Finite Group Databasebeta

← #30876572

Subgroups — #30876572

Order 17152.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863518C211yesmaximal, characteristic, complemented
2#22568936C211yesmaximal, characteristic, complemented
3C22×#14523970C211yesmaximal, characteristic, complemented
4#22568658C211yesmaximal, characteristic, complemented
5#22561103C211yesmaximal, characteristic, complemented
6#22560922C211yesmaximal, characteristic, complemented
7#22560859C211yesmaximal, characteristic, complemented
8#22560653C211yesmaximal, characteristic, complemented
9#22560538C211yesmaximal, characteristic, complemented
10#22560538C211yesmaximal, characteristic, complemented
11#22560486C211yesmaximal, characteristic, complemented
12#22560416C211yesmaximal, characteristic, complemented
13#22560056C211yesmaximal, characteristic, complemented
14#22559973C211yesmaximal, characteristic, complemented
15C67×#3002C211yesmaximal, characteristic
16C2×#14524050C2211yescharacteristic
17C2×#14524050C2211yescharacteristic
18C2×#14524050C2211yescharacteristic, complemented
19C22×#11761612C2211yescharacteristic
20C22×C4×Dic67C2211yescharacteristic
21#16863518—24no—
22#16863474—21no—
23#16863468—21no—
24#16863468—21no—
25D4×C67⋊C8—21no—
26C2×#14523979C2211yescharacteristic, complemented
27C2×#14523979C2211yescharacteristic, complemented
28#16863423C2211yescharacteristic, complemented
29C2×#14523970—24no—
30C2×#14523970C2211yescharacteristic
31C2×#14523970C2211yescharacteristic
32C2×#14523970C2211yescharacteristic
33C2×#14523970C2211yescharacteristic
34C2×#14523970C2211yescharacteristic, complemented
35C2×#14523970C2211yescharacteristic, complemented
36#16863363—21no—
37#16863363—21no—
38#16863363C2211yescharacteristic
39#16863363C2211yescharacteristic
40#16863363C2211yescharacteristic, complemented
41#16863360—21no—
42#16863360C2211yescharacteristic
43C2×C22⋊(C67⋊C8)—21no—
44C2×C22⋊(C67⋊C8)C2211yescharacteristic
45#16863352C2211yescharacteristic, complemented
46C2×#14523953C2211yescharacteristic, complemented
47C2×#14523953C2211yescharacteristic, complemented
48#16863161C2211yescharacteristic, complemented
49#16863161C2211yescharacteristic, complemented
50#16863155C2211yescharacteristic, complemented
51#16863155C2211yescharacteristic, complemented
52#16863150C2211yescharacteristic, complemented
53#16863150C2211yescharacteristic, complemented
54C22×#41×C67C2211yescharacteristic
55C2×#135×C67C2211yescharacteristic
56C2×#135×C67C2211yescharacteristic
57#525×C67C2211yescharacteristic
58#452×C67C411yescharacteristic, complemented
59#452×C67C411yescharacteristic, complemented
60#451×C67C411yescharacteristic, complemented
61#450×C67C411yescharacteristic, complemented
62#449×C67C411yescharacteristic, complemented
63#449×C67C411yescharacteristic, complemented
64#448×C67C411yescharacteristic, complemented
65#447×C67C411yescharacteristic, complemented
66#416×C67C2211yescharacteristic
67#416×C67C2211yescharacteristic
68C2×C22⋊C8×C67C2211yescharacteristic
69C23×Dic67—21no—
70#14524050—22no—
71#14524050—22no—
72#14524050—22no—
73#14524050—41no—
