Finite Group Databasebeta

← C67×#22444 #30701695

Subgroups — C67×#22444 #30701695

Order 17152.

1434 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C67C211yesmaximal, characteristic
2C2×#440×C67C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C67C211yesmaximal, characteristic, complemented
4Q8×C22⋊C4×C67C211yesmaximal, characteristic, complemented
5C67×#2339C211yesmaximal, characteristic
6C67×#1971C211yesmaximal, characteristic, complemented
7C67×#1969C211yesmaximal, characteristic, complemented
8C67×#1878C211yesmaximal, characteristic, complemented
9C67×#1878C211yesmaximal, characteristic, complemented
10C67×#1877C211yesmaximal, characteristic, complemented
11C67×#1877C211yesmaximal, 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×D4×C67C2211yescharacteristic
29C2×C4×D4×C67C2211yescharacteristic
30#440×C67—24no—
31C4×SD16×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#391×C67C2211yescharacteristic
50#391×C67C2211yescharacteristic
51#386×C67—21no—
52#386×C67—21no—
53#381×C67—21no—
54#380×C67—21no—
55#380×C67C2211yescharacteristic
56#380×C67C2211yescharacteristic
57C4×C22⋊C4×C67—21no—
58C4×C22⋊C4×C67C2211yescharacteristic
59C2×#95×C67—21no—
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×C414yescomplemented
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×C67—21no—
85C23×C4×C67—21no—
86C23×C4×C67C2311yescharacteristic
87#137×C67—232no—
88C2×Q16×C67—22no—
89C2×Q16×C67—22no—
90C2×Q16×C67—22no—
91C2×Q16×C67—22no—
92C2×Q16×C67C2×C414yescomplemented
93C2×Q16×C67C2×C414yescomplemented
94C2×SD16×C67—22no—
95C2×SD16×C67—22no—
96C2×SD16×C67C2×C414yes—
97C2×SD16×C67C2×C414yes—
98C2×SD16×C67D414yes—
99C2×SD16×C67D414yes—
100C2×M16×C67—22no—
101C2×M16×C67—22no—
102C2×M16×C67C2×C414yescomplemented
103C22×C8×C67C2311yescharacteristic
104C22×C8×C67C2311yescharacteristic
105C22×C8×C67C2311yescharacteristic
106C22×C8×C67C2311yescharacteristic
107C4×Q8×C67—22no—
108C4×Q8×C67—22no—
109C4×Q8×C67—41no—
110C4×Q8×C67—41no—
111C4×D4×C67—22no—
112C4×D4×C67—22no—
113C4×D4×C67—41no—
114C4×D4×C67—41no—
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×C67D411yescharacteristic
126C2×C22⋊C4×C67D411yescharacteristic
127C2×C42×C67—21no—
128C2×C42×C67—21no—
129C2×C42×C67C2311yescharacteristic
130C2×C42×C67C2311yescharacteristic
131#107×C67—22no—
132#106×C67—22no—
133#103×C67—22no—
134#103×C67—22no—
135#103×C67—41no—
136#103×C67—41no—
137#103×C67—41no—
138#103×C67—41no—
139#102×C67—22no—
140#102×C67—22no—
141C22⋊C8×C67—22no—
142#97×C67—22no—
143C4×C8×C67—22no—
144#95×C67—21no—
145#95×C67—21no—
146#95×C67—21no—
147#95×C67—21no—
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—28no—
169C2×Q8×C67—21no—
170C2×Q8×C67—21no—
171C2×Q8×C67—21no—
172C2×Q8×C67—21no—
173C2×Q8×C67—21no—
174C2×Q8×C67—21no—
175C2×Q8×C67—21no—
176C2×Q8×C67—21no—
177C2×Q8×C67—42no—
178C2×Q8×C67—42no—
179C2×Q8×C67—44no—
180C2×Q8×C67—44no—
181C2×Q8×C67—44no—
182C2×Q8×C67C22×C412yes—
183C2×Q8×C67C22×C412yes—
184C2×Q8×C67C22×C412yes—
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—42no—
