characteristic, complemented
13#22560049C211yesmaximal, characteristic, complemented
14#22559990C211yesmaximal, characteristic, complemented
15C67×#2896C211yesmaximal, characteristic
16C2×#14524050C2211yescharacteristic
17C2×#14524050C2211yescharacteristic
18#16863457—21no—
19#16863457—21no—
20#16863453—21no—
21#16863449—21no—
22C2×#14523979C2211yescharacteristic, complemented
23C2×#14523979C2211yescharacteristic, complemented
24#16863423C2211yescharacteristic, complemented
25#16863423C2211yescharacteristic, complemented
26C2×#14523970C2211yescharacteristic
27C2×#14523970C2211yescharacteristic
28C2×#14523970C2211yescharacteristic
29C2×#14523970C2211yescharacteristic
30#16863363—21no—
31#16863363—21no—
32#16863363C2211yescharacteristic
33#16863363C2211yescharacteristic
34#16863360—21no—
35#16863360C2211yescharacteristic
36#16863360C2211yescharacteristic
37C2×C22⋊(C67⋊C8)—21no—
38C2×C22⋊(C67⋊C8)C2211yescharacteristic
39#16863352C2211yescharacteristic, complemented
40#16863352C2211yescharacteristic, complemented
41C2×#14523953C2211yescharacteristic, complemented
42C2×C8×Dic67C2211yescharacteristic, complemented
43C4×C22⋊Dic67C2211yescharacteristic
44#16863161C2211yescharacteristic, complemented
45#16863161C2211yescharacteristic, complemented
46#16863155C2211yescharacteristic, complemented
47#16863155C2211yescharacteristic, complemented
48#16863155C2211yescharacteristic, complemented
49#16863155C2211yescharacteristic, complemented
50#16863150C2211yescharacteristic, complemented
51#16863150C2211yescharacteristic, complemented
52C22×#41×C67C2211yescharacteristic
53C22×M16×C67C2211yescharacteristic
54C2×#117×C67C2211yescharacteristic
55#419×C67C411yescharacteristic, complemented
56#419×C67C411yescharacteristic, complemented
57#418×C67C411yescharacteristic, complemented
58#418×C67C411yescharacteristic, complemented
59#417×C67C411yescharacteristic, complemented
60#417×C67C411yescharacteristic, complemented
61#417×C67C411yescharacteristic, complemented
62#417×C67C411yescharacteristic, complemented
63#416×C67C2211yescharacteristic
64#416×C67C2211yescharacteristic
65#416×C67C2211yescharacteristic
66#416×C67C2211yescharacteristic
67#14524050—22no—
68#14524050—22no—
69#14524050—41no—
70#14524050—41no—
71C2×#11761612—21no—
72C2×#11761612—21no—
73C2×#11761612C2311yescharacteristic
74C2×#11761612C2311yescharacteristic
75C2×#11761612C2311yescharacteristic
76C2×#11761612C2311yescharacteristic
77C22×C67⋊C8—21no—
78C22×C67⋊C8—21no—
79C22×C67⋊C8C2311yescharacteristic
80C22×C67⋊C8C2311yescharacteristic
81C2×C22⋊Dic67—21no—
82C2×C4×Dic67C2311yescharacteristic
83C2×C4×Dic67C2311yescharacteristic
84#14523979—41no—
85#14523979—41no—
86C4⋊(C67⋊C8)—21no—
87C4⋊(C67⋊C8)—21no—
88C4⋊(C67⋊C8)—21no—
89C4⋊(C67⋊C8)—21no—
90#14523970—22no—
91#14523970—22no—
92#14523970—41no—
93#14523970—41no—
94C22⋊(C67⋊C8)—21no—
95C22⋊(C67⋊C8)—21no—
96C22⋊(C67⋊C8)—21no—
97C22⋊(C67⋊C8)—21no—
98C22⋊(C67⋊C8)—21no—
99C22⋊(C67⋊C8)—21no—
100C22⋊(C67⋊C8)—21no—
101C22⋊(C67⋊C8)—21no—
102C22⋊(C67⋊C8)D411yescharacteristic
