Finite Group Databasebeta

← C2×#11724586 #13181612

Subgroups — C2×#11724586 #13181612

Order 1728.

6284 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×#3830C211yesmaximal, characteristic, complemented
3C2×C32×#237C211yesmaximal, characteristic, complemented
4C2×#89039C212yesmaximal, complemented
5C22×#6289C212yesmaximal, complemented
6C2×#89031C212yesmaximal, complemented
7C2×#89028C212yesmaximal, complemented
8#11724586C2116yesmaximal, direct product factor
9C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
10C2×#89022C211yesmaximal, characteristic, complemented
11C2×#89019C211yesmaximal, characteristic, complemented
12C2×#89018C211yesmaximal, characteristic, complemented
13C2×#41×C3⋊D3—31nomaximal
14C2×#64312—34nomaximal
15C23×C3⋊(C3⋊D3)C2212yes—
16C22×D3×C3⋊D3C2211yescharacteristic
17C2×C33×D4C2211yescharacteristic, complemented
18C2×#6312C2212yescomplemented
19D4×C3⋊(C3⋊D3)C2218yescomplemented
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×#638C2212yescomplemented
23C22×C3×C3⋊Dic3C2212yescomplemented
24C3×#3830C2218yescomplemented
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×C3×#634C2211yescharacteristic, complemented
27C2×C32×#67C2212yescomplemented
28C22×C32×Dic3C2212yescomplemented
29C32×#237C2218yescomplemented
30C2×C32×C4×D3C2211yescharacteristic, complemented
31C2×C32×Dic6C2211yescharacteristic, complemented
32#89039C22116yescomplemented
33C2×#6293C2212yescomplemented
34C2×#6292C2212yescomplemented
35C2×#6291C2212yescomplemented
36C2×#6289C2212yes—
37C2×#6289C2211yescharacteristic
38C2×#6289C22116yescomplemented
39C2×#6289C2212yescomplemented
40C2×#6289C2212yescomplemented
41#89031C22116yescomplemented
42C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
43#89028C22116yescomplemented
44C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
45C4×D3×C3⋊D3C2218yescomplemented
46#89022C2218yescomplemented
47#89019C2218yescomplemented
48#89018C2218yescomplemented
49C2×C32×#41—31no—
50#41×C3⋊D3—316no—
51C2×#3832—31no—
52C2×Q8×C3⋊D3—31no—
53C2×#3830—32no—
54C2×#3830D311yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×D4×C3⋊D3—32no—
57C2×D4×C3⋊D3—34no—
58C2×D4×C3⋊D3—64no—
59C2×#3828—32no—
60C2×#3828—31no—
61C22×C4×C3⋊D3—32no—
62C22×C4×C3⋊D3—31no—
63C2×C3×#237—34no—
64C2×C3×#237D314yescomplemented
65C2×#3811—38no—
66C22×#624—38no—
67C2×#3804—38no—
68C2×#3804—38no—
69#64312—364no—
70C2×C4×D32—34no—
71C2×#3799—34no—
72C2×#3799—34no—
73C2×#3797—34no—
74C23×C33C2312yes—
75C22×C3⋊(C3⋊D3)—28no—
76C22×C3⋊(C3⋊D3)C2312yes—
77C22×C3⋊(C3⋊D3)C2318yes—
78C22×C3⋊(C3⋊D3)C2311yescharacteristic
79C22×C3×C3⋊D3C2311yescharacteristic
80C22×C32×D3C2311yescharacteristic
81C2×D3×C3⋊D3—24no—
82C2×D3×C3⋊D3C2314yes—
83C33×D4C2314yescomplemented
84C2×C33×C4C2311yescharacteristic
