Finite Group Databasebeta

← C2×C4×#14524028 #31014271

Subgroups — C2×C4×#14524028 #31014271

Order 17152.

4070 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524028C211yesmaximal, characteristic
2C22×C4×D268C211yesmaximal, characteristic
3C22×C42×D67C211yesmaximal, characteristic, complemented
4C4×#14524028C2116yesmaximal, direct product factor
5C2×#16863286C211yesmaximal, characteristic, complemented
6C2×#16863285C211yesmaximal, characteristic, complemented
7C2×#16863283C211yesmaximal, characteristic, complemented
8C2×#16863282C211yesmaximal, characteristic, complemented
9C2×#16863274C211yesmaximal, characteristic
10C2×#16863267C211yesmaximal, characteristic, complemented
11C2×#16863258C211yesmaximal, characteristic, complemented
12C2×C4×Dic67⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊C4×C67C211yesmaximal, characteristic, complemented
17C23×D268C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C23×C4×D67C2211yescharacteristic
22C2×#14524028C4116yesdirect product factor
23C2×#14524028C2218yes—
24C2×C4×D268—28no—
25C2×C4×D268C2218yes—
26C22×C4⋊Dic67C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×(C2×D67)⋊C4C2211yescharacteristic
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×(C2×D67)⋊C4C2211yescharacteristic
32C22×(C2×D67)⋊C4C2211yescharacteristic
33C22×(C2×D67)⋊C4C2211yescharacteristic
34C22×(C2×D67)⋊C4C2211yescharacteristic
35C22×(C2×D67)⋊C4C2211yescharacteristic
36C22×(C2×D67)⋊C4C2211yescharacteristic
37C22×C4×Dic67C2211yescharacteristic
38C22×C4×Dic67C2211yescharacteristic
39C22×C4×Dic67C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41C2×C42×D67—28no—
42C2×C42×D67C2218yescomplemented
43#16863286C2218yescomplemented
44#16863285C2218yescomplemented
45#16863283C2218yescomplemented
46#16863282C2218yescomplemented
47#16863274C2218yes—
48#16863267C2218yescomplemented
49#16863258C2218yescomplemented
50C4×Dic67⋊C4C2218yescomplemented
51C4×(C2×D67)⋊C4C2218yescomplemented
52C4×(C2×D67)⋊C4C2218yescomplemented
53C4×(C2×D67)⋊C4C2218yescomplemented
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C2×C67⋊#95C2211yescharacteristic
62C22×C4⋊C4×C67C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C42×C67C2211yescharacteristic
65C22×C42×C67C2211yescharacteristic
66C22×C42×C67C2211yescharacteristic
67C4×C4⋊C4×C67C2218yescomplemented
68C2×#95×C67C2211yescharacteristic
69C2×#95×C67C2211yescharacteristic
70C24×D67C2311yescharacteristic
71C24×D67C2311yescharacteristic
72C22×D268—24no—
73C22×D268—24no—
74C22×D268C2×C418yes—
75C22×D268C2314yes—
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C22×C4×D67—24no—
83C22×C4×D67—24no—
84C22×C4×D67—24no—
85C22×C4×D67—24no—
86C22×C4×D67—24no—
87C22×C4×D67—24no—
88C22×C4×D67—24no—
89C22×C4×D67—24no—
90C22×C4×D67—24no—
91C22×C4×D67—24no—
