Finite Group Databasebeta

← C67×#22445 #30701696

Subgroups — C67×#22445 #30701696

Order 17152.

1406 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C67C211yesmaximal, characteristic
2C2×#441×C67C211yesmaximal, characteristic, complemented
3C2×C4×Q16×C67C211yesmaximal, characteristic, complemented
4C67×#2341C211yesmaximal, characteristic
5Q8×C22⋊C4×C67C211yesmaximal, characteristic, complemented
6C67×#1973C211yesmaximal, characteristic, complemented
7C67×#1968C211yesmaximal, characteristic, complemented
8C67×#1880C211yesmaximal, characteristic, complemented
9C67×#1880C211yesmaximal, characteristic, complemented
10C67×#1878C211yesmaximal, characteristic, complemented
11C67×#1878C211yesmaximal, characteristic, complemented
12C67×#1809C211yesmaximal, characteristic, complemented
13C67×#1788C211yesmaximal, characteristic
14C67×#1787C211yesmaximal, characteristic, complemented
15C67×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C23×Q8×C67C2211yescharacteristic
18C2×#137×C67—24no—
19C2×#137×C67—24no—
20C2×#137×C67C418yescomplemented
21C22×Q16×C67C2211yescharacteristic
22C22×Q16×C67C2211yescharacteristic
23C22×SD16×C67C2211yescharacteristic
24C22×SD16×C67C2211yescharacteristic
25C22×M16×C67C2211yescharacteristic
26C2×C4×Q8×C67C2211yescharacteristic
27C2×C4×Q8×C67C2211yescharacteristic
28C2×C4×Q8×C67C2211yescharacteristic
29C2×C4×Q8×C67C2211yescharacteristic
30#441×C67—24no—
31C4×Q16×C67—24no—
32C2×#107×C67C2211yescharacteristic
33C2×#106×C67C2211yescharacteristic
34C2×#103×C67C2211yescharacteristic
35C2×#103×C67C2211yescharacteristic
36C2×#103×C67C2211yescharacteristic
37C2×#103×C67C2211yescharacteristic
38C2×#103×C67C2211yescharacteristic
39C2×#103×C67C2211yescharacteristic
40C2×#102×C67C2211yescharacteristic
41C2×#102×C67C2211yescharacteristic
42C2×C22⋊C8×C67C2211yescharacteristic
43C2×#97×C67C2211yescharacteristic
44C2×C4×C8×C67C2211yescharacteristic
45#391×C67—21no—
46#391×C67—21no—
47#391×C67C2211yescharacteristic
48#391×C67C2211yescharacteristic
49#390×C67—21no—
50#390×C67—21no—
51#390×C67C2211yescharacteristic
52#390×C67C2211yescharacteristic
53#380×C67—21no—
54#380×C67—21no—
55#380×C67C2211yescharacteristic
56#380×C67C2211yescharacteristic
57C4×C22⋊C4×C67—21no—
58C4×C22⋊C4×C67—21no—
59C4×C22⋊C4×C67C2211yescharacteristic
60#340×C67C2211yescharacteristic
61#340×C67C2211yescharacteristic
62#336×C67C2211yescharacteristic
63#336×C67C2211yescharacteristic
64C2×#41×C67—22no—
65C2×#41×C67—22no—
66C2×#41×C67—22no—
67C2×#41×C67—41no—
68C2×#41×C67—41no—
69C2×#41×C67C2×C414yes—
70C22×Q8×C67—21no—
71C22×Q8×C67—22no—
72C22×Q8×C67—22no—
73C22×Q8×C67—22no—
74C22×Q8×C67—41no—
75C22×Q8×C67—41no—
76C22×Q8×C67C2×C414yes—
77C22×Q8×C67C2311yescharacteristic
78C22×Q8×C67C2311yescharacteristic
79C22×Q8×C67C2311yescharacteristic
80C22×D4×C67—21no—
81C22×D4×C67C2311yescharacteristic
82C23×C4×C67—21no—
83C23×C4×C67—21no—
84C23×C4×C67C2311yescharacteristic
85#137×C67—232no—
86C2×Q16×C67—22no—
87C2×Q16×C67—22no—
