Finite Group Databasebeta

← C67×#21772 #30701023

Subgroups — C67×#21772 #30701023

Order 17152.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C67C211yesmaximal, characteristic
2C2×#408×C67C211yesmaximal, characteristic, complemented
3C67×#2311C211yesmaximal, characteristic, complemented
4C67×#1895C211yesmaximal, characteristic, complemented
5C67×#1894C211yesmaximal, characteristic, complemented
6C67×#1893C211yesmaximal, characteristic, complemented
7C67×#1892C211yesmaximal, characteristic, complemented
8C67×#1875C211yesmaximal, characteristic, complemented
9C67×#1874C211yesmaximal, characteristic, complemented
10C67×#1873C211yesmaximal, characteristic, complemented
11C67×#1872C211yesmaximal, characteristic, complemented
12C67×#1824C211yesmaximal, characteristic, complemented
13C67×#1823C211yesmaximal, characteristic, complemented
14C67×#1788C211yesmaximal, characteristic, complemented
15C67×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C22×#41×C67C2211yescharacteristic
18C22×M16×C67C2211yescharacteristic
19C23×C8×C67C2211yescharacteristic
20#537×C67—24no—
21#537×C67C418yescomplemented
22C2×C22⋊Q8×C67—21no—
23C2×C22⋊Q8×C67C2211yescharacteristic
24C2×C22⋊Q8×C67C2211yescharacteristic
25C2×#121×C67—21no—
26C2×#121×C67—21no—
27C2×#121×C67—21no—
28C2×#121×C67C2211yescharacteristic
29C2×#121×C67C2211yescharacteristic
30C2×#117×C67C2211yescharacteristic
31C22×C4⋊C4×C67C2211yescharacteristic
32C22×C4⋊C4×C67C2211yescharacteristic
33C2×#103×C67C2211yescharacteristic
34C2×#103×C67C2211yescharacteristic
35C2×#103×C67C2211yescharacteristic
36C2×#103×C67C2211yescharacteristic
37C2×#102×C67C2211yescharacteristic
38C2×#102×C67C2211yescharacteristic
39C2×#102×C67C2211yescharacteristic
40C2×#102×C67C2211yescharacteristic
41#408×C67—24no—
42C2×C22⋊C8×C67C2211yescharacteristic
43C2×C22⋊C8×C67C2211yescharacteristic
44C2×C22⋊C8×C67C2211yescharacteristic
45C2×C22⋊C8×C67C2211yescharacteristic
46#391×C67—21no—
47#390×C67—21no—
48#386×C67—21no—
49#386×C67—21no—
50#380×C67C2211yescharacteristic
51#380×C67C2211yescharacteristic
52#380×C67C2211yescharacteristic
53#380×C67C2211yescharacteristic
54#340×C67C2211yescharacteristic
55#340×C67C2211yescharacteristic
56#340×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic
60#340×C67C2211yescharacteristic
61#340×C67C2211yescharacteristic
62C2×#41×C67—22no—
63C2×#41×C67—41no—
64C2×#41×C67—41no—
65C2×#41×C67—41no—
66C2×#41×C67—41no—
67C2×#41×C67—41no—
68C2×#41×C67—41no—
69C2×#41×C67—41no—
70C2×#41×C67—41no—
71C2×#41×C67C2×C414yes—
72C2×#41×C67C2×C414yescomplemented
73C2×#41×C67D414yes—
74C22×Q8×C67D411yescharacteristic
75C22×Q8×C67C2311yescharacteristic
76C22×D4×C67—21no—
77C22×D4×C67—21no—
78C22×D4×C67—21no—
79C22×D4×C67D411yescharacteristic
80C22×D4×C67D411yescharacteristic
81C22×D4×C67D411yescharacteristic
82C22×D4×C67C2311yescharacteristic
83C23×C4×C67—21no—
84C23×C4×C67—21no—
85C23×C4×C67—21no—