85#6312C2318yescomplemented
86C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊(C3⋊D3))C2314yescomplemented
88C4×C3⋊(C3⋊D3)C2314yes—
89C3×#638C2318yescomplemented
90C2×C3×C3⋊Dic3C2311yescharacteristic
91C2×C3×C3⋊Dic3C2312yes—
92C2×C3×C3⋊Dic3C2318yescomplemented
93C3×C4×C3⋊D3C2314yescomplemented
94C3×#634C2314yescomplemented
95C32×#67C2318yescomplemented
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2312yes—
98C2×C32×Dic3C2318yescomplemented
99C32×C4×D3C2314yescomplemented
100C32×Dic6C2314yescomplemented
101#6293C2318yescomplemented
102#6292C2318yescomplemented
103#6291C2318yescomplemented
104#6289C2318yes—
105#6289C2314yes—
106#6289C2318yescomplemented
107#6289C2318yescomplemented
108Dic3×C3⋊D3C2314yescomplemented
109D3×C3⋊Dic3C2314yescomplemented
110C2×D3×#41—94no—
111C2×D3×#41—91no—
112C23×C3⋊D3—32no—
113C23×C3⋊D3—38no—
114C23×C3⋊D3—31no—
115C23×C3⋊D3—68no—
116C22×D32—34no—
117C32×#41—38no—
118C2×C32×Q8—31no—
119C2×C32×D4—24no—
120C2×C32×D4—32no—
121C2×C32×D4C2×D314yescomplemented
122C2×C32×D4C2×D311yescharacteristic, complemented
123C22×C32×C4—32no—
124C22×C32×C4—31no—
125C2×#638—32no—
126C2×#638—38no—
127C2×#638—32no—
128C2×#638—68no—
129C2×#638C2×D312yescomplemented
130C22×C3⋊Dic3—31no—
131C22×C3⋊Dic3C2×D312yescomplemented
132#3832—38no—
133Q8×C3⋊D3—38no—
134#3830—316no—
135#3830C2×D318yescomplemented
136D4×C3⋊D3—38no—
137D4×C3⋊D3—332no—
138D4×C3⋊D3—316no—
139D4×C3⋊D3—632no—
140#3828—316no—
141#3828—38no—
142C2×C4⋊(C3⋊D3)—32no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4⋊(C3⋊D3)—34no—
145C2×C4⋊(C3⋊D3)—64no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—34no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—32no—
151C2×C4×C3⋊D3—32no—
152C2×C4×C3⋊D3—32no—
153C2×C4×C3⋊D3—316no—
154C2×C4×C3⋊D3—38no—
155C2×C4×C3⋊D3—64no—
156C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
157C2×#634—32no—
158C2×#634C2×D311yescharacteristic, complemented
159C2×C3×#67—38no—
160C2×C3×#67C2×D318yescomplemented
161C22×C3×Dic3—38no—
162C22×C3×Dic3C2×D318yescomplemented
163C3×#237—332no—
164C3×#237C2×D3132yescomplemented
165C2×C3×C4×D3—34no—
166C2×C3×C4×D3C2×D314yescomplemented
167C2×C3×Dic6—34no—
168C2×C3×Dic6C2×D314yescomplemented
169#3811—364no—
170C2×#627—38no—
171C2×#626—38no—
172C2×#626—38no—
173C2×#624—38no—
174C2×#624—38no—
175C2×#624—38no—
176C2×#624—34no—
177C2×#624—364no—
178#3804—364no—
179#3804—364no—
180C2×D3×Dic3—34no—
181C2×D3×Dic3—34no—
182C4×D32—332no—
183#3799—332no—
184#3799—332no—
185#3797—332no—
186C22×C33—24no—
187C22×C33C2414yes—
188C22×C33C2411yescharacteristic
189C2×C3⋊(C3⋊D3)—24no—
190C2×C3⋊(C3⋊D3)—216no—
191C2×C3⋊(C3⋊D3)#4114yescomplemented
192C2×C3⋊(C3⋊D3)C2414yes—
193C2×C3⋊(C3⋊D3)C2412yes—
194C2×C3×C3⋊D3—22no—
195C2×C3×C3⋊D3C2412yes—
196C2×C32×D3—22no—
