Finite Group Databasebeta

← C2×C67×#3346 #30740489

Subgroups — C2×C67×#3346 #30740489

Order 17152.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C67C211yesmaximal, characteristic, complemented
2C2×#553×C67C211yesmaximal, characteristic
3C67×#3346C2116yesmaximal, direct product factor
4C2×#501×C67C211yesmaximal, characteristic, complemented
5C2×#484×C67C211yesmaximal, characteristic, complemented
6C2×#481×C67C211yesmaximal, characteristic, complemented
7C2×#485×C67C211yesmaximal, characteristic, complemented
8C2×#480×C67C211yesmaximal, characteristic, complemented
9C2×#479×C67C211yesmaximal, characteristic, complemented
10C2×#474×C67C211yesmaximal, characteristic, complemented
11C2×#468×C67C211yesmaximal, characteristic, complemented
12C2×#465×C67C211yesmaximal, characteristic, complemented
13C2×#440×C67C211yesmaximal, characteristic, complemented
14C2×#435×C67C211yesmaximal, characteristic, complemented
15C2×#428×C67C211yesmaximal, characteristic, complemented
16C22×#107×C67C211yesmaximal, characteristic, complemented
17C22×SD16×C67C2211yescharacteristic
18C22×M16×C67C2211yescharacteristic
19C23×C8×C67C2211yescharacteristic
20#554×C67—24no—
21#554×C67C2218yescomplemented
22#553×C67—24no—
23#553×C67C2218yes—
24C2×C4⋊Q8×C67C2211yescharacteristic
25C2×#126×C67—21no—
26C2×#125×C67—21no—
27C2×#125×C67C2211yescharacteristic
28C2×#123×C67—21no—
29C2×C22⋊Q8×C67—21no—
30C2×C22⋊Q8×C67—21no—
31C2×C22⋊Q8×C67C2211yescharacteristic
32C2×C22⋊Q8×C67C2211yescharacteristic
33C2×#121×C67—21no—
34C2×#121×C67C2211yescharacteristic
35C2×#121×C67C2211yescharacteristic
36C2×C4×Q8×C67C2211yescharacteristic
37C2×C4×D4×C67—21no—
38C2×C4×D4×C67—21no—
39C2×C4×D4×C67C2211yescharacteristic
40C2×C4×D4×C67C2211yescharacteristic
41C2×#117×C67C2211yescharacteristic
42C22×C4⋊C4×C67C2211yescharacteristic
43C22×C4⋊C4×C67C2211yescharacteristic
44C22×C4⋊C4×C67C2211yescharacteristic
45#501×C67C2218yescomplemented
46#485×C67C2218yescomplemented
47#484×C67C2218yescomplemented
48#481×C67C2218yescomplemented
49#480×C67C2218yescomplemented
50#479×C67C2218yescomplemented
51#474×C67C2218yescomplemented
52#468×C67C2218yescomplemented
53#465×C67C2218yescomplemented
54#440×C67C2218yescomplemented
55#435×C67C2218yescomplemented
56#428×C67C2218yescomplemented
57C2×#107×C67C2211yescharacteristic
58C2×#107×C67C2211yescharacteristic
59C2×#107×C67C2211yescharacteristic
60C2×#107×C67C2211yescharacteristic
61C2×#107×C67C2211yescharacteristic
62C2×#107×C67C2211yescharacteristic
63C2×#107×C67C2218yescomplemented
64C2×#106×C67C2211yescharacteristic
65C2×#106×C67C2211yescharacteristic
66C2×#106×C67C2211yescharacteristic
67C2×C4⋊C8×C67C2211yescharacteristic
68C2×#103×C67C2211yescharacteristic
69C2×#103×C67C2211yescharacteristic
70C2×#103×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×Q8×C67C2311yescharacteristic
79C22×D4×C67—21no—
80C22×D4×C67—21no—
81C22×D4×C67D411yescharacteristic
82C22×D4×C67C2311yescharacteristic
83C23×C4×C67—21no—
