Finite Group Databasebeta

← C3×#79835 #11872576

Subgroups — C3×#79835 #11872576

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5582C211yesmaximal, characteristic
2C3×#5572C211yesmaximal, characteristic, complemented
3C32×#441C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic, complemented
5C3×#5185C211yesmaximal, characteristic, complemented
6C3×C4×#216C211yesmaximal, characteristic, complemented
7C3×C4×#215C211yesmaximal, characteristic, complemented
8C3×#4866C211yesmaximal, characteristic
9C3×#4854C211yesmaximal, characteristic, complemented
10C3×#4814C211yesmaximal, characteristic, complemented
11C3×#4806C211yesmaximal, characteristic
12C3×#4798C211yesmaximal, characteristic, complemented
13C3×#4793C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4709C211yesmaximal, characteristic, complemented
16C3×#3121—31nomaximal
17#79835C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C3×#896—21no—
29C3×#895C2211yescharacteristic
30C3×#894—21no—
31C3×#892—21no—
32C3×#892C2211yescharacteristic
33C3×#888C2211yescharacteristic
34C3×#887—21no—
35C3×#887C2211yescharacteristic
36C3×#876—21no—
37C3×#875—21no—
38C3×C4×D12C2211yescharacteristic
39C3×#872—21no—
40C3×#872C2211yescharacteristic
41C3×C4×Dic6—21no—
42C3×C4×Dic6C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#97C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
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×#807C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#542—31no—
62C3×#519—31no—
63#5582C2×C311yescharacteristic
64#5572C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#477—31no—
68C3×#475—31no—
69C3×#464—31no—
70C3×#464—31no—
71C3×#451—31no—
72C3×#448—31no—
73C3×#441—21no—
74C3×#441D311yescharacteristic, complemented
75C3×#441C2×C311yescharacteristic, complemented
76C3×#440—31no—
77C3×C4×Q16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5186C2×C311yescharacteristic, complemented
81#5185C2×C311yescharacteristic, complemented
82C4×#216C2×C311yescharacteristic, complemented
83C4×#215C2×C311yescharacteristic, complemented
84#4866C2×C311yescharacteristic
85#4854C2×C311yescharacteristic, complemented
86#4814C2×C311yescharacteristic, complemented
87#4806C2×C311yescharacteristic
88#4798C2×C311yescharacteristic, complemented
89#4793C2×C311yescharacteristic, complemented
90#4710C2×C311yescharacteristic, complemented
91#4709C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C32×Q16—22no—
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C42—21no—
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114C3×#216—22no—
115C3×#215—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
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⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
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#3121—31noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C22×C311yescharacteristic
144C2×C3×Q16—21no—
145C2×C3×Q16—31no—
146C2×C3×Q16C2×D311yescharacteristic
147C2×C3×Q16C22×C311yescharacteristic
148C2×C3×SD16—31no—
149C2×C3×SD16—31no—
150C3×C4⋊Q8—31no—
151C3×#126—61no—
152C3×#124—31no—
153C3×#124—61no—
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—61no—
157C3×#121—31no—
158C3×C4×Q8—21no—
159C3×C4×Q8—21no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—61no—
164C3×C4×Q8—61no—
165C3×C4×Q8C2×D311yescharacteristic
166C3×C4×Q8C2×D311yescharacteristic
167C3×C4×Q8C22×C311yescharacteristic
168C3×C4×Q8C22×C311yescharacteristic
169C3×C4×D4—31no—
170C3×#117—31no—
171C3×#117—31no—
172C3×#117—61no—
173C3×#117—61no—
174#947C22×C311yescharacteristic
175#946C22×C311yescharacteristic
176Q8×Dic3C22×C311yescharacteristic
177C2×#216C22×C311yescharacteristic
178C2×#215C22×C311yescharacteristic
179C2×#204C22×C311yescharacteristic
180#896—21no—
181#895C22×C311yescharacteristic
182#894—21no—
183#892—21no—
184#892C22×C311yescharacteristic
185#888C22×C311yescharacteristic
186#887—21no—
187#887C22×C311yescharacteristic
188#876—21no—
189#875—21no—
190C4×D12C22×C311yescharacteristic
191#872—21no—
192#872C22×C311yescharacteristic
193C4×Dic6—21no—
194C4×Dic6C22×C311yescharacteristic
195C3×#107—31no—
196C3×#107—31no—
197C3×#106—21no—
198C3×#106—31no—
199C3×#106C2×D311yescharacteristic
200C3×#106C22×C311yescharacteristic