74#14524050—41no—
75#14524050—41no—
76C2×#11761612—21no—
77C2×#11761612—21no—
78C2×#11761612—21no—
79C2×#11761612—22no—
80C2×#11761612—21no—
81C2×#11761612—41no—
82C2×#11761612C2311yescharacteristic
83C2×#11761612C2311yescharacteristic
84C2×#11761612C2311yescharacteristic
85C2×#11761612C2311yescharacteristic
86C22×C67⋊C8—21no—
87C22×C67⋊C8—21no—
88C22×C67⋊C8—21no—
89C22×C67⋊C8—21no—
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92C2×C4×Dic67—22no—
93C2×C4×Dic67—21no—
94C2×C4×Dic67—41no—
95C2×C4×Dic67C2311yescharacteristic
96C2×C4×Dic67C2311yescharacteristic
97#14523979—22no—
98#14523979—41no—
99C4⋊(C67⋊C8)—21no—
100C4⋊(C67⋊C8)—21no—
101#14523970—22no—
102#14523970—22no—
103#14523970—22no—
104#14523970—22no—
105#14523970—41no—
106#14523970D414yescomplemented
107C22⋊(C67⋊C8)—21no—
108C22⋊(C67⋊C8)—21no—
109C22⋊(C67⋊C8)—21no—
110C22⋊(C67⋊C8)—21no—
111C22⋊(C67⋊C8)—21no—
112C22⋊(C67⋊C8)—21no—
113C22⋊(C67⋊C8)—21no—
114C22⋊(C67⋊C8)—21no—
115C22⋊(C67⋊C8)D411yescharacteristic
116C22⋊(C67⋊C8)D411yescharacteristic
117C22⋊(C67⋊C8)D411yescharacteristic
118C22⋊(C67⋊C8)D411yescharacteristic
119#14523954—21no—
120#14523953—22no—
121#14523953—41no—
122C4×C67⋊C8—21no—
123C2×#41×C67—21no—
124C2×#41×C67—21no—
125C2×#41×C67—22no—
126C2×#41×C67—22no—
127C2×#41×C67—41no—
128C2×#41×C67—41no—
129C2×#41×C67C2×C411yescharacteristic
130C2×#41×C67C2×C411yescharacteristic
131C2×#41×C67C2311yescharacteristic
132C2×#41×C67C2311yescharacteristic
133C2×#41×C67C2311yescharacteristic
134C22×Q8×C67C2×C411yescharacteristic
135C22×D4×C67—21no—
136C22×D4×C67C2×C411yescharacteristic
137C23×C4×C67—21no—
138C23×C4×C67C2311yescharacteristic
139#135×C67—22no—
140#135×C67—22no—
141#135×C67—41no—
142#135×C67—41no—
143C2×Q16×C67C2×C411yescharacteristic, complemented
144C2×Q16×C67C2×C411yescharacteristic, complemented
145C2×SD16×C67C2×C411yescharacteristic, complemented
146C2×SD16×C67C2×C411yescharacteristic, complemented
147C2×SD16×C67C2×C411yescharacteristic, complemented
148C2×SD16×C67C2×C411yescharacteristic, complemented
149C2×D8×C67C2×C411yescharacteristic, complemented
150C2×D8×C67C2×C411yescharacteristic, complemented
151C22×C8×C67C2311yescharacteristic
152C22×C8×C67C2311yescharacteristic
153#123×C67—21no—
154C22⋊Q8×C67C2×C411yescharacteristic
155C22⋊Q8×C67C2×C411yescharacteristic
156#121×C67C2×C411yescharacteristic
157#121×C67C2×C411yescharacteristic
158#120×C67—21no—
159C4×D4×C67—21no—
160C4×D4×C67—21no—
161#117×C67C2311yescharacteristic
162#103×C67C2×C411yescharacteristic, complemented
163#103×C67C2×C411yescharacteristic, complemented
164#103×C67C2×C411yescharacteristic, complemented
165#103×C67C2×C411yescharacteristic, complemented
166#102×C67C2×C411yescharacteristic, complemented
167#102×C67C2×C411yescharacteristic, complemented
168#102×C67C2×C411yescharacteristic, complemented
169#102×C67C2×C411yescharacteristic, complemented
170C22⋊C8×C67C2×C411yescharacteristic
171C22⋊C8×C67C2×C411yescharacteristic
172C22⋊C8×C67C2×C411yescharacteristic
173C22⋊C8×C67C2×C411yescharacteristic
174C22×Dic67—21no—
175C22×Dic67—21no—
176C22×Dic67—42no—