92C22×C4×D67C2×C418yescomplemented
93C22×C4×D67D418yes—
94C22×C4×D67C2314yes—
95C22×C4×D67C2314yes—
96C22×C4×D67C2314yes—
97C22×C4×D67C2314yes—
98#14524028C2×C4164yesdirect product factor
99C4×D268—232no—
100C2×C4⋊Dic67—24no—
101C2×C4⋊Dic67C2314yes—
102C2×Dic67⋊C4—24no—
103C2×Dic67⋊C4C2×C418yescomplemented
104C2×Dic67⋊C4C2314yes—
105C2×Dic67⋊C4C2314yes—
106C2×(C2×D67)⋊C4—24no—
107C2×(C2×D67)⋊C4—24no—
108C2×(C2×D67)⋊C4—24no—
109C2×(C2×D67)⋊C4—24no—
110C2×(C2×D67)⋊C4—24no—
111C2×(C2×D67)⋊C4C2×C418yescomplemented
112C2×(C2×D67)⋊C4C2×C418yescomplemented
113C2×(C2×D67)⋊C4C2×C418yescomplemented
114C2×(C2×D67)⋊C4C2314yes—
115C2×(C2×D67)⋊C4C2314yes—
116C2×(C2×D67)⋊C4C2314yes—
117C2×(C2×D67)⋊C4C2314yes—
118C2×(C2×D67)⋊C4C2314yes—
119C2×(C2×D67)⋊C4C2314yes—
120C2×(C2×D67)⋊C4C2314yes—
121C2×(C2×D67)⋊C4C2314yes—
122C2×C4×Dic67—24no—
123C2×C4×Dic67—24no—
124C2×C4×Dic67—24no—
125C2×C4×Dic67—24no—
126C2×C4×Dic67C2314yes—
127C2×C4×Dic67C2314yes—
128C2×C4×Dic67C2314yes—
129C2×C4×Dic67C2314yes—
130C42×D67—232no—
131C67⋊#95C2314yes—
132C67⋊#95C2314yes—
133C67⋊#95C2314yes—
134C67⋊#95C2314yes—
135C67⋊#95C2314yes—
136C67⋊#95C2314yes—
137C67⋊#95C2314yes—
138C67⋊#95C2314yes—
139C23×C4×C67C2311yescharacteristic
140C23×C4×C67C2311yescharacteristic
141C23×C4×C67C2311yescharacteristic
142C23×C4×C67C2311yescharacteristic
143C23×C4×C67C2311yescharacteristic
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2311yescharacteristic
146C2×C4⋊C4×C67—24no—
147C2×C4⋊C4×C67C2×C418yescomplemented
148C2×C4⋊C4×C67C2314yes—
149C2×C4⋊C4×C67C2314yes—
150C2×C42×C67—24no—
151C2×C42×C67—24no—
152C2×C42×C67—24no—
153C2×C42×C67C2314yes—
154C2×C42×C67C2314yes—
155C2×C42×C67C2314yes—
156#95×C67C2314yes—
157#95×C67C2314yes—
158C23×D67—22no—
159C23×D67—22no—
160C23×D67—22no—
161C23×D67—22no—
162C23×D67—22no—
163C23×D67—22no—
164C23×D67—22no—
165C23×D67—22no—
166C23×D67—22no—
167C23×D67—22no—
168C23×D67C22×C414yes—
169C23×D67C22×C414yes—
170C23×D67C2×D414yes—
171C23×D67#4114yes—
172C23×D67C2412yes—
173C23×D67C2412yes—
174C2×D268—232no—
175C2×D268—28no—
176C2×D268—28no—
177C2×D268C22×C4116yes—
178C22×Dic67—22no—
179C22×Dic67—22no—
180C22×Dic67—22no—
181C22×Dic67—22no—
182C22×Dic67—22no—
183C22×Dic67—22no—
184C22×Dic67—22no—
185C22×Dic67—22no—
186C22×Dic67—22no—
187C22×Dic67—22no—
188C22×Dic67—22no—
189C22×Dic67—22no—
190C22×Dic67—22no—
191C22×Dic67—22no—
192C22×Dic67C22×C414yes—
193C22×Dic67C22×C414yes—
194C22×Dic67C2×D414yes—
195C22×Dic67#4114yes—
196C22×Dic67C2412yes—
197C22×Dic67C2412yes—
198C22×Dic67C2412yes—
199C22×Dic67C2412yes—
200C22×Dic67C2412yes—
201C22×Dic67C2412yes—
202C2×C4×D67—232no—
203C2×C4×D67—232no—
204C2×C4×D67—28no—
205C2×C4×D67—28no—
206C2×C4×D67—28no—
207C2×C4×D67—232no—
208C2×C4×D67—28no—
209C2×C4×D67—28no—
210C2×C4×D67—28no—