192C2×D4×C67—42no—
193C2×D4×C67C22×C412yes—
194C2×D4×C67C2×D412yes—
195C2×D4×C67C2×D412yes—
196C22×C4×C67—21no—
197C22×C4×C67—21no—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—21no—
201C22×C4×C67—24no—
202C22×C4×C67—21no—
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×C67—42no—
214C22×C4×C67—42no—
215C22×C4×C67—42no—
216C22×C4×C67—42no—
217C22×C4×C67—81no—
218C22×C4×C67—81no—
219C22×C4×C67C22×C412yes—
220C22×C4×C67C2×D411yescharacteristic
221C22×C4×C67C2×D411yescharacteristic
222C22×C4×C67C2×D411yescharacteristic
223C22×C4×C67C2×D411yescharacteristic
224C22×C4×C67C2×D411yescharacteristic
225C22×C4×C67#4112yes—
226C22×C4×C67C2411yescharacteristic
227Q16×C67—28no—
228Q16×C67—28no—
229SD16×C67—28no—
230SD16×C67C22⋊C4116yescomplemented
231M16×C67—28no—
232C2×C8×C67—21no—
233C2×C8×C67—21no—
234C2×C8×C67—21no—
235C2×C8×C67—21no—
236C2×C8×C67—21no—
237C2×C8×C67—21no—
238C2×C8×C67—21no—
239C2×C8×C67—21no—
240C2×C8×C67C22×C412yes—
241C2×C8×C67C22×C412yes—
242C2×C8×C67C2×D412yes—
243C2×C8×C67C2×D412yes—
244C4⋊C4×C67—21no—
245C4⋊C4×C67—21no—
246C4⋊C4×C67—21no—
247C4⋊C4×C67—21no—
248C4⋊C4×C67—21no—
249C4⋊C4×C67—21no—
250C4⋊C4×C67—21no—
251C4⋊C4×C67—21no—
252C4⋊C4×C67—42no—
253C4⋊C4×C67—42no—
254C22⋊C4×C67—22no—
255C22⋊C4×C67—41no—
256C22⋊C4×C67—42no—
257C22⋊C4×C67—42no—
258C22⋊C4×C67—42no—
259C22⋊C4×C67—81no—
260C42×C67—21no—
261C42×C67—21no—
262C42×C67—21no—
263C42×C67—21no—
264C42×C67—42no—
265C42×C67—42no—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—21no—
270C23×C67—21no—
271C23×C67—21no—
272C23×C67—21no—
273C23×C67—21no—
274C23×C67—21no—
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—48no—
289Q8×C67—41no—
290Q8×C67—41no—
291Q8×C67—41no—
292Q8×C67—41no—
293Q8×C67C2×C22⋊C414yes—
294D4×C67—22no—
295D4×C67—22no—
296D4×C67—22no—
297D4×C67—48no—
298D4×C67C2×C22⋊C414yes—
299C2×C4×C67—22no—
300C2×C4×C67—21no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—21no—
304C2×C4×C67—21no—
305C2×C4×C67—21no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—21no—
313C2×C4×C67—21no—
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—48no—
322C2×C4×C67—48no—
323C2×C4×C67—41no—
324C2×C4×C67—41no—
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×C67—84no—
340C2×C4×C67—84no—
341C2×C4×C67C4×D412yes—
342C2×C4×C67#13712yescomplemented
343C2×C4×C67C23×C411yescharacteristic
344C2×C4×C67C22×D411yescharacteristic
345C2×C4×C67C22×D411yescharacteristic
346C2×C4×C67C2×#4111yescharacteristic
347C2×C4×C67H(5,𝔽2)11yescharacteristic
348C2×C4×C67H(5,𝔽2)11yescharacteristic
349C8×C67—22no—
350C8×C67—41no—
351C8×C67—41no—
352C8×C67C2×C22⋊C414yes—
353C22×C67—22no—
354C22×C67—24no—
355C22×C67—22no—
356C22×C67—22no—
357C22×C67—42no—
358C22×C67—42no—
359C22×C67—42no—
360C22×C67—41no—
361C22×C67—41no—
362C22×C67—42no—
363C22×C67—42no—
364C22×C67—41no—
365C22×C67—41no—
366C22×C67—42no—
367C22×C67C2×C4×D411yescharacteristic
368C22×C67D4211yescharacteristic
369C22×C67D4211yescharacteristic
370C22×C67C2×#13711yescharacteristic
371C22×C67#57511yescharacteristic