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—21no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103C2×D311yescharacteristic
210C3×#103C2×D311yescharacteristic
211C3×#103C22×C311yescharacteristic
212C3×#103C22×C311yescharacteristic
213C3×#102—31no—
214C3×#102—31no—
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#835C22×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#807C22×C311yescharacteristic
234C4×C3⋊C8C22×C311yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3C2×D411yescharacteristic
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8—21no—
240C32×Q8#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—81no—
257C3×C4×D3—24no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—81no—
261C3×Dic6—24no—
262C3×Dic6—21no—
263C3×Dic6—81no—
264C3×Dic6#4112yes—
265C32×C8—21no—
266C32×C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#542—31no—
270#519—31no—
271#485—31no—
272#482—31no—
273#477—31no—
274#475—31no—
275#464—31no—
276#464—31no—
277#451—31no—
278#448—31no—
279#441C3×D311yescharacteristic, complemented
280#440—31no—
281C4×Q16—31no—
282C4×SD16—31no—
283#433—31no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8—31no—
287C2×C3×Q8—61no—
288C2×C3×Q8—61no—
289C2×C3×Q8—62no—
290C2×C3×Q8—62no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C2×C3×Q8C23×C311yescharacteristic
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300D3×Q8—22no—
301D3×Q8—22no—
302C2×D12—21no—
303C2×D12C23×C311yescharacteristic
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3C23×C311yescharacteristic
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6C23×C311yescharacteristic
310C3×Q16—24no—
311C3×Q16—22no—
312C3×Q16—22no—
313C3×Q16—62no—
314C3×SD16—62no—
315C3×SD16—62no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—31no—
319C2×C3×C8—31no—
320C2×C3×C8C22×D311yescharacteristic
321C2×C3×C8C22×D311yescharacteristic
322C2×C3×C8C23×C311yescharacteristic
323C2×C3×C8C23×C311yescharacteristic
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—41no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C4⋊C4C23×C311yescharacteristic
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—21no—
356C3×C42—21no—
357C3×C42—21no—
358C3×C42—31no—
359C3×C42—41no—
360C3×C42—41no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42—61no—
365C3×C42C22×D311yescharacteristic
366C3×C42C23×C311yescharacteristic
367#216—22no—
368#215—22no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4C3×D411yescharacteristic
376(C2×D3)⋊C4C3×D411yescharacteristic
377C4⋊Dic3—21no—
378C4⋊Dic3C23×C311yescharacteristic
379C4⋊Dic3C23×C311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4C3×D411yescharacteristic
385Dic3⋊C4C3×D411yescharacteristic
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3C23×C311yescharacteristic
391C2×C3⋊C8C23×C311yescharacteristic
392C2×C3⋊C8C23×C311yescharacteristic
393#204—22no—
394C22×C32C22×D411yescharacteristic
395C2×C3×D3—21no—
396C2×C3×D3—21no—
397C2×C3×D3—21no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C32×C4—22no—
402C32×C4—21no—
403C32×C4—21no—
404C32×C4—41no—
405C32×C4—41no—
406C32×C4—41no—
407C32×C4C2×#4111yescharacteristic
408C32×C4C2×#4111yescharacteristic
409C3×Dic3—21no—
410C3×Dic3—22no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C22×Q8—31no—
416C2×Q16—31no—
417C2×Q16C2×C3×D311yescharacteristic
418C2×SD16—31no—
419C2×SD16—31no—
420C4⋊Q8—31no—
421#126—61no—
422#124—31no—
423#124—61no—
424#123—61no—
425C22⋊Q8—31no—
426C22⋊Q8—61no—
427#121—31no—
428C4×Q8—31no—
429C4×Q8—31no—
430C4×Q8—31no—
431C4×Q8—61no—
432C4×Q8—61no—
433C4×Q8C2×C3×D311yescharacteristic
434C4×Q8C2×C3×D311yescharacteristic
435C4×D4—31no—
436#117—31no—
437#117—31no—
438#117—61no—
439#117—61no—
440#107—31no—
441#107—31no—
442#106—31no—
443#106C2×C3×D311yescharacteristic
444C4⋊C8—31no—
445C4⋊C8—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103—31no—
450#103C2×C3×D311yescharacteristic
451#103C2×C3×D311yescharacteristic
452#102—31no—
453#102—31no—
454C22⋊C8—31no—
455C22⋊C8—31no—
456#97C2×C3×D311yescharacteristic
457C4×C8—31no—
458C23×C3—31no—
459C23×C3—61no—
460C22×D3—21no—
461C22×D3C2×C3×D411yescharacteristic
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—22no—
465C3×Q8—21no—
466C3×Q8—21no—
