Finite Group Databasebeta

← #13170812

Subgroups — #13170812

Order 1728.

1642 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#625C211yesmaximal, characteristic
2#11723685C211yesmaximal, characteristic, complemented
3#11723506C212yesmaximal, complemented
4#11723459C211yesmaximal, characteristic, complemented
5C3×D3×(C2×D3)⋊C4C212yesmaximal, complemented
6C3×C4×#625C211yesmaximal, characteristic, complemented
7#11722938C211yesmaximal, characteristic, complemented
8#11722936C212yesmaximal, complemented
9Dic3×#625C211yesmaximal, characteristic, complemented
10#11722917C211yesmaximal, characteristic, complemented
11#11722902C212yesmaximal, complemented
12#10595056—32nomaximal
13#10594181—31nomaximal
14C22×C3×D32C2212yes—
15C2×C32×C4×D3C2212yescomplemented
16C2×#6295C2211yescharacteristic
17C2×#6294C2212yescomplemented
18C2×#6290C2212yes—
19C2×Dic3×C3⋊D3C2212yescomplemented
20C2×D3×C3⋊Dic3C2211yescharacteristic
21C2×C3×#625C2211yescharacteristic
22C2×C3×D3×Dic3C2212yescomplemented
23D3×#625C418yescomplemented
24#88857C2211yescharacteristic, complemented
25C3×#3752C2212yescomplemented
26C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C32×(C2×D3)⋊C4C2211yescharacteristic
28#88815C2211yescharacteristic, complemented
29#88806C2211yescharacteristic, complemented
30(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
31(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
32Dic3×C3⋊Dic3C2212yescomplemented
33Dic3×C3⋊Dic3C2211yescharacteristic, complemented
34C3×#3724C2211yescharacteristic, complemented
35C3×#3722C2212yescomplemented
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C2×D3×#67—32no—
39C22×#625—31no—
40C4×#638—32no—
41#64086—31no—
42C3×C4×#67—32no—
43C2×C3×(C2×D3)⋊C4—32no—
44C3×D3×C22⋊C4—32no—
45Dic3×#67—32no—
46D3×#217—32no—
47D3×#217—32no—
48#63957—31no—
49#63952—32no—
50#63921—32no—
51D3×(C2×D3)⋊C4D312yescomplemented
52#63902—32no—
53#63902—31no—
54#63902—31no—
55C4×#625—31no—
56C4×#625D311yescharacteristic, complemented
57#63881—32no—
58#63880—32no—
59#63879—32no—
60#63879—32no—
61#63879—32no—
62#63879—62no—
63#63878—32no—
64#63877—32no—
65#63877—61no—
66C22×C3×C3⋊D3C2312yes—
67C22×C32×D3C2311yescharacteristic
68C22×C32×D3C2312yes—
69C2×C3×D32—42no—
70C2×C3×D32—42no—
71C2×C3×D32C2×C418yescomplemented
72C2×C33×C4C2311yescharacteristic
73C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
74C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
75C2×C3×C3⋊Dic3C2311yescharacteristic
76C2×C3×C3⋊Dic3C2312yes—
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C32×Dic3C2311yescharacteristic
79C2×C32×Dic3C2312yes—
80C32×C4×D3—42no—
81#6295C2×C414yescomplemented
82#6294—42no—
83#6290C2×C418yescomplemented
84Dic3×C3⋊D3—42no—