372C22×C67#57711yescharacteristic
373C22×C67#57811yescharacteristic
374C4×C67—22no—
375C4×C67—24no—
376C4×C67—22no—
377C4×C67—42no—
378C4×C67—42no—
379C4×C67—41no—
380C4×C67—41no—
381C4×C67—41no—
382C4×C67—81no—
383C4×C67—81no—
384C4×C67—81no—
385C4×C67—81no—
386C4×C67C22×C22⋊C411yescharacteristic
387C4×C67#51811yescharacteristic
388C4×C67#54611yescharacteristic
389C4×C67#54611yescharacteristic
390#22444C6711yesmaximal, characteristic, direct product factor, Sylow
391C2×C67—42no—
392C2×C67—44no—
393C2×C67D4×C22⋊C411yescharacteristic
394C2×C67C4×#13711yescharacteristic
395C2×C67#294711yescharacteristic
396C2×C67#326611yescharacteristic
397C2×C67#326911yescharacteristic
398C2×C67#327511yescharacteristic
399C2×C67#327611yescharacteristic
400C22×#137C2×C6711yescharacteristic
401C2×#440C2×C6711yescharacteristic, complemented
402C2×C4×SD16C2×C6711yescharacteristic, complemented
403Q8×C22⋊C4C2×C6711yescharacteristic, complemented
404#2339C2×C6711yescharacteristic
405#1971C2×C6711yescharacteristic, complemented
406#1969C2×C6711yescharacteristic, complemented
407#1878C2×C6711yescharacteristic, complemented
408#1878C2×C6711yescharacteristic, complemented
409#1877C2×C6711yescharacteristic, complemented
410#1877C2×C6711yescharacteristic, complemented
411#1809C2×C6711yescharacteristic, complemented
412#1788C2×C6711yescharacteristic
413#1787C2×C6711yescharacteristic, complemented
414#1753C2×C6711yescharacteristic, complemented
415C67#2244411yescharacteristic, direct product factor, Sylow
416C22×#41C22×C6711yescharacteristic
417C23×Q8C22×C6711yescharacteristic
418C2×#137—24no—
419C2×#137—24no—
420C2×#137C4×C6718yescomplemented
421C22×Q16C22×C6711yescharacteristic
422C22×Q16C22×C6711yescharacteristic
423C22×SD16C22×C6711yescharacteristic
424C22×SD16C22×C6711yescharacteristic
425C22×M16C22×C6711yescharacteristic
426C2×C4×Q8C22×C6711yescharacteristic
427C2×C4×Q8C22×C6711yescharacteristic
428C2×C4×D4C22×C6711yescharacteristic
429C2×C4×D4C22×C6711yescharacteristic
430#440—24no—
431C4×SD16—24no—
432C2×#107C22×C6711yescharacteristic
433C2×#106C22×C6711yescharacteristic
434C2×#103C22×C6711yescharacteristic
435C2×#103C22×C6711yescharacteristic
436C2×#103C22×C6711yescharacteristic
437C2×#103C22×C6711yescharacteristic
438C2×#103C22×C6711yescharacteristic
439C2×#103C22×C6711yescharacteristic
440C2×#102C22×C6711yescharacteristic
441C2×#102C22×C6711yescharacteristic
442C2×C22⋊C8C22×C6711yescharacteristic
443C2×#97C22×C6711yescharacteristic
444C2×C4×C8C22×C6711yescharacteristic
445#391—21no—
446#391—21no—
447#391C22×C6711yescharacteristic
448#391C22×C6711yescharacteristic
449#391C22×C6711yescharacteristic
450#391C22×C6711yescharacteristic
451#386—21no—
452#386—21no—
453#381—21no—
454#380—21no—
455#380C22×C6711yescharacteristic
456#380C22×C6711yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4C22×C6711yescharacteristic
459C2×#95—21no—
460#340C22×C6711yescharacteristic
461#340C22×C6711yescharacteristic
462#336C22×C6711yescharacteristic
463#336C22×C6711yescharacteristic
