Finite Group Databasebeta

← C3×#79789 #11873192

Subgroups — C3×#79789 #11873192

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5572C211yesmaximal, characteristic, complemented
2C3×#5562C211yesmaximal, characteristic
3C32×#440C211yesmaximal, characteristic, complemented
4C3×#5170C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic, complemented
6C3×C4×#215C211yesmaximal, characteristic, complemented
7C3×C4×#214C211yesmaximal, characteristic, complemented
8C3×#4885C211yesmaximal, characteristic, complemented
9C3×#4877C211yesmaximal, characteristic, complemented
10C3×#4806C211yesmaximal, characteristic, complemented
11C3×#4796C211yesmaximal, characteristic, complemented
12C3×#4784C211yesmaximal, characteristic, complemented
13C3×#4762C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4709C211yesmaximal, characteristic, complemented
16C3×#3126—31nomaximal
17#79789C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C3×#940C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×#930—21no—
28C3×#929—21no—
29C2×C3×#204C2211yescharacteristic
30C3×#895C2211yescharacteristic
31C3×#892—21no—
32C3×#892C2211yescharacteristic
33C3×#890C2211yescharacteristic
34C3×#887—21no—
35C3×#887C2211yescharacteristic
36C3×#884—21no—
37C3×#883—21no—
38C3×C4×D12C2211yescharacteristic
39C3×#872—21no—
40C3×#872C2211yescharacteristic
41C3×C4×Dic6—21no—
42C3×C4×Dic6C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#97C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#540—31no—
62C3×#519—31no—
63#5572C2×C311yescharacteristic, complemented
64#5562C2×C311yescharacteristic
65C3×#482—31no—
66C3×#482—31no—
67C3×#479—31no—
68C3×#479—31no—
69C3×#460—31no—
70C3×#460—31no—
71C3×#448—31no—
72C3×#448—31no—
73C3×#440—21no—
74C3×#440—31no—
75C3×#440D311yescharacteristic, complemented
76C3×#440C2×C311yescharacteristic, complemented
77C3×C4×SD16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5170C2×C311yescharacteristic, complemented
81#5163C2×C311yescharacteristic, complemented
82C4×#215C2×C311yescharacteristic, complemented
83C4×#214C2×C311yescharacteristic, complemented
84#4885C2×C311yescharacteristic, complemented
85#4877C2×C311yescharacteristic, complemented
86#4806C2×C311yescharacteristic, complemented
87#4796C2×C311yescharacteristic, complemented
88#4784C2×C311yescharacteristic, complemented
89#4762C2×C311yescharacteristic, complemented
90#4710C2×C311yescharacteristic, complemented
91#4709C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—22no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C32×SD16—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116C3×#217—21no—
117C3×#215—22no—
118C3×#214—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141#3126—31noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C22×C311yescharacteristic
144C2×C3×SD16—21no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C2×C3×SD16C2×D311yescharacteristic
149C2×C3×SD16C22×C311yescharacteristic
150C3×#127—31no—
151C3×#125—31no—
152C3×#123—61no—
153C3×#123—61no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#121—61no—
158C3×C4×Q8—21no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—61no—
163C3×C4×Q8—61no—
164C3×C4×Q8C2×D311yescharacteristic
165C3×C4×Q8C22×C311yescharacteristic
166C3×C4×D4—21no—
167C3×C4×D4—31no—
168C3×C4×D4C2×D311yescharacteristic
169C3×C4×D4C22×C311yescharacteristic
170C3×#117—31no—
171C3×#117—31no—
172C3×#117—61no—
173C3×#117—61no—
174Q8×Dic3C22×C311yescharacteristic
175C2×#215C22×C311yescharacteristic
176#940C22×C311yescharacteristic
177#938C22×C311yescharacteristic
178C2×#214C22×C311yescharacteristic
179#930—21no—
180#929—21no—
181C2×#204C22×C311yescharacteristic
182#895C22×C311yescharacteristic
183#892—21no—
184#892C22×C311yescharacteristic
185#890C22×C311yescharacteristic
186#887—21no—
187#887C22×C311yescharacteristic
188#884—21no—
189#883—21no—
190C4×D12C22×C311yescharacteristic
191#872—21no—
192#872C22×C311yescharacteristic
193C4×Dic6—21no—
194C4×Dic6C22×C311yescharacteristic
195C3×#107—21no—
196C3×#107—31no—
197C3×#107C2×D311yescharacteristic
198C3×#107C22×C311yescharacteristic
199C3×#106—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103C2×D311yescharacteristic
208C3×#103C22×C311yescharacteristic
209C3×#102—21no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102C2×D311yescharacteristic
214C3×#102C22×C311yescharacteristic
215C3×C22⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×#97—21no—
218C3×#97C2×D311yescharacteristic
219C3×#97C22×C311yescharacteristic
220C3×C4×C8—31no—
221#835C22×C311yescharacteristic