103C22⋊(C67⋊C8)D411yescharacteristic
104C22⋊(C67⋊C8)D411yescharacteristic
105C22⋊(C67⋊C8)D411yescharacteristic
106#14523954—21no—
107#14523954—21no—
108#14523953—41no—
109C4×C67⋊C8—21no—
110C4×C67⋊C8—21no—
111C8×Dic67—41no—
112C67⋊#95—21no—
113C2×#41×C67—21no—
114C2×#41×C67—21no—
115C2×#41×C67—22no—
116C2×#41×C67—22no—
117C2×#41×C67—41no—
118C2×#41×C67—41no—
119C2×#41×C67C2×C411yescharacteristic
120C2×#41×C67C2×C411yescharacteristic
121C2×#41×C67C2311yescharacteristic
122C2×#41×C67C2311yescharacteristic
123C22×Q8×C67C2×C411yescharacteristic
124C22×D4×C67—21no—
125C22×D4×C67C2×C411yescharacteristic
126C23×C4×C67—21no—
127C23×C4×C67C2311yescharacteristic
128C2×M16×C67—41no—
129C2×M16×C67—41no—
130C2×M16×C67C2×C411yescharacteristic
131C2×M16×C67C2×C411yescharacteristic
132C2×M16×C67C2×C411yescharacteristic
133C2×M16×C67C2×C411yescharacteristic
134C22×C8×C67C2311yescharacteristic
135C22×C8×C67C2311yescharacteristic
136#117×C67—21no—
137#117×C67—21no—
138#117×C67C2×C411yescharacteristic
139#117×C67C2×C411yescharacteristic
140#117×C67C2311yescharacteristic
141#117×C67C2311yescharacteristic
142C2×C4⋊C4×C67C2×C411yescharacteristic
143C2×C4⋊C4×C67C2×C411yescharacteristic
144C2×C22⋊C4×C67—21no—
145C2×C42×C67—21no—
146#103×C67C2×C411yescharacteristic
147#103×C67C2×C411yescharacteristic
148#103×C67C2×C411yescharacteristic
149#103×C67C2×C411yescharacteristic
150#103×C67C2×C411yescharacteristic
151#103×C67C2×C411yescharacteristic
152#103×C67C2×C411yescharacteristic
153#103×C67C2×C411yescharacteristic
154#102×C67C2×C411yescharacteristic
155#102×C67C2×C411yescharacteristic
156#102×C67C2×C411yescharacteristic
157#102×C67C2×C411yescharacteristic
158#102×C67C2×C411yescharacteristic
159#102×C67C2×C411yescharacteristic
160#102×C67C2×C411yescharacteristic
161#102×C67C2×C411yescharacteristic
162C22×Dic67—21no—
163C22×Dic67—21no—
164#11761612—21no—
165#11761612—21no—
166#11761612—21no—
167#11761612—21no—
168#11761612—21no—
169#11761612—21no—
170#11761612—21no—
171#11761612—21no—
172#11761612—42no—
173#11761612—42no—
174C2×C67⋊C8—21no—
175C2×C67⋊C8—21no—
176C2×C67⋊C8—21no—
177C2×C67⋊C8—21no—
178C2×C67⋊C8—21no—
179C2×C67⋊C8—21no—
180C2×C67⋊C8—21no—
181C2×C67⋊C8—21no—
182C2×C67⋊C8—42no—
183C2×C67⋊C8—42no—
184C2×C67⋊C8C2×D411yescharacteristic
185C2×C67⋊C8C2×D411yescharacteristic
186C2×C67⋊C8C2×D411yescharacteristic
187C2×C67⋊C8C2×D411yescharacteristic
188C22⋊Dic67—42no—
189C4×Dic67—21no—
190C4×Dic67—21no—
191C4×Dic67—21no—
192C4×Dic67—21no—
193C24×C67—21no—
194C24×C67#4111yescharacteristic
195#41×C67—21no—
196#41×C67—21no—
197#41×C67—22no—
198#41×C67—22no—
199#41×C67—21no—
200#41×C67—21no—
201#41×C67—21no—
202#41×C67—21no—
203#41×C67—42no—
204#41×C67—42no—
205#41×C67—41no—
206#41×C67—41no—
207#41×C67—42no—
208#41×C67—42no—
209#41×C67#4112yes—
210#41×C67#4112yes—
211C2×Q8×C67—21no—
212C2×Q8×C67—22no—
213C2×Q8×C67—41no—
214C2×Q8×C67C22×C411yescharacteristic
215C2×Q8×C67C22×C411yescharacteristic
216C2×D4×C67—21no—
217C2×D4×C67—22no—
218C2×D4×C67—21no—
219C2×D4×C67—21no—