86C23×C4×C67C2311yescharacteristic
87C23×C4×C67C2311yescharacteristic
88C23×C4×C67C2311yescharacteristic
89C2×M16×C67—22no—
90C2×M16×C67—41no—
91C2×M16×C67—41no—
92C22×C8×C67—22no—
93C22×C8×C67—41no—
94C22×C8×C67—41no—
95C22×C8×C67C2311yescharacteristic
96C22×C8×C67C2311yescharacteristic
97C22×C8×C67C2311yescharacteristic
98C22×C8×C67C2311yescharacteristic
99C22⋊Q8×C67—28no—
100C22⋊Q8×C67—22no—
101C22⋊Q8×C67—22no—
102C22⋊Q8×C67C2×C414yes—
103C22⋊Q8×C67C2×C414yescomplemented
104#121×C67—28no—
105#121×C67—28no—
106#121×C67—28no—
107#121×C67—22no—
108#121×C67—22no—
109#121×C67C2×C414yes—
110#121×C67C2×C414yescomplemented
111#117×C67—41no—
112#117×C67—41no—
113C2×C4⋊C4×C67—21no—
114C2×C4⋊C4×C67—22no—
115C2×C4⋊C4×C67—21no—
116C2×C4⋊C4×C67—21no—
117C2×C4⋊C4×C67—21no—
118C2×C4⋊C4×C67—41no—
119C2×C4⋊C4×C67—41no—
120C2×C4⋊C4×C67C2×C414yescomplemented
121C2×C4⋊C4×C67C2311yescharacteristic
122C2×C4⋊C4×C67C2311yescharacteristic
123C2×C4⋊C4×C67C2311yescharacteristic
124C2×C4⋊C4×C67C2311yescharacteristic
125C2×C4⋊C4×C67C2311yescharacteristic
126C2×C4⋊C4×C67C2311yescharacteristic
127C2×C22⋊C4×C67—21no—
128C2×C22⋊C4×C67—21no—
129C2×C22⋊C4×C67—21no—
130C2×C22⋊C4×C67—21no—
131C2×C22⋊C4×C67—21no—
132C2×C22⋊C4×C67—21no—
133C2×C22⋊C4×C67—21no—
134C2×C22⋊C4×C67—21no—
135C2×C22⋊C4×C67—21no—
136C2×C42×C67—21no—
137#103×C67—41no—
138#103×C67—41no—
139#103×C67—41no—
140#103×C67—41no—
141#102×C67—41no—
142#102×C67—41no—
143#102×C67—41no—
144#102×C67—41no—
145C22⋊C8×C67—22no—
146C22⋊C8×C67—22no—
147C22⋊C8×C67—22no—
148C22⋊C8×C67—22no—
149#95×C67—21no—
150#95×C67—21no—
151#95×C67—21no—
152#95×C67—21no—
153C24×C67—21no—
154C24×C67C2×D411yescharacteristic
155C24×C67C2×D411yescharacteristic
156C24×C67C2×D411yescharacteristic
157#41×C67—44no—
158#41×C67—44no—
159#41×C67—44no—
160#41×C67—44no—
161#41×C67—44no—
162#41×C67—44no—
163#41×C67—44no—
164#41×C67—44no—
165C2×Q8×C67—21no—
166C2×Q8×C67—21no—
167C2×Q8×C67—21no—
168C2×Q8×C67—21no—
169C2×Q8×C67—21no—
170C2×Q8×C67—41no—
171C2×Q8×C67—41no—
172C2×Q8×C67C22⋊C414yes—
173C2×Q8×C67C22×C412yes—
174C2×D4×C67—24no—
175C2×D4×C67—24no—
176C2×D4×C67—24no—
177C2×D4×C67—21no—
178C2×D4×C67—21no—
179C2×D4×C67—21no—
180C2×D4×C67—21no—
181C2×D4×C67—21no—
182C2×D4×C67—41no—
183C2×D4×C67—41no—
184C2×D4×C67—41no—
185C2×D4×C67—41no—
186C2×D4×C67—41no—
187C2×D4×C67—41no—
188C2×D4×C67—42no—
189C2×D4×C67—42no—
190C2×D4×C67—81no—
191C2×D4×C67—81no—
192C2×D4×C67—81no—
193C2×D4×C67—81no—
194C2×D4×C67C22⋊C414yes—
195C2×D4×C67C22⋊C414yes—
196C2×D4×C67C22⋊C414yes—
197C2×D4×C67C22×C412yes—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—21no—
201C22×C4×C67—21no—
202C22×C4×C67—21no—
203C22×C4×C67—21no—
204C22×C4×C67—21no—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
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—21no—
216C22×C4×C67—21no—
217C22×C4×C67—21no—
218C22×C4×C67—21no—
219C22×C4×C67—42no—
220C22×C4×C67—42no—
221C22×C4×C67—42no—
222C22×C4×C67—81no—