211C2×C4×D67—28no—
212C2×C4×D67—28no—
213C2×C4×D67—28no—
214C2×C4×D67—28no—
215C2×C4×D67—416no—
216C2×C4×D67C22×C4116yescomplemented
217C2×C4×D67C2×D4116yes—
218C4⋊Dic67—28no—
219Dic67⋊C4—28no—
220Dic67⋊C4C22×C4116yescomplemented
221(C2×D67)⋊C4—28no—
222(C2×D67)⋊C4—28no—
223(C2×D67)⋊C4—28no—
224(C2×D67)⋊C4—28no—
225(C2×D67)⋊C4—28no—
226(C2×D67)⋊C4C22×C4116yescomplemented
227(C2×D67)⋊C4C22×C4116yescomplemented
228(C2×D67)⋊C4C22×C4116yescomplemented
229C4×Dic67—28no—
230C4×Dic67—28no—
231C4×Dic67—28no—
232C4×Dic67—28no—
233C24×C67C2411yescharacteristic
234C22×C4×C67—22no—
235C22×C4×C67—22no—
236C22×C4×C67—22no—
237C22×C4×C67—22no—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67—22no—
243C22×C4×C67—22no—
244C22×C4×C67—22no—
245C22×C4×C67—22no—
246C22×C4×C67—22no—
247C22×C4×C67—22no—
248C22×C4×C67C22×C414yes—
249C22×C4×C67C22×C414yes—
250C22×C4×C67C22×C414yes—
251C22×C4×C67C2×D414yes—
252C22×C4×C67#4114yes—
253C22×C4×C67#4114yes—
254C22×C4×C67#4114yes—
255C22×C4×C67C2412yes—
256C22×C4×C67C2412yes—
257C22×C4×C67C2412yes—
258C22×C4×C67C2412yes—
259C22×C4×C67C2412yes—
260C22×C4×C67C2412yes—
261C22×C4×C67C2412yes—
262C4⋊C4×C67—28no—
263C4⋊C4×C67C22×C4116yescomplemented
264C42×C67—28no—
265C42×C67—28no—
266C42×C67—28no—
267C23×C67C23×C412yes—
268C23×C67C22×D412yes—
269C23×C67C2×#4112yes—
270C23×C67C2×#4112yes—
271C23×C67C2×#4112yes—
272C23×C67C2×#4112yes—
273C23×C67C2×#4112yes—
274C23×C67C2511yescharacteristic
275C22×D67—28no—
276C22×D67—28no—
277C22×D67—28no—
278C22×D67—28no—
279C22×D67—28no—
280C22×D67—28no—
281C22×D67—22no—
282C22×D67—22no—
283C22×D67—22no—
284C22×D67—22no—
285C22×D67—28no—
286C22×D67—28no—
287C22×D67—28no—
288C22×D67—22no—
289C22×D67—22no—
290C22×D67—22no—
291C22×D67—22no—
292C22×D67—22no—
293C22×D67—22no—
294C22×D67—44no—
295C22×D67—44no—
296C22×D67—44no—
297C22×D67—44no—
298C22×D67C4×D4116yes—
299C22×D67C23×C414yes—
300C22×D67C23×C414yes—
301C22×D67C22×D414yes—
302C22×D67C2×#4114yes—
303C2×C4×C67—28no—
304C2×C4×C67—28no—
305C2×C4×C67—28no—
306C2×C4×C67—28no—
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—22no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—22no—
321C2×C4×C67—44no—
322C2×C4×C67—44no—
323C2×C4×C67#123116yescomplemented
324C2×C4×C67C23×C414yes—
325C2×C4×C67C23×C414yes—
326C2×C4×C67C23×C414yes—
327C2×C4×C67C22×D414yes—
328C2×C4×C67C2×#4114yes—
329C2×C4×C67C2×#4114yes—
330C2×C4×C67C2×#4114yes—
331C2×Dic67—28no—
332C2×Dic67—28no—
333C2×Dic67—28no—
334C2×Dic67—28no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—22no—
338C2×Dic67—22no—
339C2×Dic67—22no—
340C2×Dic67—22no—
341C2×Dic67—22no—
342C2×Dic67—22no—
343C2×Dic67—22no—
344C2×Dic67—22no—
345C2×Dic67—22no—
346C2×Dic67—22no—
347C2×Dic67—22no—
348C2×Dic67—22no—
349C2×Dic67—44no—
350C2×Dic67—44no—
351C2×Dic67C23×C414yes—