197C2×C32×D3C2412yes—
198D3×C3⋊D3—28no—
199C33×C4C2412yes—
200C3⋊(C3⋊Dic3)C2412yes—
201C3×C3⋊Dic3C2412yes—
202C3×C3⋊Dic3C2414yes—
203C32×Dic3C2412yes—
204C32×Dic3C2414yes—
205C2×C3×#41—34no—
206C2×C3×#41—91no—
207D3×#41—964no—
208D3×#41—916no—
209C2×#239—94no—
210C2×#239—91no—
211C2×D3×Q8—94no—
212C2×D3×Q8—91no—
213C2×#237—34no—
214C2×#237—98no—
215C2×#237—92no—
216C2×#237C3⋊D311yescharacteristic, complemented
217C2×D3×D4—98no—
218C2×D3×D4—94no—
219C2×D3×D4—91no—
220C2×D3×D4—92no—
221C2×D3×D4—184no—
222C2×#235—94no—
223C2×#235—98no—
224C2×#235—92no—
225C2×#235—91no—
226C22×C4×D3—94no—
227C22×C4×D3—98no—
228C22×C4×D3—92no—
229C22×C4×D3—91no—
230C23×C32—28no—
231C23×C32—31no—
232C23×C32C22×D318yes—
233C23×C32C22×D312yes—
234C22×C3⋊D3—31no—
235C22×C3⋊D3—32no—
236C22×C3⋊D3—38no—
237C22×C3⋊D3—34no—
238C22×C3⋊D3—34no—
239C22×C3⋊D3—38no—
240C22×C3⋊D3—332no—
241C22×C3⋊D3—64no—
242C22×C3⋊D3—68no—
243C22×C3⋊D3—632no—
244C22×C3⋊D3—64no—
245C22×C3⋊D3—68no—
246C22×C3⋊D3—632no—
247C22×C3⋊D3—1232no—
248C22×C3⋊D3C22×D311yescharacteristic
249C22×C3×D3—34no—
250C22×C3×D3C22×D314yes—
251C2×D32—316no—
252C2×D32—616no—
253C32×Q8—34no—
254C32×D4—216no—
255C32×D4—38no—
256C32×D4C22×D3116yescomplemented
257C32×D4C22×D314yescomplemented
258C2×C32×C4—24no—
259C2×C32×C4—32no—
260C2×C32×C4—31no—
261C2×C32×C4—38no—
262C2×C32×C4—34no—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D311yescharacteristic
265#638—38no—
266#638—38no—
267#638—332no—
268#638—632no—
269#638C22×D318yescomplemented
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—34no—
272C2×C3⋊Dic3—34no—
273C2×C3⋊Dic3—64no—
274C2×C3⋊Dic3C22×D312yes—
275C2×C3⋊Dic3C22×D311yescharacteristic
276C2×C3⋊Dic3C22×D318yescomplemented
277C4⋊(C3⋊D3)—38no—
278C4⋊(C3⋊D3)—34no—
279C4⋊(C3⋊D3)—316no—
280C4⋊(C3⋊D3)—616no—
281C4×C3⋊D3—34no—
282C4×C3⋊D3—34no—
283C4×C3⋊D3—34no—
284C4×C3⋊D3—38no—
285C4×C3⋊D3—38no—
286C4×C3⋊D3—38no—
287C4×C3⋊D3—316no—
288C4×C3⋊D3—616no—
289C4×C3⋊D3C22×D314yescomplemented
290#634—38no—
291#634C22×D314yescomplemented
292C3×#67—332no—
293C3×#67C22×D3132yescomplemented
294C2×C3×Dic3—34no—
295C2×C3×Dic3—38no—
296C2×C3×Dic3—332no—
297C2×C3×Dic3C22×D314yes—
298C2×C3×Dic3C22×D318yes—
299C2×C3×Dic3C22×D3132yescomplemented
300C3×C4×D3—316no—
301C3×C4×D3C22×D3116yescomplemented
302C3×Dic6—316no—
303C3×Dic6C22×D3116yescomplemented
304#627—332no—
305#626—332no—
306#626—332no—
307#624—332no—
308#624—316no—
309#624—332no—
310#624—332no—
311D3×Dic3—316no—
312D3×Dic3—316no—
313C22×#41—271noSylow
314C2×C33—24no—
315C2×C33C2×#4112yescomplemented
316C2×C33C2511yescharacteristic
317C3⋊(C3⋊D3)—24no—
318C3⋊(C3⋊D3)C2×#4114yescomplemented
319C3×C3⋊D3—22no—
320C32×D3—22no—
321C23×D3—94no—
322C23×D3—98no—
323C23×D3—92no—
324C23×D3—91no—
325C23×D3—188no—
326C3×#41—332no—
