Finite Group Databasebeta

← C2×C67×#3347 #30740490

Subgroups — C2×C67×#3347 #30740490

Order 17152.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C67C211yesmaximal, characteristic, complemented
2C2×#553×C67C211yesmaximal, characteristic, complemented
3C67×#3347C2116yesmaximal, direct product factor
4C2×#501×C67C211yesmaximal, characteristic, complemented
5C2×#482×C67C211yesmaximal, characteristic, complemented
6C2×#482×C67C211yesmaximal, characteristic, complemented
7C2×#482×C67C211yesmaximal, characteristic, complemented
8C2×#480×C67C211yesmaximal, characteristic, complemented
9C2×#478×C67C211yesmaximal, characteristic, complemented
10C2×#474×C67C211yesmaximal, characteristic, complemented
11C2×#469×C67C211yesmaximal, characteristic, complemented
12C2×#466×C67C211yesmaximal, characteristic, complemented
13C2×#442×C67C211yesmaximal, characteristic, complemented
14C2×#435×C67C211yesmaximal, characteristic, complemented
15C2×#428×C67C211yesmaximal, characteristic, complemented
16C2×#427×C67C211yesmaximal, characteristic, complemented
17C22×D8×C67C2211yescharacteristic
18C22×M16×C67C2211yescharacteristic
19C23×C8×C67C2211yescharacteristic
20#555×C67—24no—
21#555×C67C2218yescomplemented
22#553×C67—24no—
23#553×C67C2218yescomplemented
24C2×C4⋊Q8×C67C2211yescharacteristic
25C2×#126×C67—21no—
26C2×#125×C67C2211yescharacteristic
27C2×#124×C67—21no—
28C2×#124×C67—21no—
29C2×#123×C67—21no—
30C2×#121×C67—21no—
31C2×#121×C67—21no—
32C2×#121×C67C2211yescharacteristic
33C2×#121×C67C2211yescharacteristic
34C2×#121×C67C2211yescharacteristic
35C2×#121×C67C2211yescharacteristic
36C2×C4×D4×C67—21no—
37C2×C4×D4×C67C2211yescharacteristic
38C2×C4×D4×C67C2211yescharacteristic
39C2×C4×D4×C67C2211yescharacteristic
40C2×#117×C67—21no—
41C2×#117×C67C2211yescharacteristic
42C2×#117×C67C2211yescharacteristic
43C2×#117×C67C2211yescharacteristic
44C22×C4⋊C4×C67C2211yescharacteristic
45#501×C67C2218yescomplemented
46#482×C67C2218yescomplemented
47#482×C67C2218yescomplemented
48#482×C67C2218yescomplemented
49#480×C67C2218yescomplemented
50#478×C67C2218yescomplemented
51#474×C67C2218yescomplemented
52#469×C67C2218yescomplemented
53#466×C67C2218yescomplemented
54#442×C67C2218yescomplemented
55#435×C67C2218yescomplemented
56#428×C67C2218yescomplemented
57#427×C67C2218yescomplemented
58C2×#107×C67C2211yescharacteristic
59C2×#107×C67C2211yescharacteristic
60C2×#107×C67C2211yescharacteristic
61C2×#107×C67C2211yescharacteristic
62C2×#107×C67C2211yescharacteristic
63C2×#106×C67C2211yescharacteristic
64C2×#106×C67C2211yescharacteristic
65C2×#106×C67C2211yescharacteristic
66C2×#106×C67C2211yescharacteristic
67C2×C4⋊C8×C67C2211yescharacteristic
68C2×#102×C67C2211yescharacteristic
69C2×#102×C67C2211yescharacteristic
70C2×#102×C67C2211yescharacteristic
71C2×#102×C67C2211yescharacteristic
72C2×#102×C67C2211yescharacteristic
73C2×#102×C67C2211yescharacteristic
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×C22⋊C8×C67C2211yescharacteristic
76C2×#97×C67C2211yescharacteristic
77C22×Q8×C67—21no—
78C22×D4×C67—21no—
79C22×D4×C67—21no—
80C22×D4×C67—21no—
81C22×D4×C67—21no—