223C22×C4×C67—81no—
224C22×C4×C67—81no—
225C22×C4×C67—81no—
226C22×C4×C67C22×C412yes—
227C22×C4×C67C22×C412yes—
228C22×C4×C67C22×C412yes—
229C22×C4×C67C2×D411yescharacteristic
230C22×C4×C67C2×D411yescharacteristic
231C22×C4×C67C2×D411yescharacteristic
232C22×C4×C67C2×D412yes—
233C22×C4×C67C2×D412yes—
234C22×C4×C67C2×D412yes—
235C22×C4×C67C2411yescharacteristic
236M16×C67—44no—
237C2×C8×C67—21no—
238C2×C8×C67—21no—
239C2×C8×C67—21no—
240C2×C8×C67—21no—
241C2×C8×C67—21no—
242C2×C8×C67—21no—
243C2×C8×C67—21no—
244C2×C8×C67—21no—
245C2×C8×C67—21no—
246C2×C8×C67—21no—
247C2×C8×C67—21no—
248C2×C8×C67—21no—
249C2×C8×C67—44no—
250C4⋊C4×C67—24no—
251C4⋊C4×C67—24no—
252C4⋊C4×C67—24no—
253C4⋊C4×C67—21no—
254C4⋊C4×C67—21no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67—21no—
257C4⋊C4×C67—21no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67—21no—
260C4⋊C4×C67—21no—
261C4⋊C4×C67—21no—
262C4⋊C4×C67—21no—
263C4⋊C4×C67—42no—
264C4⋊C4×C67C22×C412yes—
265C4⋊C4×C67C22×C412yes—
266C22⋊C4×C67—24no—
267C22⋊C4×C67—24no—
268C22⋊C4×C67—24no—
269C22⋊C4×C67—24no—
270C22⋊C4×C67—42no—
271C22⋊C4×C67—81no—
272C22⋊C4×C67—81no—
273C22⋊C4×C67—81no—
274C22⋊C4×C67—81no—
275C42×C67—42no—
276C23×C67—21no—
277C23×C67—21no—
278C23×C67—21no—
279C23×C67—21no—
280C23×C67—21no—
281C23×C67—21no—
282C23×C67—21no—
283C23×C67—21no—
284C23×C67—21no—
285C23×C67—21no—
286C23×C67—21no—
287C23×C67—21no—
288C23×C67—21no—
289C23×C67—21no—
290C23×C67—21no—
291C23×C67—21no—
292C23×C67—21no—
293C23×C67—21no—
294C23×C67—22no—
295C23×C67—41no—
296C23×C67—41no—
297C23×C67—41no—
298C23×C67—41no—
299C23×C67—41no—
300C23×C67—41no—
301C23×C67C2×C22⋊C412yes—
302C23×C67C2×C22⋊C412yes—
303C23×C67C2×C22⋊C412yes—
304C23×C67C22×D411yescharacteristic
305Q8×C67—22no—
306Q8×C67—22no—
307Q8×C67—44no—
308Q8×C67—41no—
309Q8×C67—41no—
310D4×C67—22no—
311D4×C67—22no—
312D4×C67—44no—
313D4×C67—44no—
314D4×C67—44no—
315D4×C67—48no—
316D4×C67—41no—
317D4×C67—41no—
318D4×C67—84no—
319D4×C67—84no—
320C2×C4×C67—21no—
321C2×C4×C67—21no—
322C2×C4×C67—21no—
323C2×C4×C67—21no—
324C2×C4×C67—21no—
325C2×C4×C67—21no—
326C2×C4×C67—22no—
327C2×C4×C67—22no—
328C2×C4×C67—22no—
329C2×C4×C67—22no—
330C2×C4×C67—22no—
331C2×C4×C67—22no—
332C2×C4×C67—22no—
333C2×C4×C67—22no—
334C2×C4×C67—22no—
335C2×C4×C67—22no—
336C2×C4×C67—22no—
337C2×C4×C67—22no—
338C2×C4×C67—22no—
339C2×C4×C67—22no—
340C2×C4×C67—22no—
341C2×C4×C67—48no—
342C2×C4×C67—41no—
343C2×C4×C67—41no—
344C2×C4×C67—41no—
345C2×C4×C67—41no—
346C2×C4×C67—41no—
347C2×C4×C67—41no—
348C2×C4×C67—41no—
349C2×C4×C67—41no—
350C2×C4×C67—41no—
351C2×C4×C67—41no—
352C2×C4×C67—41no—
353C2×C4×C67—41no—
354C2×C4×C67—41no—
355C2×C4×C67—41no—
356C2×C4×C67—41no—
357C2×C4×C67—41no—
358C2×C4×C67—41no—
359C2×C4×C67—41no—
360C2×C4×C67—84no—
361C2×C4×C67—84no—
362C2×C4×C67C2×C22⋊C412yes—
363C2×C4×C67C2×C22⋊C412yes—
364C2×C4×C67C2×C22⋊C412yes—
365C2×C4×C67C23×C411yescharacteristic