467C3×Q8—21no—
468C3×Q8—21no—
469C3×Q8—22no—
470C3×Q8—32no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—64no—
474C3×Q8—61no—
475C3×Q8—241no—
476C3×Q8#23512yes—
477C3×Q8C3×#4112yes—
478C3×D4—61no—
479C3×D4—61no—
480C3×D4—241no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—64no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—241no—
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4C2×C3×D411yescharacteristic
509C2×C3×C4C2×C3×D411yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C24×C311yescharacteristic
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3C2×C3×D411yescharacteristic
516C2×Dic3C2×C3×D411yescharacteristic
517C2×Dic3C2×C3×D411yescharacteristic
518D12—21no—
519D12—21no—
520D12—81no—
521C4×D3—24no—
522C4×D3—21no—
523C4×D3—21no—
524C4×D3—81no—
525Dic6—24no—
526Dic6—21no—
527Dic6—81no—
528Dic6C3×#4112yes—
529C3×C8—22no—
530C3×C8—21no—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—41no—
535C3×C8—61no—
536C3×C8—61no—
537C3⋊C8—21no—
538C3⋊C8—21no—
539C2×C32#52511yescharacteristic
540C2×C32#57711yescharacteristic
541C2×C32#57811yescharacteristic
542C3×D3—41no—
543C3×D3—81no—
544C2×Q8—31no—
545C2×Q8—61no—
546C2×Q8—61no—
547C2×Q8—62no—
548C2×Q8—62no—
549C2×Q8C22×C3×D311yescharacteristic
550C2×Q8C22×C3×D311yescharacteristic
551C2×D4—31no—
552C2×D4—61no—
553C22×C4—31no—
554C22×C4—61no—
555C22×C4—61no—
556Q16—22no—
557Q16—62no—
558SD16—62no—
559SD16—62no—
560C2×C8—31no—
561C2×C8—31no—
562C2×C8C22×C3×D311yescharacteristic
563C2×C8C22×C3×D311yescharacteristic
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4C22×C3×D311yescharacteristic
576C4⋊C4C22×C3×D311yescharacteristic
577C22⋊C4—31no—
578C22⋊C4—31no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C22⋊C4—61no—
582C22⋊C4—61no—
583C22⋊C4—61no—
584C22⋊C4—61no—
585C42—21no—
586C42—21no—
587C42—31no—
588C42—61no—
589C42—61no—
590C42—61no—
591C42—61no—
592C42C22×C3×D311yescharacteristic
593C22×C3—21no—
594C22×C3—61no—
595C22×C3—61no—
596C22×C3—61no—
597C22×C3—121no—
598C22×C3—121no—
599C22×C3—121no—
600C22×C3C2×D3×D411yescharacteristic
601C22×C3C22×C3×D411yescharacteristic
602C2×D3—21no—
603C2×D3—21no—
604C2×D3—21no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—41no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—22no—
613C3×C4—22no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—61no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—62no—
630C3×C4—81no—
631C3×C4—81no—
632C3×C4—121no—
633C3×C4—121no—
634C3×C4C2×#23511yescharacteristic
635C3×C4D3×#4111yescharacteristic
636C3×C4C2×C3×#4111yescharacteristic
637C3×C4C2×C3×#4111yescharacteristic
638Dic3—21no—
639Dic3—21no—
640Dic3—21no—
641Dic3—22no—
642Dic3—41no—
643Dic3—41no—
644C32#312111yescharacteristic, complemented, Sylow
645C23—31no—
646C23—61no—
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—32no—
651Q8—64no—
652Q8—61no—
653Q8—241no—
654Q8C3×#23512yes—
655D4—61no—
656D4—61no—
657D4—241no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—64no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—241no—
672C2×C4C3×D3×D411yescharacteristic
673C2×C4C3×D3×D411yescharacteristic
674C2×C4C23×C3×D311yescharacteristic
675C8—21no—
676C8—21no—
677C8—61no—
678C8—61no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—121no—
683C2×C3—241no—
684C2×C3#554711yescharacteristic
685C2×C3#577811yescharacteristic
686C2×C3#577911yescharacteristic
687C2×C3C3×#52511yescharacteristic
688C2×C3C3×#57711yescharacteristic
689C2×C3C3×#57811yescharacteristic
690D3—41no—
691D3—81no—
692C22—61no—
693C22—61no—
694C22—61no—
695C22—121no—
696C22—121no—
697C22—121no—
698C22C2×C3×D3×D411yescharacteristic
699C4—21no—
700C4—21no—
701C4—22no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—61no—
706C4—61no—
707C4—61no—
708C4—62no—
709C4—121no—
710C4—121no—
711C4C2×C3×#23511yescharacteristic
712C4C3×D3×#4111yescharacteristic
713C3—21no—
714C3#7983511yescharacteristic, direct product factor
715C3C3×#312111yescharacteristic, complemented
716C2—121no—
717C2—241no—
718C2C3×#554711yescharacteristic
719C2C3×#577811yescharacteristic
720C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radicalC3×#895C22
hypercenterC3×#441D3
hypocenterC3C3×#3121
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#441