85D3×C3⋊Dic3C2×C414yescomplemented
86C3×#625C2×C414yescomplemented
87C3×D3×Dic3—42no—
88#5545—91no—
89#5486—92no—
90C23×C3×D3—32no—
91C23×C3×D3—32no—
92C22×D32C2×D312yes—
93C22×C32×C4—32no—
94C2×#638—32no—
95C22×C3⋊Dic3—31no—
96C2×C4×C3⋊D3—32no—
97C2×C3×#67—32no—
98C22×C3×Dic3—32no—
99C2×C3×C4×D3—22no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3C2×D312yescomplemented
102C2×C3×C4×D3C2×D312yescomplemented
103D3×#67—316no—
104C2×#626—32no—
105C2×#625—32no—
106C2×#625—32no—
107C2×#625—31no—
108C2×#625—38no—
109C2×#625—62no—
110C2×#625C2×D311yescharacteristic
111C2×#624—32no—
112C2×D3×Dic3—32no—
113C2×D3×Dic3—32no—
114C2×D3×Dic3—32no—
115C2×D3×Dic3—32no—
116C2×D3×Dic3—32no—
117C2×D3×Dic3—61no—
118C2×D3×Dic3—62no—
119C2×D3×Dic3C2×D312yescomplemented
120C32×C22⋊C4—31no—
121#3757—31no—
122#3757—32no—
123#3752C2×D312yescomplemented
124#3750—31no—
125#3750—32no—
126#3750—31no—
127#3750—61no—
128#3750—62no—
129#3750—121no—
130C4×C3⋊Dic3—31no—
131C4×C3⋊Dic3—32no—
132C4×C3⋊Dic3C2×D311yescharacteristic, complemented
133C3×#217—32no—
134C3×#217—32no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—62no—
143C3×(C2×D3)⋊C4C2×D312yes—
144C3×Dic3⋊C4—32no—
145C3×C4×Dic3—32no—
146C3×C4×Dic3—61no—
147#3724—31no—
148#3724—32no—
149#3724—61no—
150#3724C2×D311yescharacteristic, complemented
151Dic3⋊Dic3—32no—
152#3722C2×D312yescomplemented
153(C2×D3)⋊Dic3—32no—
154(C2×D3)⋊Dic3—32no—
155(C2×D3)⋊Dic3—32no—
156(C2×D3)⋊Dic3—61no—
157(C2×D3)⋊Dic3—62no—
158(C2×D3)⋊Dic3C2×D312yes—
159(C2×D3)⋊Dic3C2×D312yescomplemented
160Dic32—32no—
161Dic32—32no—
162Dic32—32no—
163Dic32—61no—
164Dic32—62no—
165C22×C33C2411yescharacteristic
166C2×C3×C3⋊D3—22no—
167C2×C3×C3⋊D3—22no—
168C2×C3×C3⋊D3C22×C414yes—
169C2×C32×D3—22no—
170C2×C32×D3—22no—
171C2×C32×D3—21no—
172C2×C32×D3—21no—
173C2×C32×D3C22×C414yes—
174C2×C32×D3C22×C412yes—
175C3×D32—48no—
176C33×C4—21no—
177C3⋊(C3⋊Dic3)—21no—
178C3⋊(C3⋊Dic3)C22×C412yes—
179C3×C3⋊Dic3—22no—
180C3×C3⋊Dic3—21no—
181C3×C3⋊Dic3C22×C412yes—
182C32×Dic3—22no—
183C32×Dic3—21no—
184C22×#67—92no—
185C2×D3×D4—91no—
186C3×C4×D4—91no—
187C2×C3×C22⋊C4—92no—
188C2×#217—92no—
189D4×Dic3—91no—
190C4×#67—32no—
191C4×#67—92no—
192C4×#67—92no—
193C4×#67—92no—
194C4×#67—92no—
195C4×#67—182no—
196C2×(C2×D3)⋊C4—32no—
197#893—91no—
198#892—91no—
199#67⋊C4—92no—
200#67⋊C4—92no—
201#67⋊C4—92no—
202#67⋊C4—92no—
203#67⋊C4—92no—
204D3×C22⋊C4—32no—
205D3×C22⋊C4—92no—
206D3×C22⋊C4—92no—
207#877—92no—
208#877—92no—
209#877—181no—
210C4×D12—91no—
211#872—91no—
212C23×C32—31no—
213C23×C32—32no—
214C22×C3⋊D3C22×D312yes—
215C22×C3×D3—21no—
216C22×C3×D3—22no—
217C22×C3×D3—32no—
218C22×C3×D3—32no—
219C22×C3×D3—38no—
220C22×C3×D3—38no—
221C22×C3×D3—62no—
222C22×C3×D3—122no—
223C22×C3×D3—122no—
224C22×C3×D3—122no—