366C2×C4×C67C22×D411yescharacteristic
367C2×C4×C67H(5,𝔽2)11yescharacteristic
368C2×C4×C67H(5,𝔽2)11yescharacteristic
369C2×C4×C67H(5,𝔽2)11yescharacteristic
370C2×C4×C67H(5,𝔽2)11yescharacteristic
371C8×C67—41no—
372C8×C67—41no—
373C8×C67—41no—
374C8×C67—41no—
375C22×C67—22no—
376C22×C67—22no—
377C22×C67—22no—
378C22×C67—22no—
379C22×C67—22no—
380C22×C67—22no—
381C22×C67—22no—
382C22×C67—22no—
383C22×C67—22no—
384C22×C67—41no—
385C22×C67—41no—
386C22×C67—41no—
387C22×C67—41no—
388C22×C67—41no—
389C22×C67—41no—
390C22×C67—41no—
391C22×C67—41no—
392C22×C67—41no—
393C22×C67—41no—
394C22×C67—41no—
395C22×C67—41no—
396C22×C67—42no—
397C22×C67—42no—
398C22×C67—42no—
399C22×C67—81no—
400C22×C67—81no—
401C22×C67—81no—
402C22×C67—81no—
403C22×C67C22×C22⋊C411yescharacteristic
404C22×C67#53411yescharacteristic
405C22×C67#53411yescharacteristic
406C22×C67#57611yescharacteristic
407C22×C67#57711yescharacteristic
408C22×C67#57711yescharacteristic
409C22×C67#57811yescharacteristic
410C4×C67—22no—
411C4×C67—22no—
412C4×C67—22no—
413C4×C67—42no—
414C4×C67—42no—
415C4×C67—42no—
416C4×C67—81no—
417C4×C67—81no—
418C4×C67—81no—
419C4×C67—81no—
420C4×C67#51811yescharacteristic
421C4×C67#51811yescharacteristic
422C4×C67#53411yescharacteristic
423C4×C67#53411yescharacteristic
424#21772C6711yesmaximal, characteristic, direct product factor, Sylow
425C2×C67—42no—
426C2×C67—42no—
427C2×C67—42no—
428C2×C67—82no—
429C2×C67#230811yescharacteristic
430C2×C67#289711yescharacteristic
431C2×C67#289811yescharacteristic
432C2×C67#319811yescharacteristic
433C2×C67#320111yescharacteristic
434C2×C67#320311yescharacteristic
435C2×C67#320411yescharacteristic
436C2×#537C2×C6711yescharacteristic
437C2×#408C2×C6711yescharacteristic, complemented
438#2311C2×C6711yescharacteristic, complemented
439#1895C2×C6711yescharacteristic, complemented
440#1894C2×C6711yescharacteristic, complemented
441#1893C2×C6711yescharacteristic, complemented
442#1892C2×C6711yescharacteristic, complemented
443#1875C2×C6711yescharacteristic, complemented
444#1874C2×C6711yescharacteristic, complemented
445#1873C2×C6711yescharacteristic, complemented
446#1872C2×C6711yescharacteristic, complemented
447#1824C2×C6711yescharacteristic, complemented
448#1823C2×C6711yescharacteristic, complemented
449#1788C2×C6711yescharacteristic, complemented
450#1788C2×C6711yescharacteristic, complemented
451C67#2177211yescharacteristic, direct product factor, Sylow
452C22×#41C22×C6711yescharacteristic
453C22×#41C22×C6711yescharacteristic
454C22×M16C22×C6711yescharacteristic
455C23×C8C22×C6711yescharacteristic
456#537—24no—
457#537C4×C6718yescomplemented
458C2×C22⋊Q8—21no—
459C2×C22⋊Q8C22×C6711yescharacteristic
460C2×C22⋊Q8C22×C6711yescharacteristic
461C2×#121—21no—
462C2×#121—21no—
463C2×#121—21no—
464C2×#121C22×C6711yescharacteristic
465C2×#121C22×C6711yescharacteristic
466C2×#117C22×C6711yescharacteristic
467C22×C4⋊C4C22×C6711yescharacteristic
