Finite Group Databasebeta

← C3×#79383 #11872108

Subgroups — C3×#79383 #11872108

Order 1152.

860 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5534C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3C32×#433C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4844C211yesmaximal, characteristic, complemented
6C3×#4844C211yesmaximal, characteristic, complemented
7C3×#4842C211yesmaximal, characteristic, complemented
8C3×#4737C211yesmaximal, characteristic, complemented
9C3×#4732C211yesmaximal, characteristic
10C3×#4731C211yesmaximal, characteristic, complemented
11C3×#4723C211yesmaximal, characteristic, complemented
12C3×#4711C211yesmaximal, characteristic, complemented
13C3×#4710C211yesmaximal, characteristic, complemented
14C3×C4×D24C211yesmaximal, characteristic, complemented
15C3×C4×#204C211yesmaximal, characteristic, complemented
16C3×#3118—31nomaximal
17#79383C311yesmaximal, characteristic, direct product factor
18C22×C3×D12C2211yescharacteristic
19C32×#117C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C3×#926C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C2×C3×D24C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C3×#898—21no—
28C3×#896—21no—
29C3×#893—21no—
30C3×#893—21no—
31C3×#885—21no—
32C3×#883—21no—
33C3×D3×C22⋊C4—21no—
34C3×D3×C22⋊C4—21no—
35C3×#875C2211yescharacteristic, complemented
36C3×C4×D12C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic, complemented
41C3×#869C2211yescharacteristic, complemented
42C3×C4×Dic6C2211yescharacteristic, complemented
43C32×C4⋊C8C2211yescharacteristic, complemented
44C32×C4⋊C8C2211yescharacteristic, complemented
45C32×C22⋊C8C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C32×#97C2211yescharacteristic, complemented
48C32×C4×C8C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#821C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#818C2211yescharacteristic, complemented
56C3×#818C2211yescharacteristic, complemented
57C3×#817C2211yescharacteristic, complemented
58C3×#817C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61C3×#542—31no—
62C3×#518—31no—
63#5534C2×C311yescharacteristic, complemented
64#5521C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#476—31no—
68C3×#474—31no—
69C3×#463—31no—
70C3×#463—31no—
71C3×#450—31no—
72C3×#447—31no—
73C3×#442—31no—
74C3×#440—31no—
75C3×C4×SD16—31no—
76C3×C4×D8—31no—
77C3×#433—21no—
78C3×#433D311yescharacteristic, complemented
79C3×#433C2×C311yescharacteristic, complemented
80#4846C2×C311yescharacteristic, complemented
81#4844C2×C311yescharacteristic, complemented
82#4844C2×C311yescharacteristic, complemented
83#4842C2×C311yescharacteristic, complemented
84#4737C2×C311yescharacteristic, complemented
85#4732C2×C311yescharacteristic
86#4731C2×C311yescharacteristic, complemented
87#4723C2×C311yescharacteristic, complemented
88#4711C2×C311yescharacteristic, complemented
89#4710C2×C311yescharacteristic, complemented
90C4×D24C2×C311yescharacteristic, complemented
91C4×#204C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×D12—21no—
96C2×C3×D12—22no—
97C2×C3×D12—22no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4D411yescharacteristic
113C32×C4⋊C4D411yescharacteristic
114C32×C22⋊C4D411yescharacteristic
115C32×C22⋊C4D411yescharacteristic
116C32×C42C2311yescharacteristic
117C32×C42C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×D24—22no—
138C3×D24—22no—
139C3×#204—22no—
140C3×#204—22no—
141#3118—31noSylow
142C22×C3×D4—31no—
143C22×D12C22×C311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C2×C3×D8—31no—
147C2×C3×D8—31no—
148C3×C4⋊Q8—31no—
149C3×#126—61no—
150C3×#124—31no—
151C3×#124—61no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C3×#121—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—61no—
163C3×C4×D4—61no—
164C3×#117—21no—
165C3×#117—31no—
166C3×#117C2×D311yescharacteristic
167C3×#117C22×C311yescharacteristic
168C2×C3×C22⋊C4—61no—
169C2×C3×C22⋊C4—61no—
170#930C22×C311yescharacteristic
171#926C22×C311yescharacteristic
172#924C22×C311yescharacteristic
173C2×D24C22×C311yescharacteristic
174C2×D24C22×C311yescharacteristic
175C2×#204C22×C311yescharacteristic
176C2×#204C22×C311yescharacteristic
177#898—21no—
178#896—21no—
179#893—21no—
180#893—21no—
181#885—21no—
182#883—21no—
183D3×C22⋊C4—21no—
184D3×C22⋊C4—21no—
185#875C22×C311yescharacteristic, complemented
186C4×D12C22×C311yescharacteristic
187C4×D12C22×C311yescharacteristic
188C4×D12C22×C311yescharacteristic
189C4×D12C22×C311yescharacteristic
190C4×D12C22×C311yescharacteristic, complemented
191#869C22×C311yescharacteristic, complemented
192C4×Dic6C22×C311yescharacteristic, complemented