177C22×Dic67—42no—
178C22×Dic67—42no—
179#11761612—21no—
180#11761612—21no—
181#11761612—21no—
182#11761612—21no—
183#11761612—21no—
184#11761612—21no—
185#11761612—21no—
186#11761612—42no—
187#11761612—42no—
188#11761612—42no—
189#11761612—42no—
190#11761612C2×D412yes—
191C2×C67⋊C8—21no—
192C2×C67⋊C8—21no—
193C2×C67⋊C8—21no—
194C2×C67⋊C8—21no—
195C2×C67⋊C8—21no—
196C2×C67⋊C8—21no—
197C2×C67⋊C8—21no—
198C2×C67⋊C8—21no—
199C2×C67⋊C8—42no—
200C2×C67⋊C8—42no—
201C2×C67⋊C8—42no—
202C2×C67⋊C8—42no—
203C2×C67⋊C8C2×D411yescharacteristic
204C2×C67⋊C8C2×D411yescharacteristic
205C2×C67⋊C8C2×D411yescharacteristic
206C2×C67⋊C8C2×D411yescharacteristic
207C4×Dic67—21no—
208C4×Dic67—21no—
209C4×Dic67—21no—
210C4×Dic67—42no—
211C4×Dic67C2×D412yes—
212C24×C67—21no—
213C24×C67#4111yescharacteristic
214#41×C67—21no—
215#41×C67—21no—
216#41×C67—22no—
217#41×C67—22no—
218#41×C67—21no—
219#41×C67—21no—
220#41×C67—21no—
221#41×C67—21no—
222#41×C67—21no—
223#41×C67—21no—
224#41×C67—21no—
225#41×C67—21no—
226#41×C67—42no—
227#41×C67—42no—
228#41×C67—41no—
229#41×C67—41no—
230#41×C67—42no—
231#41×C67—42no—
232#41×C67C2×D412yes—
233#41×C67#4112yes—
234C2×Q8×C67—21no—
235C2×Q8×C67—22no—
236C2×Q8×C67—41no—
237C2×Q8×C67C22×C411yescharacteristic
238C2×Q8×C67C22×C411yescharacteristic
239C2×Q8×C67C22×C411yescharacteristic
240C2×D4×C67—21no—
241C2×D4×C67—22no—
242C2×D4×C67—21no—
243C2×D4×C67—21no—
244C2×D4×C67—21no—
245C2×D4×C67—21no—
246C2×D4×C67—21no—
247C2×D4×C67—21no—
248C2×D4×C67—21no—
249C2×D4×C67—41no—
250C2×D4×C67—42no—
251C2×D4×C67—42no—
252C2×D4×C67C22×C411yescharacteristic
253C2×D4×C67C22×C411yescharacteristic
254C2×D4×C67C22×C411yescharacteristic
255C22×C4×C67—21no—
256C22×C4×C67—21no—
257C22×C4×C67—21no—
258C22×C4×C67—21no—
259C22×C4×C67—21no—
260C22×C4×C67—21no—
261C22×C4×C67—21no—
262C22×C4×C67—21no—
263C22×C4×C67—21no—
264C22×C4×C67—21no—
265C22×C4×C67—42no—
266C22×C4×C67—42no—
267C22×C4×C67C22×C411yescharacteristic
268C22×C4×C67C22×C411yescharacteristic
269C22×C4×C67C2×D411yescharacteristic
270C22×C4×C67C2×D411yescharacteristic
271C22×C4×C67#4111yescharacteristic
272C22×C4×C67C2411yescharacteristic
273Q16×C67—22no—
274Q16×C67—41no—
275SD16×C67—22no—
276SD16×C67—22no—
277SD16×C67—41no—
278SD16×C67—41no—
279D8×C67—22no—
280D8×C67—41no—
281C2×C8×C67—21no—
282C2×C8×C67—21no—
283C2×C8×C67—21no—
284C2×C8×C67—21no—
285C2×C8×C67C22×C411yescharacteristic
286C2×C8×C67C22×C411yescharacteristic
287C2×C8×C67C22×C411yescharacteristic
288C2×C8×C67C22×C411yescharacteristic
289C4⋊C4×C67—21no—
290C4⋊C4×C67—21no—
291C4⋊C4×C67C22×C411yescharacteristic
292C4⋊C4×C67C22×C411yescharacteristic
293C22⋊C4×C67—21no—
294C22⋊C4×C67—21no—
295C22⋊C4×C67—21no—
296C22⋊C4×C67—21no—
297C22⋊C4×C67—21no—
298C42×C67—21no—
299C23×C67—21no—
300C23×C67—21no—
301C23×C67—21no—
302C23×C67—22no—
303C23×C67—21no—
304C23×C67—21no—
305C23×C67—41no—
306C23×C67—42no—
307C23×C67—42no—
308C23×C67—81no—
309C23×C67C4×D411yescharacteristic
310C23×C67C4×D411yescharacteristic
311C23×C67C2×#4111yescharacteristic
312Q8×C67—21no—
313Q8×C67—21no—
314Q8×C67—21no—
315Q8×C67—21no—