220C2×D4×C67—21no—
221C2×D4×C67—21no—
222C2×D4×C67—41no—
223C2×D4×C67—42no—
224C2×D4×C67—42no—
225C2×D4×C67C22×C411yescharacteristic
226C2×D4×C67C22×C411yescharacteristic
227C22×C4×C67—21no—
228C22×C4×C67—21no—
229C22×C4×C67—21no—
230C22×C4×C67—21no—
231C22×C4×C67—21no—
232C22×C4×C67—21no—
233C22×C4×C67—21no—
234C22×C4×C67—21no—
235C22×C4×C67—21no—
236C22×C4×C67—21no—
237C22×C4×C67—21no—
238C22×C4×C67—42no—
239C22×C4×C67—42no—
240C22×C4×C67C22×C411yescharacteristic
241C22×C4×C67C22×C411yescharacteristic
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2×D411yescharacteristic
244C22×C4×C67#4111yescharacteristic
245C22×C4×C67C2411yescharacteristic
246M16×C67—41no—
247M16×C67—41no—
248M16×C67—41no—
249M16×C67—41no—
250C2×C8×C67—21no—
251C2×C8×C67—21no—
252C2×C8×C67—21no—
253C2×C8×C67—21no—
254C2×C8×C67C22×C411yescharacteristic
255C2×C8×C67C22×C411yescharacteristic
256C2×C8×C67C22×C411yescharacteristic
257C2×C8×C67C22×C411yescharacteristic
258C4⋊C4×C67—21no—
259C4⋊C4×C67—21no—
260C4⋊C4×C67C22×C411yescharacteristic
261C4⋊C4×C67C22×C411yescharacteristic
262C4⋊C4×C67C22×C411yescharacteristic
263C4⋊C4×C67C22×C411yescharacteristic
264C22⋊C4×C67—21no—
265C22⋊C4×C67—21no—
266C22⋊C4×C67—21no—
267C22⋊C4×C67—21no—
268C42×C67—21no—
269C42×C67—21no—
270C42×C67—21no—
271C42×C67—21no—
272C23×C67—21no—
273C23×C67—21no—
274C23×C67—21no—
275C23×C67—21no—
276C23×C67—41no—
277C23×C67—41no—
278C23×C67—42no—
279C23×C67—42no—
280C23×C67—81no—
281C23×C67C4×D411yescharacteristic
282C23×C67C4×D411yescharacteristic
283C23×C67C2×#4111yescharacteristic
284Q8×C67—21no—
285Q8×C67—21no—
286Q8×C67—21no—
287Q8×C67—42no—
288Q8×C67#11712yes—
289D4×C67—22no—
290D4×C67—22no—
291D4×C67—21no—
292D4×C67—21no—
293D4×C67—21no—
294D4×C67—42no—
295D4×C67—42no—
296D4×C67—42no—
297D4×C67—41no—
298D4×C67—41no—
299D4×C67#11712yes—
300C2×C4×C67—21no—
301C2×C4×C67—21no—
302C2×C4×C67—21no—
303C2×C4×C67—21no—
304C2×C4×C67—21no—
305C2×C4×C67—21no—
306C2×C4×C67—21no—
307C2×C4×C67—21no—
308C2×C4×C67—21no—
309C2×C4×C67—21no—
310C2×C4×C67—21no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—21no—
314C2×C4×C67—21no—
315C2×C4×C67—21no—
316C2×C4×C67—21no—
317C2×C4×C67—21no—
318C2×C4×C67—42no—
319C2×C4×C67—42no—
320C2×C4×C67—42no—
321C2×C4×C67—42no—
322C2×C4×C67—41no—
323C2×C4×C67—41no—
324C2×C4×C67—81no—
325C2×C4×C67C4×D411yescharacteristic
326C2×C4×C67C4×D411yescharacteristic
327C2×C4×C67C23×C411yescharacteristic
328C2×C4×C67C22×D411yescharacteristic
329C2×C4×C67C2×#4111yescharacteristic
330C2×C4×C67C2×#4111yescharacteristic
331C2×C4×C67H(5,𝔽2)11yescharacteristic
332C2×C4×C67H(5,𝔽2)11yescharacteristic
333C2×Dic67—22no—
334C2×Dic67—41no—
335C2×Dic67—41no—
336C2×Dic67—41no—
337C2×Dic67—41no—
338C2×Dic67—41no—
339C8×C67—21no—
340C8×C67—21no—
341C8×C67—21no—
342C8×C67—21no—
343C67⋊C8—21no—
344C67⋊C8—21no—
345C67⋊C8—21no—
346C67⋊C8—21no—
347C67⋊C8—41no—
348C67⋊C8—41no—
349C67⋊C8—41no—
350C67⋊C8—41no—
351C22×C67—21no—
352C22×C67—21no—
353C22×C67—21no—
354C22×C67—21no—
355C22×C67—22no—
356C22×C67—21no—
357C22×C67—21no—