88C2×Q16×C67C2×C414yes—
89C2×Q16×C67C2×C414yes—
90C2×Q16×C67D414yes—
91C2×Q16×C67D414yes—
92C2×SD16×C67—22no—
93C2×SD16×C67—22no—
94C2×SD16×C67—22no—
95C2×SD16×C67—22no—
96C2×SD16×C67C2×C414yes—
97C2×SD16×C67C2×C414yes—
98C2×M16×C67—22no—
99C2×M16×C67—22no—
100C2×M16×C67C2×C414yes—
101C22×C8×C67C2311yescharacteristic
102C22×C8×C67C2311yescharacteristic
103C22×C8×C67C2311yescharacteristic
104C22×C8×C67C2311yescharacteristic
105C4×Q8×C67—22no—
106C4×Q8×C67—22no—
107C4×Q8×C67—22no—
108C4×Q8×C67—22no—
109C4×Q8×C67—41no—
110C4×Q8×C67—41no—
111C4×Q8×C67—41no—
112C4×Q8×C67—41no—
113C2×C4⋊C4×C67—21no—
114C2×C4⋊C4×C67—21no—
115C2×C4⋊C4×C67—21no—
116C2×C4⋊C4×C67—21no—
117C2×C4⋊C4×C67C2311yescharacteristic
118C2×C4⋊C4×C67C2311yescharacteristic
119C2×C4⋊C4×C67C2311yescharacteristic
120C2×C4⋊C4×C67C2311yescharacteristic
121C2×C22⋊C4×C67—21no—
122C2×C22⋊C4×C67—21no—
123C2×C22⋊C4×C67—21no—
124C2×C22⋊C4×C67—21no—
125C2×C22⋊C4×C67—21no—
126C2×C22⋊C4×C67—21no—
127C2×C22⋊C4×C67D411yescharacteristic
128C2×C22⋊C4×C67D411yescharacteristic
129C2×C42×C67—21no—
130C2×C42×C67—21no—
131C2×C42×C67—21no—
132C2×C42×C67—21no—
133C2×C42×C67C2311yescharacteristic
134C2×C42×C67C2311yescharacteristic
135#107×C67—22no—
136#106×C67—22no—
137#103×C67—22no—
138#103×C67—22no—
139#103×C67—22no—
140#103×C67—22no—
141#103×C67—41no—
142#103×C67—41no—
143#102×C67—41no—
144#102×C67—41no—
145C22⋊C8×C67—22no—
146#97×C67—22no—
147C4×C8×C67—22no—
148#95×C67—21no—
149#95×C67—21no—
150#95×C67—21no—
151#95×C67—21no—
152#95×C67—21no—
153#95×C67—21no—
154#95×C67D411yescharacteristic
155#95×C67D411yescharacteristic
156C24×C67—21no—
157C24×C67C2×D411yescharacteristic
158#41×C67—28no—
159#41×C67—44no—
160#41×C67—44no—
161#41×C67—44no—
162C2×Q8×C67—24no—
163C2×Q8×C67—21no—
164C2×Q8×C67—21no—
165C2×Q8×C67—21no—
166C2×Q8×C67—21no—
167C2×Q8×C67—21no—
168C2×Q8×C67—21no—
169C2×Q8×C67—21no—
170C2×Q8×C67—28no—
171C2×Q8×C67—21no—
172C2×Q8×C67—21no—
173C2×Q8×C67—21no—
174C2×Q8×C67—21no—
175C2×Q8×C67—42no—
176C2×Q8×C67—42no—
177C2×Q8×C67—44no—
178C2×Q8×C67—44no—
179C2×Q8×C67—44no—
180C2×Q8×C67C22×C412yes—
181C2×Q8×C67C22×C412yes—
182C2×Q8×C67C22×C412yes—
183C2×Q8×C67C2×D412yes—
184C2×Q8×C67C2×D412yes—
185C2×Q8×C67C2×D412yes—
186C2×Q8×C67C2×D412yes—
187C2×D4×C67—24no—
188C2×D4×C67—21no—
189C2×D4×C67—21no—
190C2×D4×C67—21no—
191C2×D4×C67—21no—
192C2×D4×C67—21no—
193C2×D4×C67—42no—
194C2×D4×C67—42no—
195C2×D4×C67C22×C412yes—
196C22×C4×C67—21no—
197C22×C4×C67—21no—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—21no—
201C22×C4×C67—21no—
202C22×C4×C67—24no—
203C22×C4×C67—21no—
204C22×C4×C67—24no—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—21no—
208C22×C4×C67—21no—
209C22×C4×C67—42no—
210C22×C4×C67—42no—
211C22×C4×C67—42no—
212C22×C4×C67—42no—
213C22×C4×C67C22×C412yes—
214C22×C4×C67C2×D411yescharacteristic
215C22×C4×C67C2×D411yescharacteristic
216C22×C4×C67C2×D411yescharacteristic
217C22×C4×C67C2×D411yescharacteristic
218C22×C4×C67C2×D411yescharacteristic