316Q8×C67—21no—
317Q8×C67—42no—
318Q8×C67C4×D412yes—
319D4×C67—22no—
320D4×C67—22no—
321D4×C67—21no—
322D4×C67—21no—
323D4×C67—21no—
324D4×C67—21no—
325D4×C67—21no—
326D4×C67—42no—
327D4×C67—42no—
328D4×C67—42no—
329D4×C67—41no—
330D4×C67—41no—
331D4×C67—41no—
332D4×C67—41no—
333D4×C67—42no—
334D4×C67—81no—
335D4×C67C4×D412yes—
336C2×C4×C67—21no—
337C2×C4×C67—21no—
338C2×C4×C67—21no—
339C2×C4×C67—21no—
340C2×C4×C67—21no—
341C2×C4×C67—21no—
342C2×C4×C67—21no—
343C2×C4×C67—21no—
344C2×C4×C67—21no—
345C2×C4×C67—22no—
346C2×C4×C67—21no—
347C2×C4×C67—21no—
348C2×C4×C67—22no—
349C2×C4×C67—21no—
350C2×C4×C67—21no—
351C2×C4×C67—21no—
352C2×C4×C67—21no—
353C2×C4×C67—42no—
354C2×C4×C67—42no—
355C2×C4×C67—42no—
356C2×C4×C67—41no—
357C2×C4×C67—41no—
358C2×C4×C67—41no—
359C2×C4×C67—41no—
360C2×C4×C67C4×D411yescharacteristic
361C2×C4×C67C4×D411yescharacteristic
362C2×C4×C67C23×C411yescharacteristic
363C2×C4×C67C22×D411yescharacteristic
364C2×C4×C67C22×D411yescharacteristic
365C2×C4×C67C2×#4111yescharacteristic
366C2×C4×C67H(5,𝔽2)11yescharacteristic
367C2×C4×C67H(5,𝔽2)11yescharacteristic
368C2×Dic67—22no—
369C2×Dic67—22no—
370C2×Dic67—41no—
371C2×Dic67—41no—
372C2×Dic67—41no—
373C2×Dic67—48no—
374C2×Dic67—41no—
375C8×C67—21no—
376C8×C67—21no—
377C8×C67—21no—
378C8×C67—21no—
379C67⋊C8—21no—
380C67⋊C8—21no—
381C67⋊C8—22no—
382C67⋊C8—21no—
383C67⋊C8—21no—
384C67⋊C8—41no—
385C67⋊C8—41no—
386C67⋊C8—41no—
387C22×C67—21no—
388C22×C67—21no—
389C22×C67—21no—
390C22×C67—21no—
391C22×C67—21no—
392C22×C67—22no—
393C22×C67—21no—
394C22×C67—21no—
395C22×C67—42no—
396C22×C67—42no—
397C22×C67—41no—
398C22×C67—41no—
399C22×C67—41no—
400C22×C67—41no—
401C22×C67—41no—
402C22×C67—41no—
403C22×C67—41no—
404C22×C67—41no—
405C22×C67—84no—
406C22×C67#44412yescomplemented
407C22×C67C2×C4×D411yescharacteristic
408C22×C67#54611yescharacteristic
409C22×C67#55111yescharacteristic
410C4×C67—21no—
411C4×C67—21no—
412C4×C67—22no—
413C4×C67—41no—
414C4×C67—41no—
415C4×C67—41no—
416C4×C67—41no—
417C4×C67C2×C4×D411yescharacteristic
418C4×C67#51811yescharacteristic
419C4×C67D4211yescharacteristic
420C4×C67#54611yescharacteristic
421Dic67—42no—
422Dic67—42no—
423#22886—671nomaximal, Sylow
424C2×C67—21no—
425C2×C67—22no—
426C2×C67—21no—
427C2×C67—41no—
428C2×C67—42no—
429C2×C67—81no—
430C2×C67—81no—
431C2×C67#235811yescharacteristic
432C2×C67C2×#44411yescharacteristic
433C2×C67#295611yescharacteristic
434#3002D6711yescharacteristic
435C2×#444—671no—
436#2933—671no—
437C22×#104—671no—
438#2880—671no—
439#1975—671no—
440#1938—671no—
441#1929—671no—
442#1896—671no—
443#1876—671no—
444#1876—671no—
445#1866—671no—
446#1855—671no—
447#1765—671no—
448#1749—671no—
449C67#2288611yescharacteristic, complemented, Sylow
450C22×#41C2×D6711yescharacteristic
451C2×#135C2×D6711yescharacteristic
452C2×#135C2×D6711yescharacteristic
453C2×#131—671no—
454C2×#131—671no—
455C2×#131—671no—
456C22×M16—671no—
457#525C2×D6711yescharacteristic
458C22×C42—671no—
459#452Dic6711yescharacteristic, complemented
460#452Dic6711yescharacteristic, complemented
461#451Dic6711yescharacteristic, complemented