327C3×#41—98no—
328C2×C3×Q8—34no—
329C2×C3×Q8—91no—
330C2×C3×D4—24no—
331C2×C3×D4—38no—
332C2×C3×D4—92no—
333C2×C3×D4D3214yescomplemented
334C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
335C22×C3×C4—38no—
336C22×C3×C4—34no—
337C22×C3×C4—92no—
338C22×C3×C4—91no—
339C2×#67—38no—
340C2×#67—98no—
341C2×#67—98no—
342C2×#67—92no—
343C2×#67—92no—
344C2×#67—188no—
345C2×#67C2×C3⋊D312yescomplemented
346C22×Dic3—38no—
347C22×Dic3—94no—
348C22×Dic3—91no—
349C22×Dic3C2×C3⋊D312yescomplemented
350#239—932no—
351#239—98no—
352D3×Q8—932no—
353D3×Q8—98no—
354#237—332no—
355#237—964no—
356#237—916no—
357#237C2×C3⋊D318yescomplemented
358D3×D4—964no—
359D3×D4—932no—
360D3×D4—98no—
361D3×D4—916no—
362D3×D4—1832no—
363#235—932no—
364#235—964no—
365#235—916no—
366#235—98no—
367C2×D12—98no—
368C2×D12—92no—
369C2×D12—94no—
370C2×D12—91no—
371C2×D12—184no—
372C2×C4×D3—34no—
373C2×C4×D3—932no—
374C2×C4×D3—94no—
375C2×C4×D3—98no—
376C2×C4×D3—98no—
377C2×C4×D3—98no—
378C2×C4×D3—964no—
379C2×C4×D3—94no—
380C2×C4×D3—91no—
381C2×C4×D3—94no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—92no—
385C2×C4×D3—92no—
386C2×C4×D3—92no—
387C2×C4×D3—916no—
388C2×C4×D3—98no—
389C2×C4×D3—184no—
390C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
391C2×Dic6—34no—
392C2×Dic6—98no—
393C2×Dic6—92no—
394C2×Dic6C2×C3⋊D311yescharacteristic, complemented
395C22×C32—24no—
396C22×C32—24no—
397C22×C32—216no—
398C22×C32—216no—
399C22×C32—32no—
400C22×C32—416no—
401C22×C32—62no—
402C22×C32C23×D3116yes—
403C22×C32C23×D314yes—
404C22×C32C23×D314yes—
405C22×C32C23×D311yescharacteristic
406C2×C3⋊D3—22no—
407C2×C3⋊D3—34no—
408C2×C3⋊D3—32no—
409C2×C3⋊D3—34no—
410C2×C3⋊D3—316no—
411C2×C3⋊D3—38no—
412C2×C3⋊D3—316no—
413C2×C3⋊D3—616no—
414C2×C3⋊D3—68no—
415C2×C3⋊D3—616no—
416C2×C3⋊D3—68no—
417C2×C3⋊D3—616no—
418C2×C3⋊D3—64no—
419C2×C3⋊D3—664no—
420C2×C3⋊D3—616no—
421C2×C3⋊D3—1264no—
422C2×C3⋊D3—1216no—
423C2×C3⋊D3C23×D312yes—
424C2×C3×D3—28no—
425C2×C3×D3—38no—
426C2×C3×D3—68no—
427C2×C3×D3C23×D318yes—
428D32—632no—
429C32×C4—28no—
430C32×C4—34no—
431C32×C4—32no—
432C32×C4C23×D318yes—
433C32×C4C23×D312yes—
434C3⋊Dic3—32no—
435C3⋊Dic3—38no—
436C3⋊Dic3—68no—
437C3⋊Dic3C23×D314yes—
438C3⋊Dic3C23×D312yes—
439C3×Dic3—38no—
440C3×Dic3—316no—
441C3×Dic3C23×D318yes—
442C3×Dic3C23×D3116yes—
443C2×#41—31no—
444C2×#41—91no—
445C2×#41—272no—
446C2×#41—271no—
447C2×#41—272no—
448C2×#41—271no—
449C2×#41—2716no—
450C22×Q8—271no—
451C22×D4—272no—
452C22×D4—271no—
453C23×C4—272no—
454C23×C4—271no—
455C33C22×#4111yescharacteristic, complemented, Sylow
456C23×C3—28no—
457C23×C3—34no—
458C23×C3—91no—
459C23×C3C2×D3218yes—
460C23×C3C22×C3⋊D312yes—
461C22×D3—34no—
462C22×D3—916no—
463C22×D3—94no—
464C22×D3—91no—
465C22×D3—98no—
466C22×D3—932no—
467C22×D3—92no—
468C22×D3—98no—