84C23×C4×C67—21no—
85C23×C4×C67—21no—
86C23×C4×C67—21no—
87C23×C4×C67C2311yescharacteristic
88C23×C4×C67C2311yescharacteristic
89C2×SD16×C67—24no—
90C2×SD16×C67C2314yes—
91C2×M16×C67—24no—
92C2×M16×C67C2314yes—
93C22×C8×C67—24no—
94C22×C8×C67C2314yes—
95C22×C8×C67C2311yescharacteristic
96C22×C8×C67C2311yescharacteristic
97C22×C8×C67C2311yescharacteristic
98C22×C8×C67C2311yescharacteristic
99C4⋊Q8×C67—22no—
100C4⋊Q8×C67C2314yes—
101#126×C67—28no—
102#125×C67—28no—
103#125×C67—22no—
104#125×C67C2314yes—
105#123×C67—28no—
106C22⋊Q8×C67—22no—
107C22⋊Q8×C67—22no—
108C22⋊Q8×C67—28no—
109C22⋊Q8×C67—28no—
110C22⋊Q8×C67C2314yes—
111C22⋊Q8×C67C2314yes—
112#121×C67—28no—
113#121×C67—22no—
114#121×C67—22no—
115#121×C67C2314yes—
116#121×C67C2314yes—
117C4×Q8×C67—22no—
118C4×Q8×C67C2314yes—
119C4×D4×C67—28no—
120C4×D4×C67—28no—
121C4×D4×C67—22no—
122C4×D4×C67D414yes—
123C4×D4×C67C2314yes—
124C4×D4×C67C2314yes—
125#117×C67—22no—
126#117×C67C2314yes—
127C2×C4⋊C4×C67—21no—
128C2×C4⋊C4×C67—21no—
129C2×C4⋊C4×C67—21no—
130C2×C4⋊C4×C67—22no—
131C2×C4⋊C4×C67—22no—
132C2×C4⋊C4×C67—22no—
133C2×C4⋊C4×C67—21no—
134C2×C4⋊C4×C67—21no—
135C2×C4⋊C4×C67—21no—
136C2×C4⋊C4×C67—21no—
137C2×C4⋊C4×C67—21no—
138C2×C4⋊C4×C67—21no—
139C2×C4⋊C4×C67D411yescharacteristic
140C2×C4⋊C4×C67C2314yes—
141C2×C4⋊C4×C67C2314yes—
142C2×C4⋊C4×C67C2314yes—
143C2×C4⋊C4×C67C2311yescharacteristic
144C2×C4⋊C4×C67C2311yescharacteristic
145C2×C4⋊C4×C67C2311yescharacteristic
146C2×C4⋊C4×C67C2311yescharacteristic
147C2×C4⋊C4×C67C2311yescharacteristic
148C2×C4⋊C4×C67C2311yescharacteristic
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×C67—21no—
155C2×C22⋊C4×C67D411yescharacteristic
156C2×C22⋊C4×C67D411yescharacteristic
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#107×C67C2314yes—
166#106×C67C2314yes—
167#106×C67C2314yes—
168#106×C67C2314yes—
169C4⋊C8×C67C2314yes—
170#103×C67C2314yes—
171#103×C67C2314yes—
172#103×C67C2314yes—
173#102×C67C2314yes—
174#102×C67C2314yes—
175#102×C67C2314yes—
176C22⋊C8×C67C2314yes—
177C22⋊C8×C67C2314yes—
178#97×C67C2314yes—
179C24×C67—21no—
180C24×C67C2×D411yescharacteristic
181C24×C67C2×D411yescharacteristic
182C2×Q8×C67—21no—
183C2×Q8×C67—24no—
184C2×Q8×C67—22no—
185C2×Q8×C67—22no—
186C2×Q8×C67—82no—
187C2×Q8×C67C2412yes—
188C2×D4×C67—24no—
189C2×D4×C67—24no—
190C2×D4×C67—24no—
191C2×D4×C67—21no—
192C2×D4×C67—22no—
193C2×D4×C67—22no—
194C2×D4×C67—44no—
195C2×D4×C67—82no—
196C2×D4×C67C2×D414yes—
197C2×D4×C67C2412yes—
198C22×C4×C67—22no—
199C22×C4×C67—22no—
200C22×C4×C67—22no—
201C22×C4×C67—22no—
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—24no—
210C22×C4×C67—24no—
211C22×C4×C67—24no—
212C22×C4×C67—24no—
213C22×C4×C67—82no—
214C22×C4×C67—82no—
215C22×C4×C67—82no—
216C22×C4×C67—82no—
217C22×C4×C67C2×D412yes—
218C22×C4×C67C2×D412yes—
219C22×C4×C67C2×D411yescharacteristic
220C22×C4×C67C2×D411yescharacteristic
221C22×C4×C67C2×D411yescharacteristic
222C22×C4×C67C2×D411yescharacteristic