225C22×C3×D3—122no—
226C22×C3×D3C22×D312yes—
227C22×C3×D3C22×D312yes—
228C22×C3×D3C22×D312yes—
229C2×D32—42no—
230C2×D32—42no—
231C2×D32C4×D318yescomplemented
232C2×C32×C4—21no—
233C2×C32×C4—22no—
234C2×C32×C4—32no—
235C2×C32×C4—31no—
236C2×C32×C4—41no—
237C2×C32×C4—122no—
238C2×C32×C4C22×D312yes—
239C2×C32×C4C22×D311yescharacteristic
240#638—38no—
241C2×C3⋊Dic3—31no—
242C2×C3⋊Dic3—32no—
243C2×C3⋊Dic3—34no—
244C2×C3⋊Dic3—32no—
245C2×C3⋊Dic3—31no—
246C2×C3⋊Dic3—62no—
247C2×C3⋊Dic3—61no—
248C2×C3⋊Dic3—61no—
249C2×C3⋊Dic3—62no—
250C2×C3⋊Dic3—121no—
251C2×C3⋊Dic3—121no—
252C2×C3⋊Dic3C22×D312yes—
253C2×C3⋊Dic3C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D311yescharacteristic
255C4×C3⋊D3—122no—
256C3×#67—38no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—32no—
260C2×C3×Dic3—32no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—61no—
264C2×C3×Dic3—62no—
265C2×C3×Dic3—61no—
266C2×C3×Dic3—122no—
267C2×C3×Dic3C22×D312yes—
268C2×C3×Dic3C22×D312yes—
269C2×C3×Dic3C22×D312yes—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×C4×D3—44no—
273C3×C4×D3—122no—
274#626—38no—
275#625—38no—
276#625—38no—
277#625—34no—
278#625—68no—
279#625C4×D314yescomplemented
280#624—122no—
281D3×Dic3—38no—
282D3×Dic3—42no—
283D3×Dic3—64no—
284D3×Dic3—122no—
285D3×Dic3—122no—
286D3×Dic3—124no—
287D3×Dic3—122no—
288D3×Dic3—122no—
289#518—271noSylow
290C2×C33C23×C411yescharacteristic
291C2×C33H(5,𝔽2)11yescharacteristic
292C2×C33H(5,𝔽2)11yescharacteristic
293C3×C3⋊D3—24no—
294C32×D3—22no—
295C32×D3—24no—
296C24×C3—92no—
297C23×D3—32no—
298C23×D3—32no—
299C2×C3×D4—91no—
300C22×C3×C4—32no—
301C22×C3×C4—32no—
302C22×C3×C4—62no—
303C22×C3×C4—92no—
304C2×#67—32no—
305C2×#67—92no—
306C2×#67—916no—
307C2×#67—92no—
308C2×#67—92no—
309C2×#67—92no—
310C2×#67—182no—
311C22×Dic3—32no—
312C22×Dic3—92no—
313C22×Dic3—92no—
314C22×Dic3—92no—
315C22×Dic3—181no—
316D3×D4—98no—
317C2×D12—91no—
318C2×C4×D3—32no—
319C2×C4×D3—91no—
320C2×C4×D3—92no—
321C2×C4×D3—92no—
322C2×C4×D3—92no—
323C2×C4×D3—92no—
324C2×C4×D3—182no—
325C2×C4×D3D3212yescomplemented
326C3×C4⋊C4—91no—
327C3×C22⋊C4—32no—
328C3×C22⋊C4—61no—
329C3×C22⋊C4—92no—
330C3×C22⋊C4—92no—
331C3×C22⋊C4—92no—
332C3×C22⋊C4—92no—
333C3×C42—91no—
334#217—32no—
335#217—32no—
336#217—92no—
337#217—92no—
338#217—92no—
339#217—181no—
340#217—182no—
341(C2×D3)⋊C4—32no—
342(C2×D3)⋊C4—32no—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4—32no—
345(C2×D3)⋊C4—32no—
346(C2×D3)⋊C4—32no—
347(C2×D3)⋊C4—62no—
348(C2×D3)⋊C4—91no—
349(C2×D3)⋊C4—92no—
350(C2×D3)⋊C4D3211yescharacteristic
351C4⋊Dic3—91no—
352Dic3⋊C4—32no—
353Dic3⋊C4—92no—
354Dic3⋊C4—92no—
355Dic3⋊C4—91no—
356Dic3⋊C4—92no—
357Dic3⋊C4—91no—
358Dic3⋊C4—181no—
359Dic3⋊C4—181no—
360Dic3⋊C4—182no—