Complements

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

NH ≅ G/Ntype
2. C3×#5572C2semidirect
3. C32×#441C2semidirect
4. C3×#5186C2semidirect
5. C3×#5185C2semidirect
6. C3×C4×#216C2semidirect
7. C3×C4×#215C2semidirect
9. C3×#4854C2semidirect
10. C3×#4814C2semidirect
12. C3×#4798C2semidirect
13. C3×#4793C2semidirect
14. C3×#4710C2semidirect
15. C3×#4709C2semidirect
17. #79835C3direct (N × H)
64. #5572C2×C3semidirect
74. C3×#441D3semidirect
75. C3×#441C2×C3semidirect
80. #5186C2×C3semidirect
81. #5185C2×C3semidirect
82. C4×#216C2×C3semidirect
83. C4×#215C2×C3semidirect
85. #4854C2×C3semidirect
86. #4814C2×C3semidirect
88. #4798C2×C3semidirect
89. #4793C2×C3semidirect
90. #4710C2×C3semidirect
91. #4709C2×C3semidirect
279. #441C3×D3semidirect
644. C32#3121semidirect
714. C3#79835direct (N × H)
715. C3C3×#3121semidirect

Maximal subgroups

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

subgroupindex
C3×#55822
C3×#55722
C32×#4412
C3×#51862
C3×#51852
C3×C4×#2162
C3×C4×#2152
C3×#48662
C3×#48542
C3×#48142
C3×#48062
C3×#47982
C3×#47932
C3×#47102
C3×#47092
C3×#31213
#798353