223C22×C4×C67C2412yes—
224C22×C4×C67C2412yes—
225C22×C4×C67C2411yescharacteristic
226SD16×C67—28no—
227M16×C67—28no—
228C2×C8×C67—22no—
229C2×C8×C67—22no—
230C2×C8×C67—22no—
231C2×C8×C67—28no—
232C2×C8×C67#4114yes—
233C2×C8×C67C2412yes—
234C2×C8×C67C2412yes—
235C2×C8×C67C2412yes—
236C2×C8×C67C2412yes—
237C4⋊C4×C67—21no—
238C4⋊C4×C67—21no—
239C4⋊C4×C67—21no—
240C4⋊C4×C67—24no—
241C4⋊C4×C67—24no—
242C4⋊C4×C67—21no—
243C4⋊C4×C67—21no—
244C4⋊C4×C67—24no—
245C4⋊C4×C67—24no—
246C4⋊C4×C67—24no—
247C4⋊C4×C67—24no—
248C4⋊C4×C67—24no—
249C4⋊C4×C67—24no—
250C4⋊C4×C67—24no—
251C4⋊C4×C67—21no—
252C4⋊C4×C67C2×D414yes—
253C4⋊C4×C67C2412yes—
254C4⋊C4×C67C2412yes—
255C4⋊C4×C67C2412yes—
256C4⋊C4×C67C2412yes—
257C4⋊C4×C67C2412yes—
258C4⋊C4×C67C2412yes—
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×C67C2×D412yes—
270C42×C67C2412yes—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67—42no—
278C23×C67—42no—
279C23×C67—42no—
280C23×C67#13714yes—
281C23×C67C22×D412yes—
282C23×C67C22×D412yes—
283C23×C67C22×D411yescharacteristic
284Q8×C67—22no—
285Q8×C67—22no—
286Q8×C67—42no—
287Q8×C67—84no—
288D4×C67—28no—
289D4×C67—22no—
290D4×C67—22no—
291D4×C67—48no—
292D4×C67—42no—
293D4×C67—84no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—24no—
299C2×C4×C67—24no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—42no—
312C2×C4×C67—42no—
313C2×C4×C67—42no—
314C2×C4×C67—42no—
315C2×C4×C67—42no—
316C2×C4×C67—42no—
317C2×C4×C67—42no—
318C2×C4×C67—84no—
319C2×C4×C67—84no—
320C2×C4×C67—84no—
321C2×C4×C67—84no—
322C2×C4×C67C22×D412yes—
323C2×C4×C67C22×D412yes—
324C2×C4×C67C22×D412yes—
325C2×C4×C67C22×D412yes—
326C2×C4×C67C22×D411yescharacteristic
327C2×C4×C67C2×#4112yes—
328C2×C4×C672−1+412yes—
329C2×C4×C67C2511yescharacteristic
330C8×C67—22no—
331C8×C67—22no—
332C8×C67—22no—
333C8×C67C2×#4114yes—
334C22×C67—28no—
335C22×C67—22no—
336C22×C67—22no—
337C22×C67—22no—
338C22×C67—22no—
339C22×C67—22no—
340C22×C67—44no—
341C22×C67—42no—
342C22×C67—42no—
343C22×C67—42no—
344C22×C67—84no—
345C22×C67#54712yes—
346C22×C67C2×#13714yes—
347C22×C67C2×#13712yes—
348C22×C67#57612yes—
349C22×C67C23×D411yescharacteristic
350C4×C67—22no—
351C4×C67—22no—
352C4×C67—22no—
353C4×C67—22no—
354C4×C67—42no—
355C4×C67—42no—
356C4×C67—42no—
357C4×C67—42no—
358C4×C67—42no—
359C4×C67—42no—
360C4×C67—42no—
361C4×C67#54712yes—
362C4×C67C22×#4111yescharacteristic
363C4×C67C2×2−1+411yescharacteristic
364C2×#3346C6711yesmaximal, characteristic, direct product factor, Sylow
365C2×C67—24no—
366C2×C67—42no—
367C2×C67—82no—
368C2×C67#334614yesdirect product factor
369C2×C67C2×#54711yescharacteristic
370C2×C67C22×#13711yescharacteristic
371C2×C67C2×#57611yescharacteristic
372C2×#554C2×C6711yescharacteristic, complemented
373C2×#553C2×C6711yescharacteristic
374#3346C2×C67116yesdirect product factor
375C2×#501C2×C6711yescharacteristic, complemented
376C2×#484C2×C6711yescharacteristic, complemented
377C2×#481C2×C6711yescharacteristic, complemented