219C22×C4×C67#4112yes—
220C22×C4×C67C2411yescharacteristic
221Q16×C67—28no—
222Q16×C67C22⋊C4116yescomplemented
223SD16×C67—28no—
224SD16×C67—28no—
225M16×C67—28no—
226C2×C8×C67—21no—
227C2×C8×C67—21no—
228C2×C8×C67—21no—
229C2×C8×C67—21no—
230C2×C8×C67—21no—
231C2×C8×C67—21no—
232C2×C8×C67—21no—
233C2×C8×C67—21no—
234C2×C8×C67C22×C412yes—
235C2×C8×C67C22×C412yes—
236C2×C8×C67C2×D412yes—
237C2×C8×C67C2×D412yes—
238C4⋊C4×C67—21no—
239C4⋊C4×C67—21no—
240C4⋊C4×C67—21no—
241C4⋊C4×C67—21no—
242C4⋊C4×C67—21no—
243C4⋊C4×C67—21no—
244C4⋊C4×C67—21no—
245C4⋊C4×C67—21no—
246C4⋊C4×C67—42no—
247C4⋊C4×C67—42no—
248C4⋊C4×C67—42no—
249C4⋊C4×C67—42no—
250C22⋊C4×C67—22no—
251C22⋊C4×C67—41no—
252C22⋊C4×C67—42no—
253C22⋊C4×C67—42no—
254C22⋊C4×C67—42no—
255C22⋊C4×C67—81no—
256C22⋊C4×C67—81no—
257C22⋊C4×C67—81no—
258C42×C67—21no—
259C42×C67—21no—
260C42×C67—21no—
261C42×C67—21no—
262C42×C67—42no—
263C42×C67—42no—
264C42×C67—42no—
265C42×C67—42no—
266C23×C67—21no—
267C23×C67—21no—
268C23×C67—21no—
269C23×C67—21no—
270C23×C67—21no—
271C23×C67—21no—
272C23×C67—22no—
273C23×C67—41no—
274C23×C67—41no—
275C23×C67—41no—
276C23×C67—41no—
277C23×C67—41no—
278C23×C67—41no—
279C23×C67C4×D412yes—
280C23×C67C22×D411yescharacteristic
281Q8×C67—22no—
282Q8×C67—22no—
283Q8×C67—22no—
284Q8×C67—22no—
285Q8×C67—22no—
286Q8×C67—22no—
287Q8×C67—22no—
288Q8×C67—22no—
289Q8×C67—48no—
290Q8×C67—41no—
291Q8×C67—41no—
292Q8×C67C2×C22⋊C414yes—
293Q8×C67C2×C22⋊C414yes—
294D4×C67—22no—
295D4×C67—22no—
296D4×C67—48no—
297D4×C67—41no—
298D4×C67—41no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—21no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—21no—
307C2×C4×C67—21no—
308C2×C4×C67—21no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—21no—
315C2×C4×C67—21no—
316C2×C4×C67—21no—
317C2×C4×C67—21no—
318C2×C4×C67—21no—
319C2×C4×C67—21no—
320C2×C4×C67—21no—
321C2×C4×C67—21no—
322C2×C4×C67—21no—
323C2×C4×C67—48no—
324C2×C4×C67—48no—
325C2×C4×C67—41no—
326C2×C4×C67—41no—
327C2×C4×C67—41no—
328C2×C4×C67—41no—
329C2×C4×C67—41no—
330C2×C4×C67—41no—
331C2×C4×C67—41no—
332C2×C4×C67—41no—
333C2×C4×C67—41no—
334C2×C4×C67—41no—
335C2×C4×C67—41no—
336C2×C4×C67—41no—
337C2×C4×C67—41no—
338C2×C4×C67—41no—
339C2×C4×C67C4×D412yes—
340C2×C4×C67#13712yescomplemented
341C2×C4×C67C23×C411yescharacteristic
342C2×C4×C67C22×D411yescharacteristic
343C2×C4×C67C22×D411yescharacteristic
344C2×C4×C67C2×#4111yescharacteristic
345C2×C4×C67H(5,𝔽2)11yescharacteristic
346C2×C4×C67H(5,𝔽2)11yescharacteristic
347C8×C67—22no—
348C8×C67—41no—
349C8×C67—41no—
350C8×C67C2×C22⋊C414yes—
351C22×C67—22no—
352C22×C67—22no—
353C22×C67—22no—
354C22×C67—41no—
355C22×C67—41no—
356C22×C67—41no—
357C22×C67—41no—
358C22×C67—42no—
359C22×C67—42no—
360C22×C67—42no—
361C22×C67—81no—
362C22×C67—81no—
363C22×C67—81no—
364C22×C67—81no—
365C22×C67C2×C4×D411yescharacteristic
366C22×C67D4211yescharacteristic
367C22×C67D4211yescharacteristic
368C22×C67C2×#13711yescharacteristic
369C22×C67#57511yescharacteristic