462#450Dic6711yescharacteristic, complemented
463#449Dic6711yescharacteristic, complemented
464#449Dic6711yescharacteristic, complemented
465#448Dic6711yescharacteristic, complemented
466#447Dic6711yescharacteristic, complemented
467#444—1344no—
468#436—1341no—
469#435—1341no—
470#435—1341no—
471C8×D4—1341no—
472C2×#108—671no—
473C2×#108—671no—
474#424—671no—
475C2×#104—671no—
476C2×#104—671no—
477C2×#104—671no—
478C2×#104—671no—
479C2×#104—671no—
480C2×#104—671no—
481C2×#104—1344no—
482#416C2×D6711yescharacteristic
483#416C2×D6711yescharacteristic
484#408—671no—
485#408—671no—
486#408—671no—
487#408—1341no—
488#408—1341no—
489#407—671no—
490#407—1341no—
491C2×C22⋊C8—671no—
492C2×C22⋊C8—1341no—
493C2×C22⋊C8C2×D6711yescharacteristic
494#405—671no—
495C2×#97—671no—
496C2×#97—671no—
497#341—671no—
498#341—671no—
499#339—671no—
500#339—671no—
501#336—671no—
502#336—671no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×Dic6711yescharacteristic
510C2×#41C2×Dic6711yescharacteristic
511C2×#41C22×D6711yescharacteristic
512C2×#41C22×D6711yescharacteristic
513C2×#41C22×D6711yescharacteristic
514C22×Q8C2×Dic6711yescharacteristic
515C22×D4—21no—
516C22×D4C2×Dic6711yescharacteristic
517C23×C4—21no—
518C23×C4—1341no—
519C23×C4C22×D6711yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×Dic6711yescharacteristic, complemented
525C2×Q16C2×Dic6711yescharacteristic, complemented
526C2×SD16C2×Dic6711yescharacteristic, complemented
527C2×SD16C2×Dic6711yescharacteristic, complemented
528C2×SD16C2×Dic6711yescharacteristic, complemented
529C2×SD16C2×Dic6711yescharacteristic, complemented
530C2×D8C2×Dic6711yescharacteristic, complemented
531C2×D8C2×Dic6711yescharacteristic, complemented
532#131—2681no—
533#131—2681no—
534#131—2681no—
535#131—1342no—
536#131—1342no—
537#131—1342no—
538C2×M16—2681no—
539C2×M16—671no—
540C2×M16—671no—
541C2×M16—671no—
542C2×M16—671no—
543C2×M16—1342no—
544C2×M16—1341no—
545C2×M16—1341no—
546C2×M16—1341no—
547C2×M16—1341no—
548C22×C8—671no—
549C22×C8—671no—
550C22×C8—1341no—
551C22×C8—1341no—
552C22×C8—1341no—
553C22×C8—1341no—
554C22×C8C22×D6711yescharacteristic
555C22×C8C22×D6711yescharacteristic
556#123—21no—
557C22⋊Q8C2×Dic6711yescharacteristic
558C22⋊Q8C2×Dic6711yescharacteristic
559#121C2×Dic6711yescharacteristic
560#121C2×Dic6711yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D6711yescharacteristic
565C2×C42—2681no—
566C2×C42—671no—
567C2×C42—671no—
568C2×C42—1341no—
569C2×C42—1342no—
570#108—2681no—
571#108—1342no—
572C4⋊C8—1341no—
573C4⋊C8—1341no—
574#104—2681no—
575#104—674no—
576#104—1342no—
577#104—1342no—
578#104—1342no—
579#104—1342no—
580#103C2×Dic6711yescharacteristic, complemented
581#103C2×Dic6711yescharacteristic, complemented
582#103C2×Dic6711yescharacteristic, complemented
583#103C2×Dic6711yescharacteristic, complemented
584#102C2×Dic6711yescharacteristic, complemented
585#102C2×Dic6711yescharacteristic, complemented
586#102C2×Dic6711yescharacteristic, complemented
587#102C2×Dic6711yescharacteristic, complemented
588C22⋊C8—671no—
589C22⋊C8—671no—
590C22⋊C8—671no—