361Dic3⋊C4—361no—
362C4×Dic3—32no—
363C4×Dic3—61no—
364C4×Dic3—92no—
365C4×Dic3—92no—
366C4×Dic3—92no—
367C4×Dic3—91no—
368C4×Dic3—92no—
369C4×Dic3—181no—
370C4×Dic3—182no—
371C22×C32—21no—
372C22×C32—22no—
373C22×C32—34no—
374C22×C32—32no—
375C22×C32—41no—
376C22×C32—62no—
377C22×C32—62no—
378C22×C32—61no—
379C22×C32—61no—
380C22×C32C23×D312yes—
381C22×C32C23×D311yescharacteristic
382C2×C3⋊D3—22no—
383C2×C3⋊D3—22no—
384C2×C3⋊D3C2×C4×D314yes—
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—24no—
393C2×C3×D3—34no—
394C2×C3×D3—34no—
395C2×C3×D3—42no—
396C2×C3×D3—42no—
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—64no—
400C2×C3×D3—62no—
401C2×C3×D3—62no—
402C2×C3×D3—62no—
403C2×C3×D3—62no—
404C2×C3×D3—122no—
405C2×C3×D3—122no—
406C2×C3×D3—128no—
407C2×C3×D3—128no—
408C2×C3×D3C2×C4×D314yes—
409C2×C3×D3C2×C4×D314yes—
410C2×C3×D3C2×C4×D314yes—
411D32—48no—
412C32×C4—21no—
413C32×C4—22no—
414C32×C4—42no—
415C32×C4—41no—
416C32×C4—62no—
417C32×C4—61no—
418C32×C4—81no—
419C3⋊Dic3—22no—
420C3⋊Dic3—21no—
421C3⋊Dic3—34no—
422C3⋊Dic3—32no—
423C3⋊Dic3—62no—
424C3⋊Dic3—64no—
425C3⋊Dic3—61no—
426C3⋊Dic3—62no—
427C3⋊Dic3—122no—
428C3⋊Dic3—122no—
429C3⋊Dic3—121no—
430C3⋊Dic3—241no—
431C3⋊Dic3C2×C4×D312yes—
432C3×Dic3—24no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—34no—
437C3×Dic3—41no—
438C3×Dic3—62no—
439C3×Dic3—62no—
440C3×Dic3—62no—
441C3×Dic3—62no—
442C3×Dic3—122no—
443C3×Dic3—121no—
444C22×D4—271no—
445C4×D4—91no—
446C4×D4—271no—
447C4×D4—271no—
448C4×D4—272no—
449C4×D4—272no—
450C4×D4—271no—
451#117—271no—
452#117—271no—
453C2×C22⋊C4—92no—
454C2×C22⋊C4—272no—
455C33#51811yescharacteristic, complemented, Sylow
456C23×C3—32no—
457C23×C3—32no—
458C23×C3—32no—
459C23×C3—61no—
460C23×C3—62no—
461C23×C3—98no—
462C23×C3—92no—
463C23×C3—362no—
464C23×C3—362no—
465C22×D3—32no—
466C22×D3—32no—
467C22×D3—38no—
468C22×D3—38no—
469C22×D3—62no—
470C22×D3—122no—
471C22×D3—122no—
472C22×D3—122no—
473C22×D3—122no—
474C22×D3C2×D3211yescharacteristic
475C22×D3C2×D3212yes—
476C3×D4—94no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—32no—
482C2×C3×C4—41no—
483C2×C3×C4—62no—
484C2×C3×C4—61no—
485C2×C3×C4—91no—
486C2×C3×C4—92no—
487C2×C3×C4—91no—
488C2×C3×C4—122no—
489C2×C3×C4—122no—
490C2×C3×C4—124no—
491C2×C3×C4—362no—
492C2×C3×C4C2×D3212yes—
493C2×C3×C4C2×D3211yescharacteristic
494#67—38no—
495#67—98no—
496#67—98no—
497#67—98no—
498#67—98no—
499#67—188no—
500C2×Dic3—32no—
501C2×Dic3—32no—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—62no—
507C2×Dic3—98no—
508C2×Dic3—91no—
509C2×Dic3—92no—
510C2×Dic3—91no—
511C2×Dic3—92no—
512C2×Dic3—122no—
513C2×Dic3—184no—
514C2×Dic3—182no—
515C2×Dic3—181no—
516C2×Dic3—181no—
517C2×Dic3—182no—
518C2×Dic3—361no—