352C2×Dic67C23×C414yes—
353C2×Dic67C22×D414yes—
354C2×Dic67C2×#4114yes—
355D268—232no—
356C4×D67—232no—
357C4×D67—232no—
358C4×D67—232no—
359C4×D67—416no—
360C22×C67C2×C4×D414yes—
361C22×C67C4×#4114yes—
362C22×C67C4×#4114yes—
363C22×C67C2×#12314yes—
364C22×C67#52514yes—
365C22×C67#52914yes—
366C22×C67#52914yes—
367C22×C67C24×C411yescharacteristic
368C22×C67C23×D411yescharacteristic
369C22×C67C22×#4111yescharacteristic
370C22×C67C22×#4111yescharacteristic
371C22×C67C22×#4111yescharacteristic
372C22×C67C22×#4111yescharacteristic
373C22×C67C22×#4111yescharacteristic
374C2×D67—24no—
375C2×D67—24no—
376C2×D67—24no—
377C2×D67—24no—
378C2×D67—24no—
379C2×D67—24no—
380C2×D67—232no—
381C2×D67—24no—
382C2×D67—24no—
383C2×D67—24no—
384C2×D67—42no—
385C2×D67—42no—
386C2×D67—42no—
387C2×D67—42no—
388C2×D67—416no—
389C2×D67C2×C4×D418yes—
390C4×C67—24no—
391C4×C67—24no—
392C4×C67—24no—
393C4×C67—24no—
394C4×C67—42no—
395C4×C67—42no—
396C4×C67C2×#12318yescomplemented
397Dic67—24no—
398Dic67—24no—
399Dic67—24no—
400Dic67—24no—
401Dic67—42no—
402Dic67—42no—
403C2×C4×#123—671nomaximal, Sylow
404C2×C67C4×#12318yescomplemented
405C2×C67C22×C4×D411yescharacteristic
406C2×C67C2×C4×#4111yescharacteristic
407C2×C67C2×C4×#4111yescharacteristic
408C2×C67C22×#12311yescharacteristic
409C2×C67C2×#52511yescharacteristic
410C2×C67C2×#52911yescharacteristic
411C2×C67C2×#52911yescharacteristic
412D67—28no—
413D67—44no—
414C22×#123—671no—
415C22×C4×D4—671no—
416C23×C42—671no—
417C4×#123—6716no—
418C2×#388—671no—
419C2×#388—671no—
420C2×#387—671no—
421C2×#387—671no—
422C2×#386—671no—
423C2×#385—671no—
424C2×#381—671no—
425C2×C4×C4⋊C4—671no—
426C2×C4×C4⋊C4D6711yescharacteristic, complemented
427C2×C4×C22⋊C4—671no—
428C2×C4×C22⋊C4—671no—
429C2×C4×C22⋊C4—671no—
430C67C2×C4×#12311yescharacteristic, complemented, Sylow
431C23×D4—671no—
432C24×C4—671no—
433C24×C4—671no—
434C24×C4—671no—
435C24×C4—671no—
436C2×#123—6716no—
437C2×#123—678no—
438C2×C4×D4—678no—
439C2×C4×D4—1348no—
440C22×C4⋊C4—671no—
441C22×C4⋊C4—671no—
442C22×C4⋊C4—671no—
443C22×C4⋊C4C2×D6711yescharacteristic
444C22×C4⋊C4C2×D6711yescharacteristic
445C22×C22⋊C4—671no—
446C22×C22⋊C4—671no—
447C22×C22⋊C4—671no—
448C22×C22⋊C4—671no—
449C22×C22⋊C4—671no—
450C22×C22⋊C4—671no—
451C22×C22⋊C4—671no—
452C22×C22⋊C4—671no—
453C22×C42—671no—
454C22×C42—671no—
455C22×C42—671no—
456C22×C42—671no—
457C22×C42—678no—
458C22×C42—1348no—
459C22×C42C2×D6711yescharacteristic
460C22×C42C2×D6711yescharacteristic
461C22×C42C2×D6711yescharacteristic
462#388—678no—
463#388—678no—
464#387—678no—
465#387—678no—
466#386—678no—
467#385—678no—
468#381—678no—
469C4×C4⋊C4—678no—
470C4×C4⋊C4C2×D6718yescomplemented
471C4×C22⋊C4—678no—
472C4×C22⋊C4—678no—
473C4×C22⋊C4—678no—
474C2×#95—671no—
475C2×#95—671no—
476C2×#95—671no—