222#832C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226#818C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234C4×C3⋊C8C22×C311yescharacteristic
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8#4112yes—
240C32×D4—21no—
241C32×D4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—81no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C3×#67—81no—
250C3×#67—81no—
251C3×#67—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—81no—
261C3×C4×D3—24no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×Dic6—24no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#540—31no—
273#519—31no—
274#482—31no—
275#482—31no—
276#479—31no—
277#479—31no—
278#460—31no—
279#460—31no—
280#448—31no—
281#448—31no—
282#440—31no—
283#440C3×D311yescharacteristic, complemented
284C4×SD16—31no—
285C4×SD16—31no—
286#433—31no—
287C2×C3×Q8—21no—
288C2×C3×Q8—31no—
289C2×C3×Q8—61no—
290C2×C3×Q8—62no—
291C2×C3×Q8—62no—
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C2×C3×D4—21no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C23×C311yescharacteristic
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—41no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—21no—
309C2×#67—21no—
310C2×#67—21no—
311D3×Q8—22no—
312D3×Q8—22no—
313C2×D12—21no—
314C2×D12C23×C311yescharacteristic
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3C23×C311yescharacteristic
318C2×Dic6—21no—
319C2×Dic6C23×C311yescharacteristic
320C3×SD16—24no—
321C3×SD16—22no—
322C3×SD16—22no—
323C3×SD16—62no—
324C3×SD16—62no—
325C3×SD16—62no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C23×C311yescharacteristic
333C2×C3×C8C23×C311yescharacteristic
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C23×C311yescharacteristic
351C3×C4⋊C4C23×C311yescharacteristic
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—41no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—21no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—31no—
365C3×C42—41no—
366C3×C42—61no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42—61no—
370C3×C42C22×D311yescharacteristic
371C3×C42C23×C311yescharacteristic
372#217—21no—
373#215—22no—
374#214—22no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4C3×D411yescharacteristic
379(C2×D3)⋊C4C3×D411yescharacteristic
380C4⋊Dic3—21no—
381C4⋊Dic3—21no—
382C4⋊Dic3C23×C311yescharacteristic
383C4⋊Dic3C23×C311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4C3×D411yescharacteristic
388Dic3⋊C4C3×D411yescharacteristic
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3C23×C311yescharacteristic
394C2×C3⋊C8C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396#204—22no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C32×C4—22no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3×Dic3—21no—
415C3×Dic3—22no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C22×Q8—31no—
421C2×SD16—31no—
422C2×SD16—31no—
423C2×SD16—31no—
424C2×SD16C2×C3×D311yescharacteristic
425#127—31no—
426#125—31no—
427#123—61no—
428#123—61no—
429#121—31no—
430#121—31no—
431#121—61no—
432#121—61no—
433C4×Q8—31no—
434C4×Q8—31no—
435C4×Q8—31no—
436C4×Q8—61no—
437C4×Q8—61no—
438C4×Q8C2×C3×D311yescharacteristic
439C4×D4—31no—
440C4×D4C2×C3×D311yescharacteristic
441#117—31no—
442#117—31no—
443#117—61no—
444#117—61no—
445#107—31no—
446#107C2×C3×D311yescharacteristic
447#106—31no—
448#106—31no—
449C4⋊C8—31no—
450C4⋊C8—31no—
451#103—31no—
452#103—31no—
453#103—31no—
454#103C2×C3×D311yescharacteristic
455#102—31no—
456#102—31no—
457#102—31no—
458#102C2×C3×D311yescharacteristic
459C22⋊C8—31no—
460C22⋊C8—31no—
461#97C2×C3×D311yescharacteristic
462C4×C8—31no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—31no—
466C23×C3—41no—
467C23×C3—61no—
468C22×D3—21no—
469C22×D3C2×C3×D411yescharacteristic
470C3×Q8—21no—
471C3×Q8—21no—
472C3×Q8—22no—
473C3×Q8—32no—
474C3×Q8—41no—
475C3×Q8—64no—
476C3×Q8—61no—
477C3×Q8#23512yes—
478C3×Q8C3×#4112yes—
479C3×D4—22no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—41no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—241no—
488C3×D4—241no—
489C3×D4—241no—
490C3×D4—241no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—64no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—81no—
513C2×C3×C4—81no—
514C2×C3×C4—82no—
515C2×C3×C4—241no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×C3×D411yescharacteristic
519C2×C3×C4C2×C3×D411yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C24×C311yescharacteristic
522#67—81no—
523#67—81no—
524#67—81no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3C2×C3×D411yescharacteristic
529C2×Dic3C2×C3×D411yescharacteristic
530C2×Dic3C2×C3×D411yescharacteristic
531D12—21no—