193C3×#107—31no—
194C3×#107—31no—
195C3×#106—31no—
196C3×#106—31no—
197C3×C4⋊C8—21no—
198C3×C4⋊C8—21no—
199C3×C4⋊C8C2×D311yescharacteristic, complemented
200C3×C4⋊C8C2×D311yescharacteristic, complemented
201C3×C4⋊C8C22×C311yescharacteristic, complemented
202C3×C4⋊C8C22×C311yescharacteristic, complemented
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C22⋊C8—21no—
212C3×C22⋊C8—21no—
213C3×C22⋊C8C2×D311yescharacteristic
214C3×C22⋊C8C2×D311yescharacteristic
215C3×C22⋊C8C22×C311yescharacteristic
216C3×C22⋊C8C22×C311yescharacteristic
217C3×#97—21no—
218C3×#97C2×D311yescharacteristic, complemented
219C3×#97C22×C311yescharacteristic, complemented
220C3×C4×C8—21no—
221C3×C4×C8C2×D311yescharacteristic, complemented
222C3×C4×C8C22×C311yescharacteristic, complemented
223#821C22×C311yescharacteristic
224#821C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226#821C22×C311yescharacteristic
227#821C22×C311yescharacteristic, complemented
228#821C22×C311yescharacteristic, complemented
229#818C22×C311yescharacteristic, complemented
230#818C22×C311yescharacteristic, complemented
231#817C22×C311yescharacteristic, complemented
232#817C22×C311yescharacteristic, complemented
233#816C22×C311yescharacteristic, complemented
234#816C22×C311yescharacteristic, complemented
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C3×#67—81no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C3×D12—24no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12#4112yes—
262C3×D12#4112yes—
263C3×C4×D3—81no—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—81no—
271C32×C8—21no—
272C32×C8—21no—
273C32×C8—21no—
274C32×C8—21no—
275#542—31no—
276#518—31no—
277#485—31no—
278#482—31no—
279#476—31no—
280#474—31no—
281#463—31no—
282#463—31no—
283#450—31no—
284#447—31no—
285#442—31no—
286#440—31no—
287C4×SD16—31no—
288C4×D8—31no—
289#433C3×D311yescharacteristic, complemented
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—62no—
298C2×C3×D4—62no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C22×C3×C4—21no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C23×C311yescharacteristic
309C2×#67—21no—
310C2×D12—21no—
311C2×D12—22no—
312C2×D12—22no—
313C2×D12C23×C311yescharacteristic
314C2×D12C23×C311yescharacteristic
315C2×D12C23×C311yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×Dic6—21no—
322C2×Dic6C23×C311yescharacteristic
323C3×SD16—62no—
324C3×SD16—62no—
325C3×D8—62no—
326C3×D8—62no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C23×C311yescharacteristic
336C2×C3×C8C23×C311yescharacteristic
337C2×C3×C8C23×C311yescharacteristic
338C2×C3×C8C23×C311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4D1211yescharacteristic
349C3×C4⋊C4D1211yescharacteristic
350C3×C4⋊C4C3×D411yescharacteristic
351C3×C4⋊C4C3×D411yescharacteristic
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4D1211yescharacteristic
365C3×C22⋊C4D1211yescharacteristic
366C3×C22⋊C4C3×D411yescharacteristic
367C3×C22⋊C4C3×D411yescharacteristic
368C3×C42—21no—
369C3×C42—21no—
370C3×C42—61no—
371C3×C42—61no—
372C3×C42C22×D311yescharacteristic
373C3×C42C22×D311yescharacteristic
374C3×C42C23×C311yescharacteristic
375C3×C42C23×C311yescharacteristic
376#217—21no—
377#217—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386C4⋊Dic3—21no—
387C4⋊Dic3C23×C311yescharacteristic
388C4⋊Dic3C23×C311yescharacteristic
389C4⋊Dic3C23×C311yescharacteristic
390C4⋊Dic3C23×C311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395D24—22no—
396D24—22no—
397#204—22no—
398#204—22no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—84no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—31no—
426C2×SD16—31no—
427C2×SD16—31no—
428C2×D8—31no—
429C2×D8—31no—
430C4⋊Q8—31no—
431#126—61no—
432#124—31no—
433#124—61no—
434#123—61no—
435C22⋊Q8—31no—
436C22⋊Q8—61no—
437#121—31no—
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—31no—
444C4×D4—61no—
445C4×D4—61no—
446#117—31no—
447#117C2×C3×D311yescharacteristic
448C2×C22⋊C4—61no—
449C2×C22⋊C4—61no—
450#107—31no—
451#107—31no—
452#106—31no—
453#106—31no—
454C4⋊C8C2×C3×D311yescharacteristic, complemented
455C4⋊C8C2×C3×D311yescharacteristic, complemented
456#103—31no—
457#103—31no—
458#102—31no—
459#102—31no—
460#102—31no—
461#102—31no—
462#102—31no—
463#102—31no—
464C22⋊C8C2×C3×D311yescharacteristic
465C22⋊C8C2×C3×D311yescharacteristic
466#97C2×C3×D311yescharacteristic, complemented
467C4×C8C2×C3×D311yescharacteristic, complemented
468C23×C3—21no—
469C23×C3—64no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—241no—
474C23×C3—241no—
475C23×C3C2×D1211yescharacteristic