477C2×#95—671no—
478C2×#95—671no—
479C2×#95—671no—
480C2×#95—671no—
481C2×#95—671no—
482C2×#95C2×D6711yescharacteristic
483C2×#95C2×D6711yescharacteristic
484C25—671no—
485C25—671no—
486C22×D4—678no—
487C22×D4—674no—
488C22×D4—1344no—
489C22×D4—1344no—
490C23×C4—671no—
491C23×C4—671no—
492C23×C4—671no—
493C23×C4—671no—
494C23×C4—678no—
495C23×C4—678no—
496C23×C4—674no—
497C23×C4—674no—
498C23×C4—671no—
499C23×C4—671no—
500C23×C4—674no—
501C23×C4—674no—
502C23×C4—1344no—
503C23×C4—1344no—
504C23×C4—1344no—
505C23×C4—1344no—
506C23×C4—1344no—
507C23×C4—1344no—
508C23×C4—1344no—
509C23×C4—1344no—
510C23×C4—1344no—
511C23×C4—1344no—
512C23×C4C22×D6711yescharacteristic
513C23×C4C22×D6711yescharacteristic
514C23×C4C22×D6711yescharacteristic
515C23×C4C22×D6711yescharacteristic
516C23×C4C22×D6711yescharacteristic
517C23×C4C22×D6711yescharacteristic
518C23×C4C22×D6711yescharacteristic
519#123—6764no—
520C4×D4—13432no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—678no—
523C2×C4⋊C4—674no—
524C2×C4⋊C4—674no—
525C2×C4⋊C4—674no—
526C2×C4⋊C4—1344no—
527C2×C4⋊C4—1344no—
528C2×C4⋊C4C4×D6718yescomplemented
529C2×C4⋊C4C22×D6714yes—
530C2×C4⋊C4C22×D6714yes—
531C2×C22⋊C4—678no—
532C2×C22⋊C4—678no—
533C2×C22⋊C4—678no—
534C2×C22⋊C4—674no—
535C2×C22⋊C4—674no—
536C2×C22⋊C4—674no—
537C2×C22⋊C4—674no—
538C2×C22⋊C4—674no—
539C2×C22⋊C4—674no—
540C2×C22⋊C4—674no—
541C2×C22⋊C4—674no—
542C2×C22⋊C4—1344no—
543C2×C22⋊C4—1344no—
544C2×C22⋊C4—1344no—
545C2×C22⋊C4—1344no—
546C2×C22⋊C4—1344no—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—24no—
550C2×C42—674no—
551C2×C42—674no—
552C2×C42—674no—
553C2×C42—674no—
554C2×C42—13432no—
555C2×C42—1344no—
556C2×C42—1344no—
557C2×C42—1344no—
558C2×C42—1344no—
559C2×C42C22×D6714yes—
560C2×C42C22×D6714yes—
561C2×C42C22×D6714yes—
562#95—674no—
563#95—674no—
564#95—674no—
565#95—674no—
566#95—674no—
567#95—674no—
568#95—674no—
569#95—674no—
570#95C22×D6714yes—
571#95C22×D6714yes—
572C24—674no—
573C24—674no—
574C24—674no—
575C24—672no—
576C24—674no—
577C24—672no—
578C24—1342no—
579C24—1342no—
580C24—1342no—
581C24—1342no—
582C24—1342no—
583C24—1342no—
584C24—1342no—
585C24—1342no—
586C24—1342no—
587C24—1342no—
588C24C23×D6711yescharacteristic
589C2×D4—6716no—
590C2×D4—1348no—
591C2×D4—13432no—
592C2×D4—1348no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—26816no—
608C22×C4—674no—
609C22×C4—674no—
610C22×C4—674no—
611C22×C4—674no—
612C22×C4—672no—
613C22×C4—672no—
614C22×C4—672no—
615C22×C4—672no—
616C22×C4—6716no—
617C22×C4—6716no—
618C22×C4—672no—
619C22×C4—672no—
620C22×C4—1348no—
621C22×C4—1348no—
622C22×C4—1348no—
623C22×C4—13432no—
624C22×C4—1348no—
625C22×C4—13432no—
626C22×C4—1342no—
627C22×C4—1342no—
628C22×C4—1342no—
629C22×C4—1342no—
630C22×C4—1342no—
631C22×C4—1342no—