532D12—21no—
533D12—81no—
534C4×D3—24no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—81no—
538Dic6—24no—
539Dic6—21no—
540Dic6C3×#4112yes—
541C3×C8—22no—
542C3×C8—21no—
543C3×C8—21no—
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—41no—
547C3×C8—61no—
548C3×C8—61no—
549C3⋊C8—21no—
550C3⋊C8—21no—
551C2×C32—81no—
552C2×C32#52511yescharacteristic
553C2×C32#57711yescharacteristic
554C2×C32#57711yescharacteristic
555C3×D3—41no—
556C3×D3—81no—
557C2×Q8—31no—
558C2×Q8—61no—
559C2×Q8—62no—
560C2×Q8—62no—
561C2×Q8C22×C3×D311yescharacteristic
562C2×D4—31no—
563C2×D4—61no—
564C2×D4—61no—
565C2×D4—61no—
566C2×D4—61no—
567C2×D4C22×C3×D311yescharacteristic
568C22×C4—21no—
569C22×C4—31no—
570C22×C4—61no—
571C22×C4—61no—
572SD16—22no—
573SD16—62no—
574SD16—62no—
575SD16—62no—
576C2×C8—31no—
577C2×C8—31no—
578C2×C8C22×C3×D311yescharacteristic
579C2×C8C22×C3×D311yescharacteristic
580C4⋊C4—21no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4C22×C3×D311yescharacteristic
591C4⋊C4C22×C3×D311yescharacteristic
592C22⋊C4—21no—
593C22⋊C4—31no—
594C22⋊C4—31no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C42—21no—
600C42—31no—
601C42—61no—
602C42—61no—
603C42—61no—
604C42—61no—
605C42C22×C3×D311yescharacteristic
606C22×C3—21no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3C2×D3×D411yescharacteristic
623C22×C3C22×C3×D411yescharacteristic
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—41no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—42no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—62no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C2×#23511yescharacteristic
654C3×C4D3×#4111yescharacteristic
655C3×C4C2×C3×#4111yescharacteristic
656C3×C4C2×C3×#4111yescharacteristic
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—22no—
661Dic3—41no—
662Dic3—41no—
663C32#312611yescharacteristic, complemented, Sylow
664C23—21no—
665C23—31no—
666C23—61no—
667Q8—21no—
668Q8—32no—
669Q8—64no—
670Q8—61no—
671Q8C3×#23512yes—
672D4—21no—
673D4—21no—
674D4—61no—
675D4—61no—
676D4—241no—
677D4—241no—
678D4—241no—
679D4—241no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—64no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—81no—
693C2×C4—241no—
694C2×C4C3×D3×D411yescharacteristic
695C2×C4C3×D3×D411yescharacteristic
696C2×C4C23×C3×D311yescharacteristic
697C8—21no—
698C8—21no—
699C8—61no—
700C8—61no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—82no—
705C2×C3—81no—
706C2×C3—81no—
707C2×C3—121no—
708C2×C3—241no—
709C2×C3#554711yescharacteristic
710C2×C3#577511yescharacteristic
711C2×C3#577811yescharacteristic
712C2×C3C3×#52511yescharacteristic
713C2×C3C3×#57711yescharacteristic
714C2×C3C3×#57711yescharacteristic
715D3—41no—
716D3—81no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—61no—
721C22—61no—
722C22—61no—
723C22—121no—
724C22—121no—
725C22—121no—
726C22C2×C3×D3×D411yescharacteristic
727C4—21no—
728C4—21no—
729C4—22no—
730C4—41no—
731C4—41no—
732C4—61no—
733C4—61no—
734C4—61no—
735C4—62no—
736C4—121no—
737C4—121no—
738C4C2×C3×#23511yescharacteristic
739C4C3×D3×#4111yescharacteristic
740C3—21no—
741C3#7978911yescharacteristic, direct product factor
742C3C3×#312611yescharacteristic, complemented
743C2—81no—
744C2—121no—
745C2—241no—
746C2C3×#554711yescharacteristic
747C2C3×#577511yescharacteristic
748C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC3×#5562C2
hypercenterC3×#440D3
hypocenterC3C3×#3126
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
1. C3×#5572C2semidirect
3. C32×#440C2semidirect
4. C3×#5170C2semidirect
5. C3×#5163C2semidirect
6. C3×C4×#215C2semidirect
7. C3×C4×#214C2semidirect
8. C3×#4885C2semidirect
9. C3×#4877C2semidirect
10. C3×#4806C2semidirect
11. C3×#4796C2semidirect
12. C3×#4784C2semidirect
13. C3×#4762C2semidirect
14. C3×#4710C2semidirect
15. C3×#4709C2semidirect
17. #79789C3direct (N × H)
63. #5572C2×C3semidirect
75. C3×#440D3semidirect
76. C3×#440C2×C3semidirect
80. #5170C2×C3semidirect
81. #5163C2×C3semidirect
82. C4×#215C2×C3semidirect
83. C4×#214C2×C3semidirect
84. #4885C2×C3semidirect
85. #4877C2×C3semidirect
86. #4806C2×C3semidirect
87. #4796C2×C3semidirect
88. #4784C2×C3semidirect
89. #4762C2×C3semidirect
90. #4710C2×C3semidirect
91. #4709C2×C3semidirect
283. #440C3×D3semidirect
663. C32#3126semidirect
741. C3#79789direct (N × H)
742. C3C3×#3126semidirect

Maximal subgroups

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

subgroupindex
C3×#55722
C3×#55622
C32×#4402
C3×#51702
C3×#51632
C3×C4×#2152
C3×C4×#2142
C3×#48852
C3×#48772
C3×#48062
C3×#47962
C3×#47842
C3×#47622
C3×#47102
C3×#47092
C3×#31263
#797893