476C23×C3C2×C3×D411yescharacteristic
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—24no—
480C22×D3—21no—
481C22×D3—81no—
482C22×D3—81no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—241no—
486C3×D4—32no—
487C3×D4—32no—
488C3×D4—64no—
489C3×D4—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—241no—
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—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—241no—
512C2×C3×C4—241no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4C2×D1211yescharacteristic
517C2×C3×C4C2×D1211yescharacteristic
518C2×C3×C4C2×D1211yescharacteristic
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4C2×D1211yescharacteristic
521C2×C3×C4C2×C3×D411yescharacteristic
522C2×C3×C4C2×C3×D411yescharacteristic
523C2×C3×C4C2×C3×D411yescharacteristic
524C2×C3×C4C2×C3×D411yescharacteristic
525C2×C3×C4C2×C3×D411yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C24×C311yescharacteristic
528#67—81no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534D12—24no—
535D12—21no—
536D12—21no—
537D12—21no—
538D12—21no—
539D12C3×#4112yes—
540D12C3×#4112yes—
541C4×D3—81no—
542C4×D3—81no—
543C4×D3—81no—
544C4×D3—81no—
545C4×D3—81no—
546Dic6—21no—
547Dic6—21no—
548Dic6—81no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—41no—
558C3×C8—41no—
559C3×C8—41no—
560C3×C8—41no—
561C2×C32—41no—
562C2×C32#52511yescharacteristic
563C2×C32#57611yescharacteristic
564C2×C32#57711yescharacteristic
565C3×D3—42no—
566C3×D3—42no—
567C3×D3—81no—
568C24—61no—
569C2×Q8—31no—
570C2×Q8—61no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—62no—
575C2×D4—62no—
576C2×D4—61no—
577C2×D4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4C22×C3×D311yescharacteristic
584SD16—62no—
585SD16—62no—
586D8—62no—
587D8—62no—
588C2×C8C22×C3×D311yescharacteristic
589C2×C8C22×C3×D311yescharacteristic
590C2×C8C22×C3×D311yescharacteristic
591C2×C8C22×C3×D311yescharacteristic
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4C3×D1211yescharacteristic
600C4⋊C4C3×D1211yescharacteristic
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4C3×D1211yescharacteristic
612C22⋊C4C3×D1211yescharacteristic
613C42—61no—
614C42—61no—
615C42C22×C3×D311yescharacteristic
616C42C22×C3×D311yescharacteristic
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—62no—
628C22×C3—62no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—244no—
637C22×C3C22×D1211yescharacteristic
638C22×C3C22×C3×D411yescharacteristic
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—84no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4D3×#4111yescharacteristic
672C3×C4D3×#4111yescharacteristic
673C3×C4C2×C3×#4111yescharacteristic
674C3×C4C2×C3×#4111yescharacteristic
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680C32#311811yescharacteristic, complemented, Sylow
681C23—64no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—241no—
686C23—241no—
687C23C2×C3×D1211yescharacteristic
688Q8—61no—
689Q8—61no—
690Q8—241no—
691D4—32no—
692D4—32no—
693D4—64no—
694D4—61no—
695D4—61no—
696D4—61no—
697D4—61no—
698D4—241no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—241no—
707C2×C4—241no—
708C2×C4—241no—
709C2×C4—241no—
710C2×C4—241no—
711C2×C4C2×C3×D1211yescharacteristic
712C2×C4C2×C3×D1211yescharacteristic
713C2×C4C2×C3×D1211yescharacteristic
714C2×C4C2×C3×D1211yescharacteristic
715C2×C4C2×C3×D1211yescharacteristic
716C2×C4C23×C3×D311yescharacteristic
717C8—21no—
718C8—21no—
719C8—21no—
720C8—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—41no—
725C2×C3—41no—
726C2×C3—81no—
727C2×C3—122no—
728C2×C3—122no—
729C2×C3—241no—
730C2×C3#552411yescharacteristic
731C2×C3#575111yescharacteristic
732C2×C3#575211yescharacteristic
733C2×C3C3×#52511yescharacteristic
734C2×C3C3×#57611yescharacteristic
735C2×C3C3×#57711yescharacteristic
736D3—42no—
737D3—42no—
738D3—81no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—62no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—244no—
752C22C22×C3×D1211yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—121no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—121no—
763C4C3×D3×#4111yescharacteristic
764C4C3×D3×#4111yescharacteristic
765C3—21no—
766C3#7938311yescharacteristic, direct product factor
767C3C3×#311811yescharacteristic, complemented
768C2—41no—
769C2—122no—
770C2—122no—
771C2—241no—
772C2C3×#552411yescharacteristic
773C2C3×#575111yescharacteristic
774C2C3×#575211yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#433C2
socleC22×C32C22×D4
prime radicalC3×#4732C2
hypercenterC3×#433D3
hypocenterC3C3×#3118
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#433