468C22×C4⋊C4C22×C6711yescharacteristic
469C2×#103C22×C6711yescharacteristic
470C2×#103C22×C6711yescharacteristic
471C2×#103C22×C6711yescharacteristic
472C2×#103C22×C6711yescharacteristic
473C2×#102C22×C6711yescharacteristic
474C2×#102C22×C6711yescharacteristic
475C2×#102C22×C6711yescharacteristic
476C2×#102C22×C6711yescharacteristic
477#408—24no—
478C2×C22⋊C8C22×C6711yescharacteristic
479C2×C22⋊C8C22×C6711yescharacteristic
480C2×C22⋊C8C22×C6711yescharacteristic
481C2×C22⋊C8C22×C6711yescharacteristic
482#391—21no—
483#390—21no—
484#386—21no—
485#386—21no—
486#380C22×C6711yescharacteristic
487#380C22×C6711yescharacteristic
488#380C22×C6711yescharacteristic
489#380C22×C6711yescharacteristic
490#340C22×C6711yescharacteristic
491#340C22×C6711yescharacteristic
492#340C22×C6711yescharacteristic
493#340C22×C6711yescharacteristic
494#340C22×C6711yescharacteristic
495#340C22×C6711yescharacteristic
496#340C22×C6711yescharacteristic
497#340C22×C6711yescharacteristic
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×C4×C6714yes—
508C2×#41C2×C4×C6714yescomplemented
509C2×#41D4×C6714yes—
510C22×Q8D4×C6711yescharacteristic
511C22×Q8C23×C6711yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C6711yescharacteristic
516C22×D4D4×C6711yescharacteristic
517C22×D4D4×C6711yescharacteristic
518C22×D4C23×C6711yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C6711yescharacteristic
523C23×C4C23×C6711yescharacteristic
524C23×C4C23×C6711yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C23×C6711yescharacteristic
532C22×C8C23×C6711yescharacteristic
533C22×C8C23×C6711yescharacteristic
534C22×C8C23×C6711yescharacteristic
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×C4×C6714yes—
539C22⋊Q8C2×C4×C6714yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×C4×C6714yes—
546#121C2×C4×C6714yescomplemented
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4C2×C4×C6714yescomplemented
557C2×C4⋊C4C23×C6711yescharacteristic
558C2×C4⋊C4C23×C6711yescharacteristic
559C2×C4⋊C4C23×C6711yescharacteristic
560C2×C4⋊C4C23×C6711yescharacteristic
561C2×C4⋊C4C23×C6711yescharacteristic
562C2×C4⋊C4C23×C6711yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C42—21no—
573#103—41no—
574#103—41no—
575#103—41no—
576#103—41no—
577#102—41no—
578#102—41no—
579#102—41no—
580#102—41no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C6711yescharacteristic
591C24C2×D4×C6711yescharacteristic
592C24C2×D4×C6711yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊C4×C6714yes—
609C2×Q8C22×C4×C6712yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊C4×C6714yes—
631C2×D4C22⋊C4×C6714yes—
632C2×D4C22⋊C4×C6714yes—
633C2×D4C22×C4×C6712yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C22×C4×C6712yes—
663C22×C4C22×C4×C6712yes—
664C22×C4C22×C4×C6712yes—
665C22×C4C2×D4×C6711yescharacteristic
666C22×C4C2×D4×C6711yescharacteristic
667C22×C4C2×D4×C6711yescharacteristic
