Finite Group Databasebeta

← C3×#79657 #11872398

Subgroups — C3×#79657 #11872398

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5583C211yesmaximal, characteristic, complemented
2C3×#5546C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5173C211yesmaximal, characteristic
5C3×#5162C211yesmaximal, characteristic, complemented
6C3×#5030C211yesmaximal, characteristic, complemented
7C3×#5018C211yesmaximal, characteristic, complemented
8C3×#4862C211yesmaximal, characteristic, complemented
9C3×#4857C211yesmaximal, characteristic, complemented
10C3×#4811C211yesmaximal, characteristic, complemented
11C3×#4795C211yesmaximal, characteristic, complemented
12C3×#4783C211yesmaximal, characteristic
13C3×#4766C211yesmaximal, characteristic, complemented
14C3×C4×Dic12C211yesmaximal, characteristic, complemented
15C3×#4690C211yesmaximal, characteristic, complemented
16C3×#3120—31nomaximal
17#79657C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×C4×#67—21no—
28C2×C3×Dic3⋊C4—21no—
29C2×C3×Dic12C2211yescharacteristic
30C3×#898—21no—
31C3×#897C2211yescharacteristic
32C3×D3×C4⋊C4C2211yescharacteristic
33C3×#890C2211yescharacteristic
34C3×#889—21no—
35C3×#887C2211yescharacteristic
36C3×#67⋊C4—21no—
37C3×#877—21no—
38C3×#876—21no—
39C3×#872C2211yescharacteristic
40C3×#870—21no—
41C3×C4×Dic6C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C4×C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#541—31no—
62C3×#520—31no—
63#5583C2×C311yescharacteristic, complemented
64#5546C2×C311yescharacteristic
65C3×#484—31no—
66C3×#483—31no—
67C3×#479—31no—
68C3×#478—31no—
69C3×#462—31no—
70C3×#461—31no—
71C3×#452—31no—
72C3×#452—31no—
73C3×#441—31no—
74C3×#440—31no—
75C3×C4×Q16—31no—
76C3×C4×SD16—21no—
77C3×C4×SD16D311yescharacteristic, complemented
78C3×C4×SD16C2×C311yescharacteristic, complemented
79C3×#433—31no—
80#5173C2×C311yescharacteristic
81#5162C2×C311yescharacteristic, complemented
82#5030C2×C311yescharacteristic, complemented
83#5018C2×C311yescharacteristic, complemented
84#4862C2×C311yescharacteristic, complemented
85#4857C2×C311yescharacteristic, complemented
86#4811C2×C311yescharacteristic, complemented
87#4795C2×C311yescharacteristic, complemented
88#4783C2×C311yescharacteristic
89#4766C2×C311yescharacteristic, complemented
90C4×Dic12C2×C311yescharacteristic, complemented
91#4690C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C3×#237—22no—
99C3×#237—22no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C32×SD16—22no—
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C42—21no—
112C32×C42C2311yescharacteristic
113C3×#217—21no—
114C3×#216—22no—
115C3×#214—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4D411yescharacteristic
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×Dic12—22no—
141#3120—31noSylow
142C2×C3×#41—31no—
143C2×#237C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C2×C3×SD16—21no—
147C2×C3×SD16—31no—
148C2×C3×SD16C2×D311yescharacteristic
149C2×C3×SD16C22×C311yescharacteristic
150C3×C4⋊Q8—31no—
151C3×#126—61no—
152C3×#126—61no—
153C3×#125—31no—
154C3×#125—61no—
155C3×#125—61no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—21no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8C2×D311yescharacteristic
163C3×C4×Q8C22×C311yescharacteristic
164C3×C4×D4—21no—
165C3×C4×D4—31no—
166C3×C4×D4—61no—
167C3×C4×D4—61no—
168C3×C4×D4C2×D311yescharacteristic
169C3×C4×D4C22×C311yescharacteristic
170C3×#117—31no—
171C3×#117—61no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—61no—
174#946C22×C311yescharacteristic
175#944C22×C311yescharacteristic
176C2×#216C22×C311yescharacteristic
177D4×Dic3C22×C311yescharacteristic
178C2×#214C22×C311yescharacteristic
179C4×#67—21no—
180C2×Dic3⋊C4—21no—
181C2×Dic12C22×C311yescharacteristic
182#898—21no—
183#897C22×C311yescharacteristic
184D3×C4⋊C4C22×C311yescharacteristic
185#890C22×C311yescharacteristic
186#889—21no—
187#887C22×C311yescharacteristic
188#67⋊C4—21no—
189#877—21no—
190#876—21no—
191#872C22×C311yescharacteristic
192#870—21no—
193C4×Dic6C22×C311yescharacteristic
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—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103C2×D311yescharacteristic
210C3×#103C22×C311yescharacteristic
211C3×#102—21no—
212C3×#102—31no—
213C3×#102C2×D311yescharacteristic
214C3×#102C22×C311yescharacteristic
215C3×C22⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×#97—31no—
218C3×C4×C8—21no—
219C3×C4×C8C2×D311yescharacteristic
220C3×C4×C8C22×C311yescharacteristic
221#835C22×C311yescharacteristic
222#832C22×C311yescharacteristic