519C2×Dic3—361no—
520C2×Dic3—362no—
521C2×Dic3—362no—
522C2×Dic3C2×D3212yes—
523C2×Dic3C2×D3211yescharacteristic
524D12—94no—
525C4×D3—42no—
526C4×D3—94no—
527C4×D3—122no—
528C4×D3—362no—
529C4×D3—362no—
530C4×D3—362no—
531C4×D3—362no—
532C4×D3—364no—
533C2×C32—21no—
534C2×C32—22no—
535C2×C32—22no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—22no—
539C2×C32—41no—
540C2×C32—41no—
541C2×C32—41no—
542C2×C32—64no—
543C2×C32—62no—
544C2×C32C22×C4×D312yes—
545C2×C32C22×C4×D311yescharacteristic
546C2×C32#100412yes—
547C2×C32#100412yes—
548C2×C32#100411yescharacteristic
549C2×C32#100911yescharacteristic
550C3⋊D3—24no—
551C3×D3—24no—
552C3×D3—24no—
553C3×D3—24no—
554C3×D3—42no—
555C3×D3—44no—
556C3×D3—64no—
557C3×D3—64no—
558C3×D3—124no—
559C24—92no—
560C2×D4—91no—
561C2×D4—271no—
562C2×D4—278no—
563C2×D4—272no—
564C22×C4—32no—
565C22×C4—92no—
566C22×C4—272no—
567C22×C4—272no—
568C22×C4—271no—
569C4⋊C4—91no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C22⋊C4—31no—
574C22⋊C4—92no—
575C22⋊C4—92no—
576C22⋊C4—92no—
577C22⋊C4—92no—
578C22⋊C4—271no—
579C22⋊C4—272no—
580C42—91no—
581C42—271no—
582C42—272no—
583C22×C3—21no—
584C22×C3—22no—
585C22×C3—34no—
586C22×C3—34no—
587C22×C3—34no—
588C22×C3—41no—
589C22×C3—62no—
590C22×C3—64no—
591C22×C3—62no—
592C22×C3—62no—
593C22×C3—62no—
594C22×C3—62no—
595C22×C3—62no—
596C22×C3—62no—
597C22×C3—94no—
598C22×C3—122no—
599C22×C3—122no—
600C22×C3—121no—
601C22×C3—121no—
602C22×C3—182no—
603C22×C3—182no—
604C22×C3—368no—
605C22×C3C22×D3212yes—
606C22×C3C22×D3211yescharacteristic
607C2×D3—22no—
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—22no—
611C2×D3—34no—
612C2×D3—34no—
613C2×D3—64no—
614C2×D3—62no—
615C2×D3—62no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—122no—
619C2×D3—122no—
620C2×D3—128no—
621C2×D3—128no—
622C2×D3C4×D3212yes—
623C2×D3C4×D3214yes—
624C3×C4—21no—
625C3×C4—22no—
626C3×C4—42no—
627C3×C4—41no—
628C3×C4—64no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—62no—
632C3×C4—81no—
633C3×C4—92no—
634C3×C4—121no—
635C3×C4—182no—
636C3×C4—181no—
637Dic3—21no—
638Dic3—22no—
639Dic3—34no—
640Dic3—62no—
641Dic3—62no—
642Dic3—62no—
643Dic3—62no—
644Dic3—92no—
645Dic3—94no—
646Dic3—122no—
647Dic3—121no—
648Dic3—182no—
649Dic3—184no—
650Dic3—181no—
651Dic3—182no—
652Dic3—362no—
653Dic3—362no—
654Dic3—361no—
655Dic3—721no—
656C32—21no—
657C32—22no—
658C32—41no—
659C32#548612yescomplemented
660C32#554511yescharacteristic, complemented
661C23—31no—
662C23—32no—
663C23—98no—
664C23—92no—
665C23—362no—
666C23—362no—
667D4—94no—
668D4—274no—
669D4—278no—
670C2×C4—31no—
671C2×C4—32no—
672C2×C4—91no—
673C2×C4—91no—
674C2×C4—92no—
675C2×C4—122no—
676C2×C4—274no—
677C2×C4—271no—
678C2×C4—271no—
679C2×C4—362no—