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—41no—
468C2×#41—41no—
469C2×#41C2×C4×C6714yes—
470C22×Q8—21no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—41no—
475C22×Q8—41no—
476C22×Q8C2×C4×C6714yescomplemented
477C22×Q8C23×C6711yescharacteristic
478C22×Q8C23×C6711yescharacteristic
479C22×Q8C23×C6711yescharacteristic
480C22×D4—21no—
481C22×D4C23×C6711yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—21no—
486C23×C4C23×C6711yescharacteristic
487#137—232no—
488C2×Q16—22no—
489C2×Q16—22no—
490C2×Q16—22no—
491C2×Q16—22no—
492C2×Q16C2×C4×C6714yescomplemented
493C2×Q16C2×C4×C6714yescomplemented
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16C2×C4×C6714yes—
497C2×SD16C2×C4×C6714yes—
498C2×SD16D4×C6714yes—
499C2×SD16D4×C6714yes—
500C2×M16—22no—
501C2×M16—22no—
502C2×M16C2×C4×C6714yescomplemented
503C22×C8C23×C6711yescharacteristic
504C22×C8C23×C6711yescharacteristic
505C22×C8C23×C6711yescharacteristic
506C22×C8C23×C6711yescharacteristic
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—41no—
510C4×Q8—41no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—41no—
514C4×D4—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4C23×C6711yescharacteristic
518C2×C4⋊C4C23×C6711yescharacteristic
519C2×C4⋊C4C23×C6711yescharacteristic
520C2×C4⋊C4C23×C6711yescharacteristic
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×C42C23×C6711yescharacteristic
530C2×C42C23×C6711yescharacteristic
531#107—22no—
532#106—22no—
533#103—22no—
534#103—22no—
535#103—41no—
536#103—41no—
537#103—41no—
538#103—41no—
539#102—22no—
540#102—22no—
541C22⋊C8—22no—
542#97—22no—
543C4×C8—22no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95D4×C6711yescharacteristic
555#95D4×C6711yescharacteristic
556C24—21no—
557C24C2×D4×C6711yescharacteristic
558#41—28no—
559#41—44no—
560#41—44no—
561#41—44no—
562C2×Q8—24no—
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—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—42no—
578C2×Q8—42no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8C22×C4×C6712yes—
583C2×Q8C22×C4×C6712yes—
584C2×Q8C22×C4×C6712yes—
585C2×Q8C2×D4×C6712yes—
586C2×Q8C2×D4×C6712yes—
587C2×D4—24no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4C22×C4×C6712yes—
594C2×D4C2×D4×C6712yes—
595C2×D4C2×D4×C6712yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4C22×C4×C6712yes—
620C22×C4C2×D4×C6711yescharacteristic
621C22×C4C2×D4×C6711yescharacteristic
622C22×C4C2×D4×C6711yescharacteristic
623C22×C4C2×D4×C6711yescharacteristic
624C22×C4C2×D4×C6711yescharacteristic
625C22×C4#41×C6712yes—
626C22×C4C24×C6711yescharacteristic
627Q16—28no—
628Q16—28no—
629SD16—28no—
630SD16C22⋊C4×C67116yescomplemented
631M16—28no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8C22×C4×C6712yes—
641C2×C8C22×C4×C6712yes—
642C2×C8C2×D4×C6712yes—
643C2×C8C2×D4×C6712yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—81no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—42no—
665C42—42no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23C4×D4×C6712yes—