370C22×C67#57711yescharacteristic
371C22×C67#57811yescharacteristic
372C4×C67—22no—
373C4×C67—24no—
374C4×C67—24no—
375C4×C67—22no—
376C4×C67—42no—
377C4×C67—41no—
378C4×C67—41no—
379C4×C67—41no—
380C4×C67—81no—
381C4×C67—81no—
382C4×C67—81no—
383C4×C67—81no—
384C4×C67C22×C22⋊C411yescharacteristic
385C4×C67#51811yescharacteristic
386C4×C67#54611yescharacteristic
387C4×C67#54611yescharacteristic
388#22445C6711yesmaximal, characteristic, direct product factor, Sylow
389C2×C67—42no—
390C2×C67—82no—
391C2×C67D4×C22⋊C411yescharacteristic
392C2×C67C4×#13711yescharacteristic
393C2×C67#294711yescharacteristic
394C2×C67#327011yescharacteristic
395C2×C67#327111yescharacteristic
396C2×C67#327711yescharacteristic
397C2×C67#327811yescharacteristic
398C22×#137C2×C6711yescharacteristic
399C2×#441C2×C6711yescharacteristic, complemented
400C2×C4×Q16C2×C6711yescharacteristic, complemented
401#2341C2×C6711yescharacteristic
402Q8×C22⋊C4C2×C6711yescharacteristic, complemented
403#1973C2×C6711yescharacteristic, complemented
404#1968C2×C6711yescharacteristic, complemented
405#1880C2×C6711yescharacteristic, complemented
406#1880C2×C6711yescharacteristic, complemented
407#1878C2×C6711yescharacteristic, complemented
408#1878C2×C6711yescharacteristic, complemented
409#1809C2×C6711yescharacteristic, complemented
410#1788C2×C6711yescharacteristic
411#1787C2×C6711yescharacteristic, complemented
412#1753C2×C6711yescharacteristic, complemented
413C67#2244511yescharacteristic, direct product factor, Sylow
414C22×#41C22×C6711yescharacteristic
415C23×Q8C22×C6711yescharacteristic
416C2×#137—24no—
417C2×#137—24no—
418C2×#137C4×C6718yescomplemented
419C22×Q16C22×C6711yescharacteristic
420C22×Q16C22×C6711yescharacteristic
421C22×SD16C22×C6711yescharacteristic
422C22×SD16C22×C6711yescharacteristic
423C22×M16C22×C6711yescharacteristic
424C2×C4×Q8C22×C6711yescharacteristic
425C2×C4×Q8C22×C6711yescharacteristic
426C2×C4×Q8C22×C6711yescharacteristic
427C2×C4×Q8C22×C6711yescharacteristic
428#441—24no—
429C4×Q16—24no—
430C2×#107C22×C6711yescharacteristic
431C2×#106C22×C6711yescharacteristic
432C2×#103C22×C6711yescharacteristic
433C2×#103C22×C6711yescharacteristic
434C2×#103C22×C6711yescharacteristic
435C2×#103C22×C6711yescharacteristic
436C2×#103C22×C6711yescharacteristic
437C2×#103C22×C6711yescharacteristic
438C2×#102C22×C6711yescharacteristic
439C2×#102C22×C6711yescharacteristic
440C2×C22⋊C8C22×C6711yescharacteristic
441C2×#97C22×C6711yescharacteristic
442C2×C4×C8C22×C6711yescharacteristic
443#391—21no—
444#391—21no—
445#391C22×C6711yescharacteristic
446#391C22×C6711yescharacteristic
447#390—21no—
448#390—21no—
449#390C22×C6711yescharacteristic
450#390C22×C6711yescharacteristic
451#380—21no—
452#380—21no—
453#380C22×C6711yescharacteristic
454#380C22×C6711yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4C22×C6711yescharacteristic
458#340C22×C6711yescharacteristic
459#340C22×C6711yescharacteristic
460#336C22×C6711yescharacteristic