632C22×C4—1348no—
633C22×C4—1348no—
634C22×C4—1348no—
635C22×C4—1342no—
636C22×C4—1342no—
637C22×C4—1342no—
638C22×C4—1342no—
639C22×C4—1342no—
640C22×C4—1342no—
641C22×C4—1342no—
642C22×C4—1342no—
643C22×C4—13432no—
644C22×C4—1348no—
645C22×C4—1348no—
646C22×C4—1348no—
647C22×C4C2×C4×D6714yes—
648C22×C4C2×C4×D6714yes—
649C22×C4C2×C4×D6714yes—
650C22×C4D4×D6714yes—
651C22×C4#1176162814yes—
652C22×C4#1176162814yes—
653C22×C4#1176162914yes—
654C22×C4C23×D6712yes—
655C22×C4C23×D6712yes—
656C22×C4C23×D6712yes—
657C22×C4C23×D6712yes—
658C22×C4C23×D6712yes—
659C22×C4C23×D6712yes—
660C22×C4C23×D6712yes—
661C4⋊C4—28no—
662C4⋊C4—6716no—
663C4⋊C4—1348no—
664C4⋊C4—1348no—
665C4⋊C4C2×C4×D67116yescomplemented
666C22⋊C4—6716no—
667C22⋊C4—6716no—
668C22⋊C4—6716no—
669C22⋊C4—1348no—
670C22⋊C4—1348no—
671C22⋊C4—1348no—
672C22⋊C4—1348no—
673C22⋊C4—1348no—
674C42—28no—
675C42—28no—
676C42—28no—
677C42—1348no—
678C42—1348no—
679C42—1348no—
680C42—1348no—
681C23—2684no—
682C23—2684no—
683C23—2684no—
684C23—2684no—
685C23—6716no—
686C23—674no—
687C23—674no—
688C23—674no—
689C23—674no—
690C23—1348no—
691C23—1348no—
692C23—1348no—
693C23—1342no—
694C23—1342no—
695C23—1342no—
696C23—1342no—
697C23—1342no—
698C23—1342no—
699C23—1348no—
700C23—1348no—
701C23—1348no—
702C23—1348no—
703C23—1348no—
704C23—1348no—
705C23—1342no—
706C23—1342no—
707C23—1342no—
708C23—1342no—
709C23C22×C4×D6712yes—
710C23C2×D4×D6712yes—
711C23#41×D6712yes—
712C23#41×D6712yes—
713C23C2×#1176162812yes—
714C23C2×#1176162812yes—
715C23C2×#1176162912yes—
716C23C24×D6711yescharacteristic
717D4—13432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—2684no—
739C2×C4—2684no—
740C2×C4—26816no—
741C2×C4—674no—
742C2×C4—674no—
743C2×C4—674no—
744C2×C4—674no—
745C2×C4—13432no—
746C2×C4—13432no—
747C2×C4—1342no—
748C2×C4—1342no—
749C2×C4—1342no—
750C2×C4—1342no—
751C2×C4—1342no—
752C2×C4—1342no—
753C2×C4—1348no—
754C2×C4—1348no—
755C2×C4—1348no—
756C2×C4—1348no—
757C2×C4—1342no—
758C2×C4—1342no—
759C2×C4—1342no—
760C2×C4—1342no—
761C2×C4—1342no—
762C2×C4—1342no—
763C2×C4—1342no—
764C2×C4—1342no—
765C2×C4—13432no—
766C2×C4#14524028116yesdirect product factor
767C2×C4C22×C4×D6714yes—
768C2×C4C22×C4×D6714yes—
769C2×C4C22×C4×D6714yes—
770C2×C4C2×D4×D6714yes—
771C2×C4C2×#1176162814yes—
772C2×C4C2×#1176162814yes—
773C2×C4C2×#1176162914yes—
774C22—2682no—
775C22—2682no—
776C22—2682no—
777C22—2682no—
778C22—26816no—
779C22—678no—
780C22—1344no—
781C22—1344no—
782C22—1344no—
783C22—1344no—
784C22—1344no—
785C22—1344no—
786C22—1344no—
787C22—1344no—
788C22—1344no—
789C22—13432no—
790C22C4×D4×D6714yes—
791C22C4×#1176162814yes—
792C22C4×#1176162914yes—
793C22C2×#1452402814yes—
794C22#1686390514yes—
795C22#1686392414yes—
796C22#1686393314yes—
797C22C23×C4×D6711yescharacteristic