680C2×C4—1082no—
681C2×C4—1082no—
682C2×C4D3311yescharacteristic
683C2×C3—21no—
684C2×C3—22no—
685C2×C3—21no—
686C2×C3—22no—
687C2×C3—22no—
688C2×C3—21no—
689C2×C3—41no—
690C2×C3—41no—
691C2×C3—41no—
692C2×C3—64no—
693C2×C3—64no—
694C2×C3—64no—
695C2×C3—122no—
696C2×C3—124no—
697C2×C3—184no—
698C2×C3C2×C4×D3211yescharacteristic
699C2×C3C2×C4×D3212yes—
700C2×C3#6430712yes—
701C2×C3#6431311yescharacteristic
702C2×C3#6431311yescharacteristic
703C2×C3#6433012yes—
704D3—22no—
705D3—24no—
706D3—64no—
707D3—64no—
708D3—124no—
709C22—32no—
710C22—34no—
711C22—62no—
712C22—61no—
713C22—62no—
714C22—61no—
715C22—94no—
716C22—182no—
717C22—182no—
718C22—368no—
719C22C2×D3311yescharacteristic
720C4—21no—
721C4—61no—
722C4—62no—
723C4—92no—
724C4—182no—
725C4—181no—
726C4—272no—
727C4—541no—
728C3—22no—
729C3—21no—
730C3—41no—
731C3#1059418111yescharacteristic, complemented
732C3#1059505612yescomplemented
733C2—62no—
734C2—64no—
735C2—184no—
736C2#1172438011yescharacteristic
737C2C4×D3311yescharacteristic
738C2#1172441411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×D3×#625C2
hypercenterC2×C4D33
hypocenterC33#518
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723685C2semidirect
3. #11723506C2semidirect
4. #11723459C2semidirect
5. C3×D3×(C2×D3)⋊C4C2semidirect
6. C3×C4×#625C2semidirect
7. #11722938C2semidirect
8. #11722936C2semidirect
9. Dic3×#625C2semidirect
10. #11722917C2semidirect
11. #11722902C2semidirect
15. C2×C32×C4×D3C22semidirect
17. C2×#6294C22semidirect
19. C2×Dic3×C3⋊D3C22semidirect
22. C2×C3×D3×Dic3C22semidirect
23. D3×#625C4semidirect
24. #88857C22semidirect
25. C3×#3752C22semidirect
26. C3×C4×C3⋊Dic3C22semidirect
28. #88815C22semidirect
29. #88806C22semidirect
31. (C2×D3)⋊(C3⋊Dic3)C22semidirect
32. Dic3×C3⋊Dic3C22semidirect
33. Dic3×C3⋊Dic3C22semidirect
34. C3×#3724C22semidirect
35. C3×#3722C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
51. D3×(C2×D3)⋊C4D3semidirect
56. C4×#625D3semidirect
71. C2×C3×D32C2×C4semidirect
81. #6295C2×C4semidirect
83. #6290C2×C4semidirect
85. D3×C3⋊Dic3C2×C4semidirect
86. C3×#625C2×C4semidirect
101. C2×C3×C4×D3C2×D3semidirect
102. C2×C3×C4×D3C2×D3semidirect
119. C2×D3×Dic3C2×D3semidirect
123. #3752C2×D3semidirect
132. C4×C3⋊Dic3C2×D3semidirect
150. #3724C2×D3semidirect
152. #3722C2×D3semidirect
159. (C2×D3)⋊Dic3C2×D3semidirect
231. C2×D32C4×D3semidirect
279. #625C4×D3semidirect
325. C2×C4×D3D32semidirect
455. C33#518semidirect
659. C32#5486semidirect
660. C32#5545semidirect
731. C3#10594181semidirect
732. C3#10595056semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6252
#117236852
#117235062
#117234592
C3×D3×(C2×D3)⋊C42
C3×C4×#6252
#117229382
#117229362
Dic3×#6252
#117229172
#117229022
#105950563
#105941813