358C22×C67—21no—
359C22×C67—21no—
360C22×C67—41no—
361C22×C67—41no—
362C22×C67—41no—
363C22×C67—41no—
364C22×C67—41no—
365C22×C67—81no—
366C22×C67—81no—
367C22×C67—84no—
368C22×C67C2×C4×D411yescharacteristic
369C22×C67#55111yescharacteristic
370C22×C67#55111yescharacteristic
371C4×C67—21no—
372C4×C67—21no—
373C4×C67—22no—
374C4×C67—41no—
375C4×C67—41no—
376C4×C67—41no—
377C4×C67—41no—
378C4×C67—41no—
379C4×C67C2×#11711yescharacteristic
380C4×C67#51811yescharacteristic
381C4×C67#54611yescharacteristic
382C4×C67#54611yescharacteristic
383Dic67—42no—
384Dic67—81no—
385#22588—671nomaximal, Sylow
386C2×C67—21no—
387C2×C67—21no—
388C2×C67—41no—
389C2×C67—41no—
390C2×C67—42no—
391C2×C67—81no—
392C2×C67#234211yescharacteristic
393C2×C67#295511yescharacteristic
394C2×C67#295611yescharacteristic
395#2924—671no—
396#2896D6711yescharacteristic
397#2880—671no—
398#1938—671no—
399#1937—671no—
400#1929—671no—
401#1929—671no—
402#1866—671no—
403#1866—671no—
404#1826—671no—
405#1811—671no—
406#1789—671no—
407#1765—671no—
408#1764—671no—
409#1753—671no—
410C67#2258811yescharacteristic, complemented, Sylow
411C22×#41C2×D6711yescharacteristic
412C2×#131—671no—
413C2×#131—671no—
414C22×M16C2×D6711yescharacteristic
415C2×#117C2×D6711yescharacteristic
416#433—1341no—
417#433—1341no—
418#432—1341no—
419#431—1341no—
420C2×#108—671no—
421C2×#108—671no—
422#424—671no—
423#424—671no—
424C2×#104—671no—
425C2×#104—671no—
426C2×#104—671no—
427C2×#104—671no—
428#419Dic6711yescharacteristic, complemented
429#419Dic6711yescharacteristic, complemented
430#418Dic6711yescharacteristic, complemented
431#418Dic6711yescharacteristic, complemented
432#417Dic6711yescharacteristic, complemented
433#417Dic6711yescharacteristic, complemented
434#417Dic6711yescharacteristic, complemented
435#417Dic6711yescharacteristic, complemented
436#416C2×D6711yescharacteristic
437#416C2×D6711yescharacteristic
438#416C2×D6711yescharacteristic
439#416C2×D6711yescharacteristic
440#408—671no—
441#408—671no—
442#408—1341no—
443#408—1341no—
444#407—671no—
445#407—671no—
446#407—1341no—
447C2×C22⋊C8—671no—
448C2×C22⋊C8—1341no—
449#405—671no—
450#405—671no—
451C2×#97—671no—
452C2×C4×C8—671no—
453C4×C22⋊C4—671no—
454#341—671no—
455#341—671no—
456#339—671no—
457#339—671no—
458#339—671no—
459#339—671no—
460#336—671no—
461#336—671no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×Dic6711yescharacteristic
469C2×#41C2×Dic6711yescharacteristic
470C2×#41C22×D6711yescharacteristic
471C2×#41C22×D6711yescharacteristic
472C22×Q8C2×Dic6711yescharacteristic
473C22×D4—21no—
474C22×D4C2×Dic6711yescharacteristic
475C23×C4—21no—
476C23×C4C22×D6711yescharacteristic
477#131—2681no—
478#131—2681no—
479#131—1342no—
480#131—1342no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—671no—
484C2×M16—671no—
485C2×M16—671no—
486C2×M16—671no—
487C2×M16—1341no—
488C2×M16—1341no—
489C2×M16C2×Dic6711yescharacteristic
490C2×M16C2×Dic6711yescharacteristic
491C2×M16C2×Dic6711yescharacteristic
492C2×M16C2×Dic6711yescharacteristic