461#336C22×C6711yescharacteristic
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C2×#41C2×C4×C6714yes—
468C22×Q8—21no—
469C22×Q8—22no—
470C22×Q8—22no—
471C22×Q8—22no—
472C22×Q8—41no—
473C22×Q8—41no—
474C22×Q8C2×C4×C6714yes—
475C22×Q8C23×C6711yescharacteristic
476C22×Q8C23×C6711yescharacteristic
477C22×Q8C23×C6711yescharacteristic
478C22×D4—21no—
479C22×D4C23×C6711yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C6711yescharacteristic
483#137—232no—
484C2×Q16—22no—
485C2×Q16—22no—
486C2×Q16C2×C4×C6714yes—
487C2×Q16C2×C4×C6714yes—
488C2×Q16D4×C6714yes—
489C2×Q16D4×C6714yes—
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16C2×C4×C6714yes—
495C2×SD16C2×C4×C6714yes—
496C2×M16—22no—
497C2×M16—22no—
498C2×M16C2×C4×C6714yes—
499C22×C8C23×C6711yescharacteristic
500C22×C8C23×C6711yescharacteristic
501C22×C8C23×C6711yescharacteristic
502C22×C8C23×C6711yescharacteristic
503C4×Q8—22no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8—22no—
507C4×Q8—41no—
508C4×Q8—41no—
509C4×Q8—41no—
510C4×Q8—41no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4C23×C6711yescharacteristic
516C2×C4⋊C4C23×C6711yescharacteristic
517C2×C4⋊C4C23×C6711yescharacteristic
518C2×C4⋊C4C23×C6711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4D4×C6711yescharacteristic
526C2×C22⋊C4D4×C6711yescharacteristic
527C2×C42—21no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42C23×C6711yescharacteristic
532C2×C42C23×C6711yescharacteristic
533#107—22no—
534#106—22no—
535#103—22no—
536#103—22no—
537#103—22no—
538#103—22no—
539#103—41no—
540#103—41no—
541#102—41no—
542#102—41no—
543C22⋊C8—22no—
544#97—22no—
545C4×C8—22no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95D4×C6711yescharacteristic
553#95D4×C6711yescharacteristic
554C24—21no—
555C24C2×D4×C6711yescharacteristic
556#41—28no—
557#41—44no—
558#41—44no—
559#41—44no—
560C2×Q8—24no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—28no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8C22×C4×C6712yes—
579C2×Q8C22×C4×C6712yes—
580C2×Q8C22×C4×C6712yes—
581C2×Q8C2×D4×C6712yes—
582C2×Q8C2×D4×C6712yes—
583C2×Q8C2×D4×C6712yes—
584C2×Q8C2×D4×C6712yes—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4C22×C4×C6712yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4C22×C4×C6712yes—
612C22×C4C2×D4×C6711yescharacteristic
613C22×C4C2×D4×C6711yescharacteristic
614C22×C4C2×D4×C6711yescharacteristic
615C22×C4C2×D4×C6711yescharacteristic
616C22×C4C2×D4×C6711yescharacteristic
617C22×C4#41×C6712yes—
618C22×C4C24×C6711yescharacteristic
619Q16—28no—
620Q16C22⋊C4×C67116yescomplemented
621SD16—28no—
622SD16—28no—
623M16—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8C22×C4×C6712yes—
633C2×C8C22×C4×C6712yes—
634C2×C8C2×D4×C6712yes—
635C2×C8C2×D4×C6712yes—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C22⋊C4—22no—
649C22⋊C4—41no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C22⋊C4—81no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—42no—