469C22×D3—94no—
470C22×D3—184no—
471C22×D3—188no—
472C22×D3—1832no—
473C22×D3—184no—
474C22×D3—1816no—
475C22×D3—188no—
476C22×D3—1832no—
477C22×D3—3632no—
478C22×D3C22×C3⋊D311yescharacteristic
479C3×Q8—316no—
480C3×Q8—94no—
481C3×D4—216no—
482C3×D4—332no—
483C3×D4—98no—
484C3×D4C2×D32116yescomplemented
485C3×D4C22×C3⋊D314yescomplemented
486C2×C3×C4—24no—
487C2×C3×C4—38no—
488C2×C3×C4—34no—
489C2×C3×C4—332no—
490C2×C3×C4—316no—
491C2×C3×C4—92no—
492C2×C3×C4—91no—
493C2×C3×C4—98no—
494C2×C3×C4—94no—
495C2×C3×C4C2×D3214yes—
496C2×C3×C4C22×C3⋊D311yescharacteristic
497#67—332no—
498#67—932no—
499#67—932no—
500#67—98no—
501#67—98no—
502#67—1832no—
503#67C22×C3⋊D318yescomplemented
504C2×Dic3—38no—
505C2×Dic3—34no—
506C2×Dic3—332no—
507C2×Dic3—916no—
508C2×Dic3—94no—
509C2×Dic3—91no—
510C2×Dic3—94no—
511C2×Dic3—184no—
512C2×Dic3C22×C3⋊D312yes—
513C2×Dic3C22×C3⋊D311yescharacteristic
514C2×Dic3C22×C3⋊D318yescomplemented
515D12—932no—
516D12—98no—
517D12—916no—
518D12—94no—
519D12—1816no—
520C4×D3—316no—
521C4×D3—916no—
522C4×D3—932no—
523C4×D3—932no—
524C4×D3—932no—
525C4×D3—916no—
526C4×D3—94no—
527C4×D3—916no—
528C4×D3—94no—
529C4×D3—94no—
530C4×D3—98no—
531C4×D3—98no—
532C4×D3—98no—
533C4×D3—1816no—
534C4×D3C22×C3⋊D314yescomplemented
535Dic6—316no—
536Dic6—932no—
537Dic6—98no—
538Dic6C22×C3⋊D314yescomplemented
539C2×C32—24no—
540C2×C32—28no—
541C2×C32—24no—
542C2×C32—216no—
543C2×C32—416no—
544C2×C32—62no—
545C2×C32D3×#4118yescomplemented
546C2×C32D3×#4112yescomplemented
547C2×C32C24×D314yes—
548C2×C32C24×D311yescharacteristic
549C3⋊D3—22no—
550C3⋊D3—34no—
551C3⋊D3—316no—
552C3⋊D3—616no—
553C3⋊D3—64no—
554C3⋊D3—616no—
555C3⋊D3—1216no—
556C3×D3—28no—
557C3×D3—68no—
558C24—271no—
559C24—272no—
560#41—38no—
561#41—98no—
562#41—2716no—
563#41—278no—
564#41—2716no—
565#41—278no—
566C2×Q8—31no—
567C2×Q8—91no—
568C2×Q8—272no—
569C2×Q8—278no—
570C2×D4—32no—
571C2×D4—92no—
572C2×D4—272no—
573C2×D4—272no—
574C2×D4—2716no—
575C2×D4—272no—
576C2×D4—278no—
577C2×D4—271no—
578C2×D4D3×C3⋊D311yescharacteristic, complemented
579C22×C4—32no—
580C22×C4—31no—
581C22×C4—92no—
582C22×C4—91no—
583C22×C4—271no—
584C22×C4—272no—
585C22×C4—2716no—
586C22×C4—272no—
587C22×C4—272no—
588C22×C4—278no—
589C22×C4—271no—
590C22×C4—271no—
591C22×C4—271no—
592C22×C3—216no—
593C22×C3—24no—
594C22×C3—216no—
595C22×C3—24no—
596C22×C3—38no—
597C22×C3—416no—
598C22×C3—68no—
599C22×C3—92no—
600C22×C3—182no—
601C22×C3C22×D32116yes—
602C22×C3C22×D3214yes—
603C22×C3C23×C3⋊D314yes—
604C22×C3C23×C3⋊D311yescharacteristic
605C2×D3—22no—
606C2×D3—38no—
607C2×D3—68no—
608C2×D3—916no—
609C2×D3—94no—
610C2×D3—98no—
611C2×D3—92no—
612C2×D3—916no—
613C2×D3—94no—
614C2×D3—188no—
615C2×D3—1816no—
616C2×D3—1816no—
617C2×D3—188no—
618C2×D3—1832no—