82C22×D4×C67D411yescharacteristic
83C22×D4×C67C2311yescharacteristic
84C22×D4×C67C2311yescharacteristic
85C23×C4×C67—21no—
86C23×C4×C67—21no—
87C23×C4×C67—21no—
88C23×C4×C67C2311yescharacteristic
89C23×C4×C67C2311yescharacteristic
90C2×D8×C67—24no—
91C2×D8×C67C2314yes—
92C2×M16×C67—24no—
93C2×M16×C67C2314yes—
94C22×C8×C67—24no—
95C22×C8×C67C2314yes—
96C22×C8×C67C2311yescharacteristic
97C22×C8×C67C2311yescharacteristic
98C22×C8×C67C2311yescharacteristic
99C22×C8×C67C2311yescharacteristic
100C4⋊Q8×C67—22no—
101C4⋊Q8×C67C2314yes—
102#126×C67—28no—
103#125×C67—22no—
104#125×C67C2314yes—
105#124×C67—28no—
106#124×C67—28no—
107#123×C67—28no—
108#121×C67—28no—
109#121×C67—28no—
110#121×C67—22no—
111#121×C67—22no—
112#121×C67—22no—
113#121×C67—22no—
114#121×C67C2314yes—
115#121×C67C2314yes—
116#121×C67C2314yes—
117#121×C67C2314yes—
118C4×D4×C67—28no—
119C4×D4×C67—22no—
120C4×D4×C67—22no—
121C4×D4×C67D414yes—
122C4×D4×C67C2314yes—
123C4×D4×C67C2314yes—
124C4×D4×C67C2314yes—
125#117×C67—22no—
126#117×C67—22no—
127#117×C67—22no—
128#117×C67—28no—
129#117×C67C2314yes—
130#117×C67C2314yes—
131#117×C67C2314yes—
132C2×C4⋊C4×C67—21no—
133C2×C4⋊C4×C67—22no—
134C2×C4⋊C4×C67—21no—
135C2×C4⋊C4×C67—21no—
136C2×C4⋊C4×C67—21no—
137C2×C4⋊C4×C67D411yescharacteristic
138C2×C4⋊C4×C67C2314yes—
139C2×C4⋊C4×C67C2311yescharacteristic
140C2×C4⋊C4×C67C2311yescharacteristic
141C2×C4⋊C4×C67C2311yescharacteristic
142C2×C4⋊C4×C67C2311yescharacteristic
143C2×C4⋊C4×C67C2311yescharacteristic
144C2×C4⋊C4×C67C2311yescharacteristic
145C2×C22⋊C4×C67—21no—
146C2×C22⋊C4×C67—21no—
147C2×C22⋊C4×C67—21no—
148C2×C22⋊C4×C67—21no—
149C2×C22⋊C4×C67—21no—
150C2×C22⋊C4×C67—21no—
151C2×C22⋊C4×C67—21no—
152C2×C22⋊C4×C67—21no—
153C2×C22⋊C4×C67—21no—
154C2×C22⋊C4×C67D411yescharacteristic
155C2×C22⋊C4×C67D411yescharacteristic
156C2×C42×C67—21no—
157C2×C42×C67—21no—
158C2×C42×C67—21no—
159C2×C42×C67C2311yescharacteristic
160#107×C67C2314yes—
161#107×C67C2314yes—
162#107×C67C2314yes—
163#107×C67C2314yes—
164#107×C67C2314yes—
165#106×C67C2314yes—
166#106×C67C2314yes—
167#106×C67C2314yes—
168#106×C67C2314yes—
169C4⋊C8×C67C2314yes—
170#102×C67C2314yes—
171#102×C67C2314yes—
172#102×C67C2314yes—
173#102×C67C2314yes—
174#102×C67C2314yes—
175#102×C67C2314yes—
176C22⋊C8×C67C2314yes—
177C22⋊C8×C67C2314yes—
178#97×C67C2314yes—
179C24×C67—21no—
180C24×C67—21no—
181C24×C67C2×D411yescharacteristic
182C24×C67C2×D411yescharacteristic
183C2×Q8×C67—24no—
184C2×Q8×C67—82no—
185C2×D4×C67—24no—
186C2×D4×C67—24no—
187C2×D4×C67—24no—
188C2×D4×C67—24no—
189C2×D4×C67—21no—
190C2×D4×C67—21no—
191C2×D4×C67—22no—
192C2×D4×C67—22no—
193C2×D4×C67—22no—
194C2×D4×C67—22no—
195C2×D4×C67—42no—
196C2×D4×C67—44no—
197C2×D4×C67—82no—
198C2×D4×C67—82no—
199C2×D4×C67—82no—
200C2×D4×C67C2×D414yes—
201C2×D4×C67C2412yes—
202C2×D4×C67C2412yes—
203C22×C4×C67—22no—
204C22×C4×C67—22no—
205C22×C4×C67—22no—
206C22×C4×C67—22no—
207C22×C4×C67—21no—
208C22×C4×C67—21no—
209C22×C4×C67—21no—
210C22×C4×C67—21no—
211C22×C4×C67—21no—
212C22×C4×C67—21no—
213C22×C4×C67—24no—
214C22×C4×C67—24no—
215C22×C4×C67—24no—
216C22×C4×C67—44no—
217C22×C4×C67—82no—