378C2×#485C2×C6711yescharacteristic, complemented
379C2×#480C2×C6711yescharacteristic, complemented
380C2×#479C2×C6711yescharacteristic, complemented
381C2×#474C2×C6711yescharacteristic, complemented
382C2×#468C2×C6711yescharacteristic, complemented
383C2×#465C2×C6711yescharacteristic, complemented
384C2×#440C2×C6711yescharacteristic, complemented
385C2×#435C2×C6711yescharacteristic, complemented
386C2×#428C2×C6711yescharacteristic, complemented
387C22×#107C2×C6711yescharacteristic, complemented
388C67C2×#334611yescharacteristic, direct product factor, Sylow
389C22×SD16C22×C6711yescharacteristic
390C22×M16C22×C6711yescharacteristic
391C23×C8C22×C6711yescharacteristic
392#554—24no—
393#554C22×C6718yescomplemented
394#553—24no—
395#553C22×C6718yes—
396C2×C4⋊Q8C22×C6711yescharacteristic
397C2×#126—21no—
398C2×#125—21no—
399C2×#125C22×C6711yescharacteristic
400C2×#123—21no—
401C2×C22⋊Q8—21no—
402C2×C22⋊Q8—21no—
403C2×C22⋊Q8C22×C6711yescharacteristic
404C2×C22⋊Q8C22×C6711yescharacteristic
405C2×#121—21no—
406C2×#121C22×C6711yescharacteristic
407C2×#121C22×C6711yescharacteristic
408C2×C4×Q8C22×C6711yescharacteristic
409C2×C4×D4—21no—
410C2×C4×D4—21no—
411C2×C4×D4C22×C6711yescharacteristic
412C2×C4×D4C22×C6711yescharacteristic
413C2×#117C22×C6711yescharacteristic
414C22×C4⋊C4C22×C6711yescharacteristic
415C22×C4⋊C4C22×C6711yescharacteristic
416C22×C4⋊C4C22×C6711yescharacteristic
417#501C22×C6718yescomplemented
418#485C22×C6718yescomplemented
419#484C22×C6718yescomplemented
420#481C22×C6718yescomplemented
421#480C22×C6718yescomplemented
422#479C22×C6718yescomplemented
423#474C22×C6718yescomplemented
424#468C22×C6718yescomplemented
425#465C22×C6718yescomplemented
426#440C22×C6718yescomplemented
427#435C22×C6718yescomplemented
428#428C22×C6718yescomplemented
429C2×#107C22×C6711yescharacteristic
430C2×#107C22×C6711yescharacteristic
431C2×#107C22×C6711yescharacteristic
432C2×#107C22×C6711yescharacteristic
433C2×#107C22×C6711yescharacteristic
434C2×#107C22×C6711yescharacteristic
435C2×#107C22×C6718yescomplemented
436C2×#106C22×C6711yescharacteristic
437C2×#106C22×C6711yescharacteristic
438C2×#106C22×C6711yescharacteristic
439C2×C4⋊C8C22×C6711yescharacteristic
440C2×#103C22×C6711yescharacteristic
441C2×#103C22×C6711yescharacteristic
442C2×#103C22×C6711yescharacteristic
443C2×#102C22×C6711yescharacteristic
444C2×#102C22×C6711yescharacteristic
445C2×#102C22×C6711yescharacteristic
446C2×C22⋊C8C22×C6711yescharacteristic
447C2×C22⋊C8C22×C6711yescharacteristic
448C2×#97C22×C6711yescharacteristic
449C22×Q8—21no—
450C22×Q8C23×C6711yescharacteristic
451C22×D4—21no—
452C22×D4—21no—
453C22×D4D4×C6711yescharacteristic
454C22×D4C23×C6711yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—21no—
459C23×C4C23×C6711yescharacteristic
460C23×C4C23×C6711yescharacteristic
461C2×SD16—24no—
462C2×SD16C23×C6714yes—
463C2×M16—24no—
464C2×M16C23×C6714yes—
465C22×C8—24no—
466C22×C8C23×C6711yescharacteristic
467C22×C8C23×C6714yes—