619C2×D3—1816no—
620C2×D3—1864no—
621C2×D3—1816no—
622C2×D3—184no—
623C2×D3—3664no—
624C2×D3—3616no—
625C2×D3C23×C3⋊D312yes—
626C3×C4—28no—
627C3×C4—316no—
628C3×C4—38no—
629C3×C4—94no—
630C3×C4—92no—
631C3×C4C22×D3218yes—
632C3×C4C23×C3⋊D312yes—
633Dic3—316no—
634Dic3—38no—
635Dic3—98no—
636Dic3—92no—
637Dic3—188no—
638Dic3C23×C3⋊D314yes—
639Dic3C23×C3⋊D312yes—
640C32—24no—
641C32C2×D3×#4114yescomplemented
642C32C2×D3×#4111yescharacteristic, complemented
643C23—31no—
644C23—91no—
645C23—274no—
646C23—271no—
647C23—278no—
648C23—272no—
649C23—548no—
650C23—544no—
651C23C2×D3×C3⋊D312yes—
652Q8—34no—
653Q8—94no—
654Q8—278no—
655D4—38no—
656D4—98no—
657D4—278no—
658D4—278no—
659D4—278no—
660D4—274no—
661D4C2×D3×C3⋊D314yescomplemented
662C2×C4—38no—
663C2×C4—31no—
664C2×C4—32no—
665C2×C4—34no—
666C2×C4—98no—
667C2×C4—91no—
668C2×C4—92no—
669C2×C4—94no—
670C2×C4—274no—
671C2×C4—278no—
672C2×C4—278no—
673C2×C4—278no—
674C2×C4—274no—
675C2×C4—274no—
676C2×C4—271no—
677C2×C4—274no—
678C2×C4C2×D3×C3⋊D311yescharacteristic
679C2×C3—216no—
680C2×C3—24no—
681C2×C3—28no—
682C2×C3—24no—
683C2×C3—416no—
684C2×C3—68no—
685C2×C3—182no—
686C2×C3#6431218yescomplemented
687C2×C3#41×C3⋊D312yescomplemented
688C2×C3C23×D3214yes—
689C2×C3C24×C3⋊D311yescharacteristic
690D3—22no—
691D3—68no—
692D3—916no—
693D3—94no—
694D3—1816no—
695D3—1816no—
696D3—184no—
697D3—3616no—
698C22—24no—
699C22—32no—
700C22—62no—
701C22—92no—
702C22—182no—
703C22—274no—
704C22—272no—
705C22—274no—
706C22—5416no—
707C22—548no—
708C22—544no—
709C22C22×D3×C3⋊D314yes—
710C22C22×D3×C3⋊D311yescharacteristic
711C4—32no—
712C4—34no—
713C4—92no—
714C4—94no—
715C4—272no—
716C4C22×D3×C3⋊D312yes—
717C3—24no—
718C3C2×#6431214yescomplemented
719C3C2×#41×C3⋊D311yescharacteristic, complemented
720C2—24no—
721C2—62no—
722C2—182no—
723C2—274no—
724C2—544no—
725C2#1172458612yesdirect product factor
726C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC22C22×D3×C3⋊D3
commutator, cosocleC2×C33C25
FrattiniC2C23×D3×C3⋊D3
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×D4D3×C3⋊D3
hypocenterC33C22×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊(C3⋊D3)C2semidirect
2. C2×C3×#3830C2semidirect
3. C2×C32×#237C2semidirect
4. C2×#89039C2semidirect
5. C22×#6289C2semidirect
6. C2×#89031C2semidirect
7. C2×#89028C2semidirect
8. #11724586C2direct (N × H)
9. C2×C4×D3×C3⋊D3C2semidirect
10. C2×#89022C2semidirect
11. C2×#89019C2semidirect
12. C2×#89018C2semidirect
17. C2×C33×D4C22semidirect
18. C2×#6312C22semidirect
19. D4×C3⋊(C3⋊D3)C22semidirect
20. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
22. C2×C3×#638C22semidirect
23. C22×C3×C3⋊Dic3C22semidirect
24. C3×#3830C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
26. C2×C3×#634C22semidirect
27. C2×C32×#67C22semidirect