218C22×C4×C67—82no—
219C22×C4×C67C2×D412yes—
220C22×C4×C67C2×D412yes—
221C22×C4×C67C2×D411yescharacteristic
222C22×C4×C67C2×D411yescharacteristic
223C22×C4×C67C2×D411yescharacteristic
224C22×C4×C67C2×D411yescharacteristic
225C22×C4×C67C2412yes—
226C22×C4×C67C2412yes—
227C22×C4×C67C2411yescharacteristic
228D8×C67—28no—
229M16×C67—28no—
230C2×C8×C67—22no—
231C2×C8×C67—22no—
232C2×C8×C67—22no—
233C2×C8×C67—28no—
234C2×C8×C67#4114yes—
235C2×C8×C67C2412yes—
236C2×C8×C67C2412yes—
237C2×C8×C67C2412yes—
238C2×C8×C67C2412yes—
239C4⋊C4×C67—21no—
240C4⋊C4×C67—21no—
241C4⋊C4×C67—24no—
242C4⋊C4×C67—24no—
243C4⋊C4×C67—24no—
244C4⋊C4×C67—24no—
245C4⋊C4×C67—21no—
246C4⋊C4×C67—21no—
247C4⋊C4×C67—21no—
248C4⋊C4×C67—21no—
249C4⋊C4×C67C2×D414yes—
250C4⋊C4×C67C2412yes—
251C4⋊C4×C67C2412yes—
252C4⋊C4×C67C2412yes—
253C4⋊C4×C67C2412yes—
254C4⋊C4×C67C2412yes—
255C4⋊C4×C67C2412yes—
256C22⋊C4×C67—24no—
257C22⋊C4×C67—24no—
258C22⋊C4×C67—24no—
259C22⋊C4×C67—24no—
260C22⋊C4×C67—24no—
261C22⋊C4×C67—24no—
262C22⋊C4×C67—24no—
263C22⋊C4×C67—24no—
264C22⋊C4×C67—24no—
265C22⋊C4×C67C2×D414yes—
266C22⋊C4×C67C2×D414yes—
267C42×C67—24no—
268C42×C67—24no—
269C42×C67—24no—
270C42×C67C2×D412yes—
271C42×C67C2412yes—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67—22no—
278C23×C67—22no—
279C23×C67—22no—
280C23×C67—42no—
281C23×C67—42no—
282C23×C67—42no—
283C23×C67—42no—
284C23×C67—42no—
285C23×C67—42no—
286C23×C67C22×D412yes—
287C23×C67C22×D412yes—
288C23×C67C22×D411yescharacteristic
289Q8×C67—84no—
290D4×C67—22no—
291D4×C67—22no—
292D4×C67—22no—
293D4×C67—22no—
294D4×C67—44no—
295D4×C67—48no—
296D4×C67—42no—
297D4×C67—42no—
298D4×C67—84no—
299D4×C67—84no—
300D4×C67—84no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—24no—
306C2×C4×C67—24no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—48no—
318C2×C4×C67—42no—
319C2×C4×C67—42no—
320C2×C4×C67—42no—
321C2×C4×C67—42no—
322C2×C4×C67—42no—
323C2×C4×C67—42no—
324C2×C4×C67—84no—
325C2×C4×C67—84no—
326C2×C4×C67C22×D412yes—
327C2×C4×C67C22×D412yes—
328C2×C4×C67C22×D412yes—
329C2×C4×C67C22×D412yes—
330C2×C4×C67C22×D411yescharacteristic
331C2×C4×C67C2×#4112yes—
332C2×C4×C672−1+412yes—
333C2×C4×C67C2511yescharacteristic
334C8×C67—22no—
335C8×C67—22no—
336C8×C67—22no—
337C8×C67C2×#4114yes—
338C22×C67—22no—
339C22×C67—22no—
340C22×C67—22no—
341C22×C67—22no—
342C22×C67—22no—
343C22×C67—22no—
344C22×C67—44no—
345C22×C67—44no—
346C22×C67—42no—
347C22×C67—42no—
348C22×C67—42no—
349C22×C67—42no—
350C22×C67—42no—
351C22×C67—42no—
352C22×C67—84no—
353C22×C67—84no—
354C22×C67#54712yes—
355C22×C67#57512yes—
356C22×C67#57612yes—
357C22×C67C23×D411yescharacteristic
358C4×C67—22no—
359C4×C67—22no—
360C4×C67—22no—
361C4×C67—22no—
362C4×C67—42no—
363C4×C67—42no—
364C4×C67—42no—
365C4×C67—42no—
366C4×C67—42no—
367C4×C67—42no—
368C4×C67#54712yes—
369C4×C67C22×#4111yescharacteristic
370C4×C67C2×2−1+411yescharacteristic
371C2×#3347C6711yesmaximal, characteristic, direct product factor, Sylow
372C2×C67—42no—
373C2×C67—42no—
374C2×C67—82no—
375C2×C67—82no—
376C2×C67#334714yesdirect product factor
377C2×C67C2×#54711yescharacteristic
378C2×C67C2×#57511yescharacteristic