Complements

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

NH ≅ G/Ntype
1. C3×#5534C2semidirect
2. C3×#5521C2semidirect
3. C32×#433C2semidirect
4. C3×#4846C2semidirect
5. C3×#4844C2semidirect
6. C3×#4844C2semidirect
7. C3×#4842C2semidirect
8. C3×#4737C2semidirect
10. C3×#4731C2semidirect
11. C3×#4723C2semidirect
12. C3×#4711C2semidirect
13. C3×#4710C2semidirect
14. C3×C4×D24C2semidirect
15. C3×C4×#204C2semidirect
17. #79383C3direct (N × H)
35. C3×#875C22semidirect
40. C3×C4×D12C22semidirect
41. C3×#869C22semidirect
42. C3×C4×Dic6C22semidirect
43. C32×C4⋊C8C22semidirect
44. C32×C4⋊C8C22semidirect
47. C32×#97C22semidirect
48. C32×C4×C8C22semidirect
53. C3×#821C22semidirect
54. C3×#821C22semidirect
55. C3×#818C22semidirect
56. C3×#818C22semidirect
57. C3×#817C22semidirect
58. C3×#817C22semidirect
59. C3×#816C22semidirect
60. C3×#816C22semidirect
63. #5534C2×C3semidirect
64. #5521C2×C3semidirect
78. C3×#433D3semidirect
79. C3×#433C2×C3semidirect
80. #4846C2×C3semidirect
81. #4844C2×C3semidirect
82. #4844C2×C3semidirect
83. #4842C2×C3semidirect
84. #4737C2×C3semidirect
86. #4731C2×C3semidirect
87. #4723C2×C3semidirect
88. #4711C2×C3semidirect
89. #4710C2×C3semidirect
90. C4×D24C2×C3semidirect
91. C4×#204C2×C3semidirect
185. #875C22×C3semidirect
190. C4×D12C22×C3semidirect
191. #869C22×C3semidirect
192. C4×Dic6C22×C3semidirect
199. C3×C4⋊C8C2×D3semidirect
200. C3×C4⋊C8C2×D3semidirect
201. C3×C4⋊C8C22×C3semidirect
202. C3×C4⋊C8C22×C3semidirect
218. C3×#97C2×D3semidirect
219. C3×#97C22×C3semidirect
221. C3×C4×C8C2×D3semidirect
222. C3×C4×C8C22×C3semidirect
227. #821C22×C3semidirect
228. #821C22×C3semidirect
229. #818C22×C3semidirect
230. #818C22×C3semidirect
231. #817C22×C3semidirect
232. #817C22×C3semidirect
233. #816C22×C3semidirect
234. #816C22×C3semidirect
289. #433C3×D3semidirect
454. C4⋊C8C2×C3×D3semidirect
455. C4⋊C8C2×C3×D3semidirect
466. #97C2×C3×D3semidirect
467. C4×C8C2×C3×D3semidirect
680. C32#3118semidirect
766. C3#79383direct (N × H)
767. C3C3×#3118semidirect

Maximal subgroups

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

subgroupindex
C3×#55342
C3×#55212
C32×#4332
C3×#48462
C3×#48442
C3×#48422
C3×#47372
C3×#47322
C3×#47312
C3×#47232
C3×#47112
C3×#47102
C3×C4×D242
C3×C4×#2042
C3×#31183
#793833