798C22C22×D4×D6711yescharacteristic
799C22C2×#41×D6711yescharacteristic
800C22C2×#41×D6711yescharacteristic
801C22C22×#1176162811yescharacteristic
802C22C22×#1176162811yescharacteristic
803C22C22×#1176162911yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—2682no—
811C4—2682no—
812C4—1344no—
813C4—1344no—
814C4—1344no—
815C4—1344no—
816C4C2×#1452402818yesdirect product factor
817C2—2684no—
818C2—1348no—
819C2C4×#1452402818yesdirect product factor
820C2C2×C4×D4×D6711yescharacteristic
821C2C2×C4×#1176162811yescharacteristic
822C2C2×C4×#1176162911yescharacteristic
823C2C22×#1452402811yescharacteristic
824C2C2×#1686390511yescharacteristic
825C2C2×#1686392411yescharacteristic
826C2C2×#1686393311yescharacteristic
subgroupG/H
centerC23×C4C22×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×C4×C4⋊C4×C67C2
socleC24×C67C24
prime radicalC23×D268C22
cosocleC23×C67C25
hypercenterC2×C4×C4⋊C4D67
hypocenterC67C2×C4×#123
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C42×D67C2semidirect
4. C4×#14524028C2direct (N × H)
5. C2×#16863286C2semidirect
6. C2×#16863285C2semidirect
7. C2×#16863283C2semidirect
8. C2×#16863282C2semidirect
10. C2×#16863267C2semidirect
11. C2×#16863258C2semidirect
12. C2×C4×Dic67⋊C4C2semidirect
13. C2×C4×(C2×D67)⋊C4C2semidirect
14. C2×C4×(C2×D67)⋊C4C2semidirect
15. C2×C4×(C2×D67)⋊C4C2semidirect
16. C2×C4×C4⋊C4×C67C2semidirect
22. C2×#14524028C4direct (N × H)
42. C2×C42×D67C22semidirect
43. #16863286C22semidirect
44. #16863285C22semidirect
45. #16863283C22semidirect
46. #16863282C22semidirect
48. #16863267C22semidirect
49. #16863258C22semidirect
50. C4×Dic67⋊C4C22semidirect
51. C4×(C2×D67)⋊C4C22semidirect
52. C4×(C2×D67)⋊C4C22semidirect
53. C4×(C2×D67)⋊C4C22semidirect
67. C4×C4⋊C4×C67C22semidirect
92. C22×C4×D67C2×C4semidirect
98. #14524028C2×C4direct (N × H)
103. C2×Dic67⋊C4C2×C4semidirect
111. C2×(C2×D67)⋊C4C2×C4semidirect
112. C2×(C2×D67)⋊C4C2×C4semidirect
113. C2×(C2×D67)⋊C4C2×C4semidirect
147. C2×C4⋊C4×C67C2×C4semidirect
216. C2×C4×D67C22×C4semidirect
220. Dic67⋊C4C22×C4semidirect
226. (C2×D67)⋊C4C22×C4semidirect
227. (C2×D67)⋊C4C22×C4semidirect
228. (C2×D67)⋊C4C22×C4semidirect
263. C4⋊C4×C67C22×C4semidirect
323. C2×C4×C67#123semidirect
396. C4×C67C2×#123semidirect
404. C2×C67C4×#123semidirect
426. C2×C4×C4⋊C4D67semidirect
430. C67C2×C4×#123semidirect
470. C4×C4⋊C4C2×D67semidirect
528. C2×C4⋊C4C4×D67semidirect
665. C4⋊C4C2×C4×D67semidirect
766. C2×C4#14524028direct (N × H)
816. C4C2×#14524028direct (N × H)
819. C2C4×#14524028direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240282
C22×C4×D2682
C22×C42×D672
C4×#145240282
C2×#168632862
C2×#168632852
C2×#168632832
C2×#168632822
C2×#168632742
C2×#168632672
C2×#168632582
C2×C4×Dic67⋊C42
C2×C4×(C2×D67)⋊C42
C2×C4×C4⋊C4×C672
C2×C4×#12367