379C2×C67C2×#57611yescharacteristic
380C2×#555C2×C6711yescharacteristic, complemented
381C2×#553C2×C6711yescharacteristic, complemented
382#3347C2×C67116yesdirect product factor
383C2×#501C2×C6711yescharacteristic, complemented
384C2×#482C2×C6711yescharacteristic, complemented
385C2×#482C2×C6711yescharacteristic, complemented
386C2×#482C2×C6711yescharacteristic, complemented
387C2×#480C2×C6711yescharacteristic, complemented
388C2×#478C2×C6711yescharacteristic, complemented
389C2×#474C2×C6711yescharacteristic, complemented
390C2×#469C2×C6711yescharacteristic, complemented
391C2×#466C2×C6711yescharacteristic, complemented
392C2×#442C2×C6711yescharacteristic, complemented
393C2×#435C2×C6711yescharacteristic, complemented
394C2×#428C2×C6711yescharacteristic, complemented
395C2×#427C2×C6711yescharacteristic, complemented
396C67C2×#334711yescharacteristic, direct product factor, Sylow
397C22×D8C22×C6711yescharacteristic
398C22×M16C22×C6711yescharacteristic
399C23×C8C22×C6711yescharacteristic
400#555—24no—
401#555C22×C6718yescomplemented
402#553—24no—
403#553C22×C6718yescomplemented
404C2×C4⋊Q8C22×C6711yescharacteristic
405C2×#126—21no—
406C2×#125C22×C6711yescharacteristic
407C2×#124—21no—
408C2×#124—21no—
409C2×#123—21no—
410C2×#121—21no—
411C2×#121—21no—
412C2×#121C22×C6711yescharacteristic
413C2×#121C22×C6711yescharacteristic
414C2×#121C22×C6711yescharacteristic
415C2×#121C22×C6711yescharacteristic
416C2×C4×D4—21no—
417C2×C4×D4C22×C6711yescharacteristic
418C2×C4×D4C22×C6711yescharacteristic
419C2×C4×D4C22×C6711yescharacteristic
420C2×#117—21no—
421C2×#117C22×C6711yescharacteristic
422C2×#117C22×C6711yescharacteristic
423C2×#117C22×C6711yescharacteristic
424C22×C4⋊C4C22×C6711yescharacteristic
425#501C22×C6718yescomplemented
426#482C22×C6718yescomplemented
427#482C22×C6718yescomplemented
428#482C22×C6718yescomplemented
429#480C22×C6718yescomplemented
430#478C22×C6718yescomplemented
431#474C22×C6718yescomplemented
432#469C22×C6718yescomplemented
433#466C22×C6718yescomplemented
434#442C22×C6718yescomplemented
435#435C22×C6718yescomplemented
436#428C22×C6718yescomplemented
437#427C22×C6718yescomplemented
438C2×#107C22×C6711yescharacteristic
439C2×#107C22×C6711yescharacteristic
440C2×#107C22×C6711yescharacteristic
441C2×#107C22×C6711yescharacteristic
442C2×#107C22×C6711yescharacteristic
443C2×#106C22×C6711yescharacteristic
444C2×#106C22×C6711yescharacteristic
445C2×#106C22×C6711yescharacteristic
446C2×#106C22×C6711yescharacteristic
447C2×C4⋊C8C22×C6711yescharacteristic
448C2×#102C22×C6711yescharacteristic
449C2×#102C22×C6711yescharacteristic
450C2×#102C22×C6711yescharacteristic
451C2×#102C22×C6711yescharacteristic
452C2×#102C22×C6711yescharacteristic
453C2×#102C22×C6711yescharacteristic
454C2×C22⋊C8C22×C6711yescharacteristic
455C2×C22⋊C8C22×C6711yescharacteristic
456C2×#97C22×C6711yescharacteristic
457C22×Q8—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4D4×C6711yescharacteristic
463C22×D4C23×C6711yescharacteristic
464C22×D4C23×C6711yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4C23×C6711yescharacteristic