468C22×C8C23×C6711yescharacteristic
469C22×C8C23×C6711yescharacteristic
470C22×C8C23×C6711yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8C23×C6714yes—
473#126—28no—
474#125—28no—
475#125—22no—
476#125C23×C6714yes—
477#123—28no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8C23×C6714yes—
483C22⋊Q8C23×C6714yes—
484#121—28no—
485#121—22no—
486#121—22no—
487#121C23×C6714yes—
488#121C23×C6714yes—
489C4×Q8—22no—
490C4×Q8C23×C6714yes—
491C4×D4—28no—
492C4×D4—28no—
493C4×D4—22no—
494C4×D4D4×C6714yes—
495C4×D4C23×C6714yes—
496C4×D4C23×C6714yes—
497#117—22no—
498#117C23×C6714yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4D4×C6711yescharacteristic
512C2×C4⋊C4C23×C6711yescharacteristic
513C2×C4⋊C4C23×C6711yescharacteristic
514C2×C4⋊C4C23×C6711yescharacteristic
515C2×C4⋊C4C23×C6711yescharacteristic
516C2×C4⋊C4C23×C6711yescharacteristic
517C2×C4⋊C4C23×C6714yes—
518C2×C4⋊C4C23×C6714yes—
519C2×C4⋊C4C23×C6714yes—
520C2×C4⋊C4C23×C6711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4D4×C6711yescharacteristic
528C2×C22⋊C4D4×C6711yescharacteristic
529C2×C42—21no—
530C2×C42—21no—
531C2×C42C23×C6711yescharacteristic
532#107C23×C6714yes—
533#107C23×C6714yes—
534#107C23×C6714yes—
535#107C23×C6714yes—
536#107C23×C6714yes—
537#107C23×C6714yes—
538#106C23×C6714yes—
539#106C23×C6714yes—
540#106C23×C6714yes—
541C4⋊C8C23×C6714yes—
542#103C23×C6714yes—
543#103C23×C6714yes—
544#103C23×C6714yes—
545#102C23×C6714yes—
546#102C23×C6714yes—
547#102C23×C6714yes—
548C22⋊C8C23×C6714yes—
549C22⋊C8C23×C6714yes—
550#97C23×C6714yes—
551C24—21no—
552C24C2×D4×C6711yescharacteristic
553C24C2×D4×C6711yescharacteristic
554C2×Q8—21no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—82no—
559C2×Q8C24×C6712yes—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—82no—
568C2×D4C2×D4×C6714yes—
569C2×D4C24×C6712yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4C2×D4×C6711yescharacteristic
590C22×C4C2×D4×C6711yescharacteristic
591C22×C4C2×D4×C6711yescharacteristic
592C22×C4C2×D4×C6711yescharacteristic
593C22×C4C2×D4×C6712yes—
594C22×C4C2×D4×C6712yes—
595C22×C4C24×C6712yes—
596C22×C4C24×C6712yes—
597C22×C4C24×C6711yescharacteristic
598SD16—28no—
599M16—28no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8#41×C6714yes—
605C2×C8C24×C6712yes—
606C2×C8C24×C6712yes—
607C2×C8C24×C6712yes—
608C2×C8C24×C6712yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4C2×D4×C6714yes—
625C4⋊C4C24×C6712yes—
626C4⋊C4C24×C6712yes—
627C4⋊C4C24×C6712yes—
628C4⋊C4C24×C6712yes—
629C4⋊C4C24×C6712yes—
630C4⋊C4C24×C6712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4C2×D4×C6714yes—
638C22⋊C4C2×D4×C6714yes—
639C42—24no—
640C42—24no—
641C42C2×D4×C6712yes—
642C42C24×C6712yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23#137×C6714yes—
653C23C22×D4×C6712yes—
654C23C22×D4×C6712yes—
655C23C22×D4×C6711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—84no—
660D4—28no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—42no—