591C22⋊C8—671no—
592C22⋊C8—1341no—
593C22⋊C8—1341no—
594C22⋊C8—1341no—
595C22⋊C8—1341no—
596C22⋊C8—1341no—
597C22⋊C8—1341no—
598C22⋊C8—1341no—
599C22⋊C8—1341no—
600C22⋊C8C2×Dic6711yescharacteristic
601C22⋊C8C2×Dic6711yescharacteristic
602C22⋊C8C2×Dic6711yescharacteristic
603C22⋊C8C2×Dic6711yescharacteristic
604#97—2681no—
605#97—1341no—
606#97—1342no—
607C4×C8—1341no—
608C24—21no—
609C24#1176162711yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41D4×D6712yes—
629#41#1176162712yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×Dic6711yescharacteristic
634C2×Q8C22×Dic6711yescharacteristic
635C2×Q8C22×Dic6711yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×Dic6711yescharacteristic
649C2×D4C22×Dic6711yescharacteristic
650C2×D4C22×Dic6711yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—2682no—
664C22×C4—2682no—
665C22×C4—2682no—
666C22×C4—1341no—
667C22×C4—1341no—
668C22×C4C22×Dic6711yescharacteristic
669C22×C4C22×Dic6711yescharacteristic
670C22×C4D4×D6711yescharacteristic
671C22×C4D4×D6711yescharacteristic
672C22×C4#1176162711yescharacteristic
673C22×C4C23×D6711yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—2682no—
683M16—2682no—
684M16—2682no—
685M16—2682no—
686M16—672no—
687M16—1341no—
688M16—1341no—
689M16—1341no—
690M16—1341no—
691M16—1341no—
692M16—1341no—
693M16—1341no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—2682no—
699C2×C8—2682no—
700C2×C8—2682no—
701C2×C8—2682no—
702C2×C8—671no—
703C2×C8—671no—
704C2×C8—671no—
705C2×C8—671no—
706C2×C8—1341no—
707C2×C8—1341no—
708C2×C8—1341no—
709C2×C8—1341no—
710C2×C8—1341no—
711C2×C8—1341no—
712C2×C8—1341no—
713C2×C8—1341no—
714C2×C8C22×Dic6711yescharacteristic
715C2×C8C22×Dic6711yescharacteristic
716C2×C8C22×Dic6711yescharacteristic
717C2×C8C22×Dic6711yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×Dic6711yescharacteristic
721C4⋊C4C22×Dic6711yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—2682no—
729C42—672no—
730C42—1341no—
731C42—1341no—
732C42—1341no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23D4×Dic6711yescharacteristic
744C23D4×Dic6711yescharacteristic
745C23C2×#1176162711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8D4×Dic6712yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—81no—
769D4D4×Dic6712yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—2681no—
795C2×C4—2681no—
796C2×C4—2681no—
797C2×C4—2688no—
798C2×C4—2681no—
799C2×C4—1342no—
800C2×C4—1342no—
801C2×C4D4×Dic6711yescharacteristic
802C2×C4D4×Dic6711yescharacteristic
803C2×C4C23×Dic6711yescharacteristic
804C2×C4C2×D4×D6711yescharacteristic
805C2×C4C2×D4×D6711yescharacteristic
806C2×C4C2×#1176162711yescharacteristic
807C2×C4#1452408811yescharacteristic
808C2×C4#1452408811yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—2681no—
814C8—2681no—
815C8—2681no—
816C8—1341no—
817C8—1341no—
818C8—1342no—
819C8—1341no—
820C8—1341no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22#1686351812yescomplemented
841C22C2×D4×Dic6711yescharacteristic
842C22#1686403311yescharacteristic