469C23×C4C23×C6711yescharacteristic
470C2×D8—24no—
471C2×D8C23×C6714yes—
472C2×M16—24no—
473C2×M16C23×C6714yes—
474C22×C8—24no—
475C22×C8C23×C6711yescharacteristic
476C22×C8C23×C6714yes—
477C22×C8C23×C6711yescharacteristic
478C22×C8C23×C6711yescharacteristic
479C22×C8C23×C6711yescharacteristic
480C4⋊Q8—22no—
481C4⋊Q8C23×C6714yes—
482#126—28no—
483#125—22no—
484#125C23×C6714yes—
485#124—28no—
486#124—28no—
487#123—28no—
488#121—28no—
489#121—28no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121C23×C6714yes—
495#121C23×C6714yes—
496#121C23×C6714yes—
497#121C23×C6714yes—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4D4×C6714yes—
502C4×D4C23×C6714yes—
503C4×D4C23×C6714yes—
504C4×D4C23×C6714yes—
505#117—22no—
506#117—22no—
507#117—22no—
508#117—28no—
509#117C23×C6714yes—
510#117C23×C6714yes—
511#117C23×C6714yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4D4×C6711yescharacteristic
518C2×C4⋊C4C23×C6711yescharacteristic
519C2×C4⋊C4C23×C6711yescharacteristic
520C2×C4⋊C4C23×C6714yes—
521C2×C4⋊C4C23×C6711yescharacteristic
522C2×C4⋊C4C23×C6711yescharacteristic
523C2×C4⋊C4C23×C6711yescharacteristic
524C2×C4⋊C4C23×C6711yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4D4×C6711yescharacteristic
535C2×C22⋊C4D4×C6711yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—21no—
539C2×C42C23×C6711yescharacteristic
540#107C23×C6714yes—
541#107C23×C6714yes—
542#107C23×C6714yes—
543#107C23×C6714yes—
544#107C23×C6714yes—
545#106C23×C6714yes—
546#106C23×C6714yes—
547#106C23×C6714yes—
548#106C23×C6714yes—
549C4⋊C8C23×C6714yes—
550#102C23×C6714yes—
551#102C23×C6714yes—
552#102C23×C6714yes—
553#102C23×C6714yes—
554#102C23×C6714yes—
555#102C23×C6714yes—
556C22⋊C8C23×C6714yes—
557C22⋊C8C23×C6714yes—
558#97C23×C6714yes—
559C24—21no—
560C24—21no—
561C24C2×D4×C6711yescharacteristic
562C24C2×D4×C6711yescharacteristic
563C2×Q8—24no—
564C2×Q8—82no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—82no—
578C2×D4—82no—
579C2×D4—82no—
580C2×D4C2×D4×C6714yes—
581C2×D4C24×C6712yes—
582C2×D4C24×C6712yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4C2×D4×C6711yescharacteristic
600C22×C4C2×D4×C6711yescharacteristic
601C22×C4C2×D4×C6711yescharacteristic
602C22×C4C2×D4×C6711yescharacteristic
603C22×C4C2×D4×C6712yes—
604C22×C4C2×D4×C6712yes—
605C22×C4C24×C6712yes—
606C22×C4C24×C6712yes—
607C22×C4C24×C6711yescharacteristic
608D8—28no—
609M16—28no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—28no—
614C2×C8#41×C6714yes—
615C2×C8C24×C6712yes—
616C2×C8C24×C6712yes—
617C2×C8C24×C6712yes—
618C2×C8C24×C6712yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4C2×D4×C6714yes—
630C4⋊C4C24×C6712yes—
631C4⋊C4C24×C6712yes—
632C4⋊C4C24×C6712yes—
633C4⋊C4C24×C6712yes—
634C4⋊C4C24×C6712yes—
635C4⋊C4C24×C6712yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4C2×D4×C6714yes—
646C22⋊C4C2×D4×C6714yes—
647C42—24no—
648C42—24no—
649C42—24no—
650C42C2×D4×C6712yes—
651C42C24×C6712yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23C22×D4×C6712yes—
667C23C22×D4×C6712yes—
668C23C22×D4×C6711yescharacteristic
669Q8—84no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—44no—