680C23C22×D4×C6711yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—48no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693Q8C2×C22⋊C4×C6714yes—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—48no—
698D4C2×C22⋊C4×C6714yes—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
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×C4—41no—
738C2×C4—41no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4C4×D4×C6712yes—
742C2×C4#137×C6712yescomplemented
743C2×C4C23×C4×C6711yescharacteristic
744C2×C4C22×D4×C6711yescharacteristic
745C2×C4C22×D4×C6711yescharacteristic
746C2×C4C2×#41×C6711yescharacteristic
747C2×C4H(5,𝔽2)×C6711yescharacteristic
748C2×C4H(5,𝔽2)×C6711yescharacteristic
749C8—22no—
750C8—41no—
751C8—41no—
752C8C2×C22⋊C4×C6714yes—
753C22—22no—
754C22—24no—
755C22—22no—
756C22—22no—
757C22—42no—
758C22—41no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22C2×C4×D4×C6711yescharacteristic
768C22D42×C6711yescharacteristic
769C22D42×C6711yescharacteristic
770C22C2×#137×C6711yescharacteristic
771C22#575×C6711yescharacteristic
772C22#577×C6711yescharacteristic
773C22#578×C6711yescharacteristic
774C4—22no—
775C4—22no—
776C4—24no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—42no—
781C4—42no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4C22×C22⋊C4×C6711yescharacteristic
787C4#518×C6711yescharacteristic
788C4#546×C6711yescharacteristic
789C4#546×C6711yescharacteristic
790C2—42no—
791C2—44no—
792C2D4×C22⋊C4×C6711yescharacteristic
793C2C4×#137×C6711yescharacteristic
794C2C67×#294711yescharacteristic
795C2C67×#326611yescharacteristic
796C2C67×#326911yescharacteristic
797C2C67×#327511yescharacteristic
798C2C67×#327611yescharacteristic
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×#440×C67C2semidirect
3. C2×C4×SD16×C67C2semidirect
4. Q8×C22⋊C4×C67C2semidirect
6. C67×#1971C2semidirect
7. C67×#1969C2semidirect
8. C67×#1878C2semidirect
9. C67×#1878C2semidirect
10. C67×#1877C2semidirect
11. C67×#1877C2semidirect
12. C67×#1809C2semidirect
14. C67×#1787C2semidirect
15. C67×#1753C2semidirect
20. C2×#137×C67C4semidirect
76. C22×Q8×C67C2×C4semidirect
92. C2×Q16×C67C2×C4semidirect
93. C2×Q16×C67C2×C4semidirect
102. C2×M16×C67C2×C4semidirect
230. SD16×C67C22⋊C4semidirect
342. C2×C4×C67#137semidirect
390. #22444C67direct (N × H)
401. C2×#440C2×C67semidirect
402. C2×C4×SD16C2×C67semidirect
403. Q8×C22⋊C4C2×C67semidirect
405. #1971C2×C67semidirect
406. #1969C2×C67semidirect
407. #1878C2×C67semidirect
408. #1878C2×C67semidirect
409. #1877C2×C67semidirect
410. #1877C2×C67semidirect
411. #1809C2×C67semidirect
413. #1787C2×C67semidirect
414. #1753C2×C67semidirect
415. C67#22444direct (N × H)
420. C2×#137C4×C67semidirect
476. C22×Q8C2×C4×C67semidirect
492. C2×Q16C2×C4×C67semidirect
493. C2×Q16C2×C4×C67semidirect
502. C2×M16C2×C4×C67semidirect
630. SD16C22⋊C4×C67semidirect
742. 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×#440×C672
C2×C4×SD16×C672
Q8×C22⋊C4×C672
C67×#23392
C67×#19712
C67×#19692
C67×#18782
C67×#18772
C67×#18092
C67×#17882
C67×#17872
C67×#17532
#2244467