493C22×C8—671no—
494C22×C8—671no—
495C22×C8—1341no—
496C22×C8—1341no—
497C22×C8C22×D6711yescharacteristic
498C22×C8C22×D6711yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×Dic6711yescharacteristic
502#117C2×Dic6711yescharacteristic
503#117C22×D6711yescharacteristic
504#117C22×D6711yescharacteristic
505C2×C4⋊C4C2×Dic6711yescharacteristic
506C2×C4⋊C4C2×Dic6711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1341no—
509C2×C42—21no—
510C2×C42—671no—
511C2×C42—671no—
512#108—2681no—
513#108—2681no—
514C4⋊C8—1341no—
515C4⋊C8—1341no—
516C4⋊C8—1341no—
517C4⋊C8—1341no—
518#104—2681no—
519#104—2681no—
520#104—1342no—
521#104—1342no—
522#103C2×Dic6711yescharacteristic
523#103C2×Dic6711yescharacteristic
524#103C2×Dic6711yescharacteristic
525#103C2×Dic6711yescharacteristic
526#103C2×Dic6711yescharacteristic
527#103C2×Dic6711yescharacteristic
528#103C2×Dic6711yescharacteristic
529#103C2×Dic6711yescharacteristic
530#102C2×Dic6711yescharacteristic
531#102C2×Dic6711yescharacteristic
532#102C2×Dic6711yescharacteristic
533#102C2×Dic6711yescharacteristic
534#102C2×Dic6711yescharacteristic
535#102C2×Dic6711yescharacteristic
536#102C2×Dic6711yescharacteristic
537#102C2×Dic6711yescharacteristic
538C22⋊C8—671no—
539C22⋊C8—671no—
540C22⋊C8—671no—
541C22⋊C8—671no—
542C22⋊C8—1341no—
543C22⋊C8—1341no—
544C22⋊C8—1341no—
545C22⋊C8—1341no—
546C22⋊C8—1341no—
547C22⋊C8—1341no—
548C22⋊C8—1341no—
549C22⋊C8—1341no—
550#97—2681no—
551#97—1341no—
552#97—1341no—
553C4×C8—2681no—
554C4×C8—1341no—
555C4×C8—1341no—
556#95—1341no—
557C24—21no—
558C24#1176162711yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1176162812yes—
574#41#1176162812yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×Dic6711yescharacteristic
579C2×Q8C22×Dic6711yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×Dic6711yescharacteristic
590C2×D4C22×Dic6711yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—1341no—
605C22×C4—1341no—
606C22×C4C22×Dic6711yescharacteristic
607C22×C4C22×Dic6711yescharacteristic
608C22×C4D4×D6711yescharacteristic
609C22×C4D4×D6711yescharacteristic
610C22×C4#1176162711yescharacteristic
611C22×C4C23×D6711yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—2682no—
617M16—2682no—
618M16—1341no—
619M16—1341no—
620M16—1341no—
621M16—1341no—
622M16—1341no—
623M16—1341no—
624M16—1341no—
625M16—1341no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—2682no—
631C2×C8—2682no—
632C2×C8—671no—
633C2×C8—671no—
634C2×C8—671no—
635C2×C8—671no—
636C2×C8—1341no—
637C2×C8—1341no—
638C2×C8—1341no—
639C2×C8—1341no—
640C2×C8—1341no—
641C2×C8—1341no—
642C2×C8—1341no—
643C2×C8—1341no—
644C2×C8C22×Dic6711yescharacteristic
645C2×C8C22×Dic6711yescharacteristic
646C2×C8C22×Dic6711yescharacteristic
647C2×C8C22×Dic6711yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×Dic6711yescharacteristic
651C4⋊C4C22×Dic6711yescharacteristic
652C4⋊C4C22×Dic6711yescharacteristic
653C4⋊C4C22×Dic6711yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—2682no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1341no—