675D4—48no—
676D4—42no—
677D4—42no—
678D4—84no—
679D4—84no—
680D4—84no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4C22×D4×C6712yes—
707C2×C4C22×D4×C6712yes—
708C2×C4C22×D4×C6712yes—
709C2×C4C22×D4×C6712yes—
710C2×C4C22×D4×C6711yescharacteristic
711C2×C4C2×#41×C6712yes—
712C2×C42−1+4×C6712yes—
713C2×C4C25×C6711yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8C2×#41×C6714yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—84no—
733C22—84no—
734C22#547×C6712yes—
735C22#575×C6712yes—
736C22#576×C6712yes—
737C22C23×D4×C6711yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4#547×C6712yes—
749C4C22×#41×C6711yescharacteristic
750C4C2×2−1+4×C6711yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—82no—
755C2C67×#334714yesdirect product factor
756C2C2×#547×C6711yescharacteristic
757C2C2×#575×C6711yescharacteristic
758C2C2×#576×C6711yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC2×C4C25×C67
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×C4×D4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#555×C67C2semidirect
2. C2×#553×C67C2semidirect
3. C67×#3347C2direct (N × H)
4. C2×#501×C67C2semidirect
5. C2×#482×C67C2semidirect
6. C2×#482×C67C2semidirect
7. C2×#482×C67C2semidirect
8. C2×#480×C67C2semidirect
9. C2×#478×C67C2semidirect
10. C2×#474×C67C2semidirect
11. C2×#469×C67C2semidirect
12. C2×#466×C67C2semidirect
13. C2×#442×C67C2semidirect
14. C2×#435×C67C2semidirect
15. C2×#428×C67C2semidirect
16. C2×#427×C67C2semidirect
21. #555×C67C22semidirect
23. #553×C67C22semidirect
45. #501×C67C22semidirect
46. #482×C67C22semidirect
47. #482×C67C22semidirect
48. #482×C67C22semidirect
49. #480×C67C22semidirect
50. #478×C67C22semidirect
51. #474×C67C22semidirect
52. #469×C67C22semidirect
53. #466×C67C22semidirect
54. #442×C67C22semidirect
55. #435×C67C22semidirect
56. #428×C67C22semidirect
57. #427×C67C22semidirect
371. C2×#3347C67direct (N × H)
376. C2×C67#3347direct (N × H)
380. C2×#555C2×C67semidirect
381. C2×#553C2×C67semidirect
382. #3347C2×C67direct (N × H)
383. C2×#501C2×C67semidirect
384. C2×#482C2×C67semidirect
385. C2×#482C2×C67semidirect
386. C2×#482C2×C67semidirect
387. C2×#480C2×C67semidirect
388. C2×#478C2×C67semidirect
389. C2×#474C2×C67semidirect
390. C2×#469C2×C67semidirect
391. C2×#466C2×C67semidirect
392. C2×#442C2×C67semidirect
393. C2×#435C2×C67semidirect
394. C2×#428C2×C67semidirect
395. C2×#427C2×C67semidirect
396. C67C2×#3347direct (N × H)
401. #555C22×C67semidirect
403. #553C22×C67semidirect
425. #501C22×C67semidirect
426. #482C22×C67semidirect
427. #482C22×C67semidirect
428. #482C22×C67semidirect
429. #480C22×C67semidirect
430. #478C22×C67semidirect
431. #474C22×C67semidirect
432. #469C22×C67semidirect
433. #466C22×C67semidirect
434. #442C22×C67semidirect
435. #435C22×C67semidirect
436. #428C22×C67semidirect
437. #427C22×C67semidirect
755. C2C67×#3347direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#555×C672
C2×#553×C672
C67×#33472
C2×#501×C672
C2×#482×C672
C2×#480×C672
C2×#478×C672
C2×#474×C672
C2×#469×C672
C2×#466×C672
C2×#442×C672
C2×#435×C672
C2×#428×C672
C2×#427×C672
C2×#334767