28. C22×C32×Dic3C22semidirect
29. C32×#237C22semidirect
30. C2×C32×C4×D3C22semidirect
31. C2×C32×Dic6C22semidirect
32. #89039C22semidirect
33. C2×#6293C22semidirect
34. C2×#6292C22semidirect
35. C2×#6291C22semidirect
38. C2×#6289C22semidirect
39. C2×#6289C22semidirect
40. C2×#6289C22semidirect
41. #89031C22semidirect
42. C2×Dic3×C3⋊D3C22semidirect
43. #89028C22semidirect
44. C2×D3×C3⋊Dic3C22semidirect
45. C4×D3×C3⋊D3C22semidirect
46. #89022C22semidirect
47. #89019C22semidirect
48. #89018C22semidirect
54. C2×#3830D3semidirect
64. C2×C3×#237D3semidirect
83. C33×D4C23semidirect
85. #6312C23semidirect
87. C4⋊(C3⋊(C3⋊D3))C23semidirect
89. C3×#638C23semidirect
92. C2×C3×C3⋊Dic3C23semidirect
93. C3×C4×C3⋊D3C23semidirect
94. C3×#634C23semidirect
95. C32×#67C23semidirect
98. C2×C32×Dic3C23semidirect
99. C32×C4×D3C23semidirect
100. C32×Dic6C23semidirect
101. #6293C23semidirect
102. #6292C23semidirect
103. #6291C23semidirect
106. #6289C23semidirect
107. #6289C23semidirect
108. Dic3×C3⋊D3C23semidirect
109. D3×C3⋊Dic3C23semidirect
121. C2×C32×D4C2×D3semidirect
122. C2×C32×D4C2×D3semidirect
129. C2×#638C2×D3semidirect
131. C22×C3⋊Dic3C2×D3semidirect
135. #3830C2×D3semidirect
156. C2×C4×C3⋊D3C2×D3semidirect
158. C2×#634C2×D3semidirect
160. C2×C3×#67C2×D3semidirect
162. C22×C3×Dic3C2×D3semidirect
164. C3×#237C2×D3semidirect
166. C2×C3×C4×D3C2×D3semidirect
168. C2×C3×Dic6C2×D3semidirect
191. C2×C3⋊(C3⋊D3)#41semidirect
216. C2×#237C3⋊D3semidirect
256. C32×D4C22×D3semidirect
257. C32×D4C22×D3semidirect
269. #638C22×D3semidirect
276. C2×C3⋊Dic3C22×D3semidirect
289. C4×C3⋊D3C22×D3semidirect
291. #634C22×D3semidirect
293. C3×#67C22×D3semidirect
299. C2×C3×Dic3C22×D3semidirect
301. C3×C4×D3C22×D3semidirect
303. C3×Dic6C22×D3semidirect
315. C2×C33C2×#41semidirect
318. C3⋊(C3⋊D3)C2×#41semidirect
333. C2×C3×D4D32semidirect
334. C2×C3×D4C2×C3⋊D3semidirect
345. C2×#67C2×C3⋊D3semidirect
349. C22×Dic3C2×C3⋊D3semidirect
357. #237C2×C3⋊D3semidirect
390. C2×C4×D3C2×C3⋊D3semidirect
394. C2×Dic6C2×C3⋊D3semidirect
455. C33C22×#41semidirect
484. C3×D4C2×D32semidirect
485. C3×D4C22×C3⋊D3semidirect
503. #67C22×C3⋊D3semidirect
514. C2×Dic3C22×C3⋊D3semidirect
534. C4×D3C22×C3⋊D3semidirect
538. Dic6C22×C3⋊D3semidirect
545. C2×C32D3×#41semidirect
546. C2×C32D3×#41semidirect
578. C2×D4D3×C3⋊D3semidirect
641. C32C2×D3×#41semidirect
642. C32C2×D3×#41semidirect
661. D4C2×D3×C3⋊D3semidirect
686. C2×C3#64312semidirect
687. C2×C3#41×C3⋊D3semidirect
718. C3C2×#64312semidirect
719. C3C2×#41×C3⋊D3semidirect
725. C2#11724586direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊(C3⋊D3)2
C2×C3×#38302
C2×C32×#2372
C2×#890392
C22×#62892
C2×#890312
C2×#890282
#117245862
C2×C4×D3×C3⋊D32
C2×#890222
C2×#890192
C2×#890182
C2×#41×C3⋊D33
C2×#643123