664C42—1341no—
665C42—1341no—
666C42—1341no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23D4×Dic6711yescharacteristic
677C23D4×Dic6711yescharacteristic
678C23C2×#1176162711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1452400212yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1452400212yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—2681no—
721C2×C4—2681no—
722C2×C4—2681no—
723C2×C4—2681no—
724C2×C4—2681no—
725C2×C4—1342no—
726C2×C4D4×Dic6711yescharacteristic
727C2×C4D4×Dic6711yescharacteristic
728C2×C4C23×Dic6711yescharacteristic
729C2×C4C2×D4×D6711yescharacteristic
730C2×C4C2×#1176162811yescharacteristic
731C2×C4C2×#1176162811yescharacteristic
732C2×C4#1452408811yescharacteristic
733C2×C4#1452408811yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—2681no—
739C8—2681no—
740C8—2681no—
741C8—2681no—
742C8—1341no—
743C8—1341no—
744C8—1341no—
745C8—1341no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×D4×Dic6711yescharacteristic
764C22#1686407211yescharacteristic
765C22#1686407211yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—2682no—
775C4—5361no—
776C4C2×#1452400211yescharacteristic
777C4#1686387111yescharacteristic
778C4#1686403611yescharacteristic
779C4#1686403611yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2256305811yescharacteristic
787C2#2256911211yescharacteristic
788C2#2256911911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC67×#2896C2
socleC22×C67C2×C4×D4
prime radicalC22×#41×C67C22
cosocleC22×C4×C67C24
hypercenter#2896D67
hypocenterC67#22588
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #22568867C2semidirect
3. #22560922C2semidirect
4. #22560915C2semidirect
5. #22560859C2semidirect
6. #22560859C2semidirect
7. #22560486C2semidirect
8. #22560486C2semidirect
9. #22560308C2semidirect
10. #22560251C2semidirect
12. #22560056C2semidirect
13. #22560049C2semidirect
14. #22559990C2semidirect
22. C2×#14523979C22semidirect
23. C2×#14523979C22semidirect
24. #16863423C22semidirect
25. #16863423C22semidirect
39. #16863352C22semidirect
40. #16863352C22semidirect
41. C2×#14523953C22semidirect
42. C2×C8×Dic67C22semidirect
44. #16863161C22semidirect
45. #16863161C22semidirect
46. #16863155C22semidirect
47. #16863155C22semidirect
48. #16863155C22semidirect
49. #16863155C22semidirect
50. #16863150C22semidirect
51. #16863150C22semidirect
55. #419×C67C4semidirect
56. #419×C67C4semidirect
57. #418×C67C4semidirect
58. #418×C67C4semidirect
59. #417×C67C4semidirect
60. #417×C67C4semidirect
61. #417×C67C4semidirect
62. #417×C67C4semidirect
410. C67#22588semidirect
428. #419Dic67semidirect
429. #419Dic67semidirect
430. #418Dic67semidirect
431. #418Dic67semidirect
432. #417Dic67semidirect
433. #417Dic67semidirect
434. #417Dic67semidirect
435. #417Dic67semidirect

Maximal subgroups

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

subgroupindex
#225688672
#225686582
#225609222
#225609152
#225608592
#225604862
#225603082
#225602512
#225601532
#225600562
#225600492
#225599902
C67×#28962
#2258867