661C42—42no—
662C42—42no—
663C42—42no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23C4×D4×C6712yes—
678C23C22×D4×C6711yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—48no—
688Q8—41no—
689Q8—41no—
690Q8C2×C22⋊C4×C6714yes—
691Q8C2×C22⋊C4×C6714yes—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—41no—
696D4—41no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—48no—
722C2×C4—48no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4C4×D4×C6712yes—
738C2×C4#137×C6712yescomplemented
739C2×C4C23×C4×C6711yescharacteristic
740C2×C4C22×D4×C6711yescharacteristic
741C2×C4C22×D4×C6711yescharacteristic
742C2×C4C2×#41×C6711yescharacteristic
743C2×C4H(5,𝔽2)×C6711yescharacteristic
744C2×C4H(5,𝔽2)×C6711yescharacteristic
745C8—22no—
746C8—41no—
747C8—41no—
748C8C2×C22⋊C4×C6714yes—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22C2×C4×D4×C6711yescharacteristic
764C22D42×C6711yescharacteristic
765C22D42×C6711yescharacteristic
766C22C2×#137×C6711yescharacteristic
767C22#575×C6711yescharacteristic
768C22#577×C6711yescharacteristic
769C22#578×C6711yescharacteristic
770C4—22no—
771C4—22no—
772C4—24no—
773C4—24no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—42no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4C22×C22⋊C4×C6711yescharacteristic
783C4#518×C6711yescharacteristic
784C4#546×C6711yescharacteristic
785C4#546×C6711yescharacteristic
786C2—42no—
787C2—82no—
788C2D4×C22⋊C4×C6711yescharacteristic
789C2C4×#137×C6711yescharacteristic
790C2C67×#294711yescharacteristic
791C2C67×#327011yescharacteristic
792C2C67×#327111yescharacteristic
793C2C67×#327711yescharacteristic
794C2C67×#327811yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutatorC2×C4C23×C4×C67
Frattini, cosocleC22×C4C24×C67
prime radicalC22×#41×C67C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C4×C22⋊C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#441×C67C2semidirect
3. C2×C4×Q16×C67C2semidirect
5. Q8×C22⋊C4×C67C2semidirect
6. C67×#1973C2semidirect
7. C67×#1968C2semidirect
8. C67×#1880C2semidirect
9. C67×#1880C2semidirect
10. C67×#1878C2semidirect
11. C67×#1878C2semidirect
12. C67×#1809C2semidirect
14. C67×#1787C2semidirect
15. C67×#1753C2semidirect
20. C2×#137×C67C4semidirect
222. Q16×C67C22⋊C4semidirect
340. C2×C4×C67#137semidirect
388. #22445C67direct (N × H)
399. C2×#441C2×C67semidirect
400. C2×C4×Q16C2×C67semidirect
402. Q8×C22⋊C4C2×C67semidirect
403. #1973C2×C67semidirect
404. #1968C2×C67semidirect
405. #1880C2×C67semidirect
406. #1880C2×C67semidirect
407. #1878C2×C67semidirect
408. #1878C2×C67semidirect
409. #1809C2×C67semidirect
411. #1787C2×C67semidirect
412. #1753C2×C67semidirect
413. C67#22445direct (N × H)
418. C2×#137C4×C67semidirect
620. Q16C22⋊C4×C67semidirect
738. C2×C4#137×C67semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C672
C2×#441×C672
C2×C4×Q16×C672
C67×#23412
Q8×C22⋊C4×C672
C67×#19732
C67×#19682
C67×#18802
C67×#18782
C67×#18092
C67×#17882
C67×#17872
C67×#17532
#2244567