843C22#1686407711yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—2682no—
852C4—2682no—
853C4C2×D4×Dic6711yescharacteristic
854C4#1686387111yescharacteristic
855C4#1686402811yescharacteristic
856C4#1686403311yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2#2256319311yescharacteristic
865C2C2×#1686351811yescharacteristic
866C2#2256911911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
Fitting, prime radicalC67×#3002C2
socleC22×C67C2×C4×D4
cosocleC22×C4×C67C24
hypercenter#3002D67
hypocenterC67#22886
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#16863518C2semidirect
2. #22568936C2semidirect
3. C22×#14523970C2semidirect
4. #22568658C2semidirect
5. #22561103C2semidirect
6. #22560922C2semidirect
7. #22560859C2semidirect
8. #22560653C2semidirect
9. #22560538C2semidirect
10. #22560538C2semidirect
11. #22560486C2semidirect
12. #22560416C2semidirect
13. #22560056C2semidirect
14. #22559973C2semidirect
18. C2×#14524050C22semidirect
26. C2×#14523979C22semidirect
27. C2×#14523979C22semidirect
28. #16863423C22semidirect
34. C2×#14523970C22semidirect
35. C2×#14523970C22semidirect
40. #16863363C22semidirect
45. #16863352C22semidirect
46. C2×#14523953C22semidirect
47. C2×#14523953C22semidirect
48. #16863161C22semidirect
49. #16863161C22semidirect
50. #16863155C22semidirect
51. #16863155C22semidirect
52. #16863150C22semidirect
53. #16863150C22semidirect
58. #452×C67C4semidirect
59. #452×C67C4semidirect
60. #451×C67C4semidirect
61. #450×C67C4semidirect
62. #449×C67C4semidirect
63. #449×C67C4semidirect
64. #448×C67C4semidirect
65. #447×C67C4semidirect
106. #14523970D4semidirect
143. C2×Q16×C67C2×C4semidirect
144. C2×Q16×C67C2×C4semidirect
145. C2×SD16×C67C2×C4semidirect
146. C2×SD16×C67C2×C4semidirect
147. C2×SD16×C67C2×C4semidirect
148. C2×SD16×C67C2×C4semidirect
149. C2×D8×C67C2×C4semidirect
150. C2×D8×C67C2×C4semidirect
162. #103×C67C2×C4semidirect
163. #103×C67C2×C4semidirect
164. #103×C67C2×C4semidirect
165. #103×C67C2×C4semidirect
166. #102×C67C2×C4semidirect
167. #102×C67C2×C4semidirect
168. #102×C67C2×C4semidirect
169. #102×C67C2×C4semidirect
406. C22×C67#444semidirect
449. C67#22886semidirect
459. #452Dic67semidirect
460. #452Dic67semidirect
461. #451Dic67semidirect
462. #450Dic67semidirect
463. #449Dic67semidirect
464. #449Dic67semidirect
465. #448Dic67semidirect
466. #447Dic67semidirect
524. C2×Q16C2×Dic67semidirect
525. C2×Q16C2×Dic67semidirect
526. C2×SD16C2×Dic67semidirect
527. C2×SD16C2×Dic67semidirect
528. C2×SD16C2×Dic67semidirect
529. C2×SD16C2×Dic67semidirect
530. C2×D8C2×Dic67semidirect
531. C2×D8C2×Dic67semidirect
580. #103C2×Dic67semidirect
581. #103C2×Dic67semidirect
582. #103C2×Dic67semidirect
583. #103C2×Dic67semidirect
584. #102C2×Dic67semidirect
585. #102C2×Dic67semidirect
586. #102C2×Dic67semidirect
587. #102C2×Dic67semidirect
840. C22#16863518semidirect

Maximal subgroups

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

subgroupindex
C2×#168635182
#225689362
C22×#145239702
#225686582
#225611032
#225609222
#225608592
#225606532
#225605382
#225604862
#225604162
#225600562
#225599732
C67×#30022
#2288667