668C22×C4C2×D4×C6712yes—
669C22×C4C2×D4×C6712yes—
670C22×C4C2×D4×C6712yes—
671C22×C4C24×C6711yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4C22×C4×C6712yes—
701C4⋊C4C22×C4×C6712yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊C4×C6712yes—
738C23C2×C22⋊C4×C6712yes—
739C23C2×C22⋊C4×C6712yes—
740C23C22×D4×C6711yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4C2×C22⋊C4×C6712yes—
799C2×C4C2×C22⋊C4×C6712yes—
800C2×C4C2×C22⋊C4×C6712yes—
801C2×C4C23×C4×C6711yescharacteristic
802C2×C4C22×D4×C6711yescharacteristic
803C2×C4H(5,𝔽2)×C6711yescharacteristic
804C2×C4H(5,𝔽2)×C6711yescharacteristic
805C2×C4H(5,𝔽2)×C6711yescharacteristic
806C2×C4H(5,𝔽2)×C6711yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊C4×C6711yescharacteristic
840C22#534×C6711yescharacteristic
841C22#534×C6711yescharacteristic
842C22#576×C6711yescharacteristic
843C22#577×C6711yescharacteristic
844C22#577×C6711yescharacteristic
845C22#578×C6711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4#518×C6711yescharacteristic
857C4#518×C6711yescharacteristic
858C4#534×C6711yescharacteristic
859C4#534×C6711yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2C67×#230811yescharacteristic
865C2C67×#289711yescharacteristic
866C2C67×#289811yescharacteristic
867C2C67×#319811yescharacteristic
868C2C67×#320111yescharacteristic
869C2C67×#320311yescharacteristic
870C2C67×#320411yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutatorC2×C4C23×C4×C67
Frattini, cosocleC22×C4C24×C67
prime radicalC2×#537×C67C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C22×#41×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#408×C67C2semidirect
3. C67×#2311C2semidirect
4. C67×#1895C2semidirect
5. C67×#1894C2semidirect
6. C67×#1893C2semidirect
7. C67×#1892C2semidirect
8. C67×#1875C2semidirect
9. C67×#1874C2semidirect
10. C67×#1873C2semidirect
11. C67×#1872C2semidirect
12. C67×#1824C2semidirect
13. C67×#1823C2semidirect
14. C67×#1788C2semidirect
15. C67×#1788C2semidirect
21. #537×C67C4semidirect
72. C2×#41×C67C2×C4semidirect
103. C22⋊Q8×C67C2×C4semidirect
110. #121×C67C2×C4semidirect
120. C2×C4⋊C4×C67C2×C4semidirect
424. #21772C67direct (N × H)
437. C2×#408C2×C67semidirect
438. #2311C2×C67semidirect
439. #1895C2×C67semidirect
440. #1894C2×C67semidirect
441. #1893C2×C67semidirect
442. #1892C2×C67semidirect
443. #1875C2×C67semidirect
444. #1874C2×C67semidirect
445. #1873C2×C67semidirect
446. #1872C2×C67semidirect
447. #1824C2×C67semidirect
448. #1823C2×C67semidirect
449. #1788C2×C67semidirect
450. #1788C2×C67semidirect
451. C67#21772direct (N × H)
457. #537C4×C67semidirect
508. C2×#41C2×C4×C67semidirect
539. C22⋊Q8C2×C4×C67semidirect
546. #121C2×C4×C67semidirect
556. C2×C4⋊C4C2×C4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C672
C2×#408×C672
C67×#23112
C67×#18952
C67×#18942
C67×#18932
C67×#18922
C67×#18752
C67×#18742
C67×#18732
C67×#18722
C67×#18242
C67×#18232
C67×#17882
#2177267