665D4—84no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4C22×D4×C6712yes—
695C2×C4C22×D4×C6712yes—
696C2×C4C22×D4×C6712yes—
697C2×C4C22×D4×C6712yes—
698C2×C4C22×D4×C6711yescharacteristic
699C2×C4C2×#41×C6712yes—
700C2×C42−1+4×C6712yes—
701C2×C4C25×C6711yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#41×C6714yes—
706C22—22no—
707C22—28no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22#547×C6712yes—
718C22C2×#137×C6714yes—
719C22C2×#137×C6712yes—
720C22#576×C6712yes—
721C22C23×D4×C6711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4#547×C6712yes—
734C4C22×#41×C6711yescharacteristic
735C4C2×2−1+4×C6711yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2C67×#334614yesdirect product factor
740C2C2×#547×C6711yescharacteristic
741C2C22×#137×C6711yescharacteristic
742C2C2×#576×C6711yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC2×C4C25×C67
prime radicalC2×#553×C67C2
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×#554×C67C2semidirect
3. C67×#3346C2direct (N × H)
4. C2×#501×C67C2semidirect
5. C2×#484×C67C2semidirect
6. C2×#481×C67C2semidirect
7. C2×#485×C67C2semidirect
8. C2×#480×C67C2semidirect
9. C2×#479×C67C2semidirect
10. C2×#474×C67C2semidirect
11. C2×#468×C67C2semidirect
12. C2×#465×C67C2semidirect
13. C2×#440×C67C2semidirect
14. C2×#435×C67C2semidirect
15. C2×#428×C67C2semidirect
16. C22×#107×C67C2semidirect
21. #554×C67C22semidirect
45. #501×C67C22semidirect
46. #485×C67C22semidirect
47. #484×C67C22semidirect
48. #481×C67C22semidirect
49. #480×C67C22semidirect
50. #479×C67C22semidirect
51. #474×C67C22semidirect
52. #468×C67C22semidirect
53. #465×C67C22semidirect
54. #440×C67C22semidirect
55. #435×C67C22semidirect
56. #428×C67C22semidirect
63. C2×#107×C67C22semidirect
364. C2×#3346C67direct (N × H)
368. C2×C67#3346direct (N × H)
372. C2×#554C2×C67semidirect
374. #3346C2×C67direct (N × H)
375. C2×#501C2×C67semidirect
376. C2×#484C2×C67semidirect
377. C2×#481C2×C67semidirect
378. C2×#485C2×C67semidirect
379. C2×#480C2×C67semidirect
380. C2×#479C2×C67semidirect
381. C2×#474C2×C67semidirect
382. C2×#468C2×C67semidirect
383. C2×#465C2×C67semidirect
384. C2×#440C2×C67semidirect
385. C2×#435C2×C67semidirect
386. C2×#428C2×C67semidirect
387. C22×#107C2×C67semidirect
388. C67C2×#3346direct (N × H)
393. #554C22×C67semidirect
417. #501C22×C67semidirect
418. #485C22×C67semidirect
419. #484C22×C67semidirect
420. #481C22×C67semidirect
421. #480C22×C67semidirect
422. #479C22×C67semidirect
423. #474C22×C67semidirect
424. #468C22×C67semidirect
425. #465C22×C67semidirect
426. #440C22×C67semidirect
427. #435C22×C67semidirect
428. #428C22×C67semidirect
435. C2×#107C22×C67semidirect
739. C2C67×#3346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#554×C672
C2×#553×C672
C67×#33462
C2×#501×C672
C2×#484×C672
C2×#481×C672
C2×#485×C672
C2×#480×C672
C2×#479×C672
C2×#474×C672
C2×#468×C672
C2×#465×C672
C2×#440×C672
C2×#435×C672
C2×#428×C672
C22×#107×C672
C2×#334667