223(C2×D3)⋊C8C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225#818C22×C311yescharacteristic
226#816C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234#803C22×C311yescharacteristic
235C23×C32—21no—
236C22×C3×D3C2×D411yescharacteristic
237C32×Q8—21no—
238C32×Q8—21no—
239C32×D4—21no—
240C32×D4#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C3×#67—24no—
249C2×C3×Dic3—24no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—81no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6#4112yes—
265C32×C8—21no—
266C32×C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#541—31no—
270#520—31no—
271#484—31no—
272#483—31no—
273#479—31no—
274#478—31no—
275#462—31no—
276#461—31no—
277#452—31no—
278#452—31no—
279#441—31no—
280#440—31no—
281C4×Q16—31no—
282C4×SD16C3×D311yescharacteristic, complemented
283#433—31no—
284C3×#41—62no—
285C3×#41—62no—
286C2×C3×Q8—21no—
287C2×C3×Q8—31no—
288C2×C3×Q8—31no—
289C2×C3×Q8C22×D311yescharacteristic
290C2×C3×Q8C23×C311yescharacteristic
291C2×C3×D4—21no—
292C2×C3×D4—61no—
293C2×C3×D4C22×D311yescharacteristic
294C2×C3×D4C23×C311yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—31no—
298C22×C3×C4—41no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305#237—22no—
306#237—22no—
307C2×C4×D3—21no—
308C2×C4×D3C23×C311yescharacteristic
309C2×Dic6C23×C311yescharacteristic
310C2×Dic6C23×C311yescharacteristic
311C3×Q16—62no—
312C3×Q16—62no—
313C3×SD16—24no—
314C3×SD16—22no—
315C3×SD16—22no—
316C3×SD16—62no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—31no—
320C2×C3×C8—31no—
321C2×C3×C8C22×D311yescharacteristic
322C2×C3×C8C22×D311yescharacteristic
323C2×C3×C8C23×C311yescharacteristic
324C2×C3×C8C23×C311yescharacteristic
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—41no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C23×C311yescharacteristic
347C3×C4⋊C4C23×C311yescharacteristic
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—41no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—21no—
357C3×C42—21no—
358C3×C42—21no—
359C3×C42—31no—
360C3×C42—41no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42C22×D311yescharacteristic
365C3×C42C23×C311yescharacteristic
366#217—21no—
367#216—22no—
368#214—22no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4C3×D411yescharacteristic
372(C2×D3)⋊C4C3×D411yescharacteristic
373C4⋊Dic3—21no—
374C4⋊Dic3—21no—
375C4⋊Dic3C23×C311yescharacteristic
376C4⋊Dic3C23×C311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4C3×D411yescharacteristic
386Dic3⋊C4C3×D411yescharacteristic
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3C23×C311yescharacteristic
391C2×C3⋊C8C23×C311yescharacteristic
392C2×C3⋊C8C23×C311yescharacteristic
393Dic12—22no—
394C22×C32—22no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C32×C4—21no—
402C32×C4—21no—
403C32×C4—41no—
404C32×C4—41no—
405C32×C4—41no—
406C32×C4C2×#4111yescharacteristic
407C32×C4C2×#4111yescharacteristic
408C3×Dic3—22no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C2×#41—31no—
416C2×Q16—31no—
417C2×Q16—31no—
418C2×SD16—31no—
419C2×SD16C2×C3×D311yescharacteristic
420C4⋊Q8—31no—
421#126—61no—
422#126—61no—
423#125—31no—
424#125—61no—
425#125—61no—
426C22⋊Q8—31no—
427C22⋊Q8—31no—
428C4×Q8—31no—
429C4×Q8—31no—
430C4×Q8—31no—
431C4×Q8C2×C3×D311yescharacteristic
432C4×D4—31no—
433C4×D4—61no—
434C4×D4—61no—
435C4×D4C2×C3×D311yescharacteristic
436#117—31no—
437#117—61no—
438C2×C4⋊C4—31no—
439C2×C4⋊C4—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#103—31no—
451#103C2×C3×D311yescharacteristic
452#102—31no—
453#102C2×C3×D311yescharacteristic
454C22⋊C8—31no—
455C22⋊C8—31no—
456#97—31no—
457C4×C8C2×C3×D311yescharacteristic
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—31no—
461C23×C3—41no—
462C22×D3C2×C3×D411yescharacteristic
463C3×Q8—22no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—21no—
467C3×Q8—21no—
468C3×Q8—32no—
469C3×Q8—41no—
470C3×Q8—61no—
471C3×Q8—61no—
472C3×Q8—61no—
473C3×D4—21no—
474C3×D4—21no—
475C3×D4—22no—
476C3×D4—41no—
477C3×D4—64no—
478C3×D4#23512yes—
479C3×D4C3×#4112yes—
480C2×C3×C4—21no—
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—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—64no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—81no—
503C2×C3×C4—81no—
504C2×C3×C4—82no—
505C2×C3×C4—241no—
506C2×C3×C4—241no—
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4C2×C3×D411yescharacteristic
510C2×C3×C4C2×C3×D411yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C24×C311yescharacteristic
513#67—24no—
514C2×Dic3—24no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—81no—
520C2×Dic3C2×C3×D411yescharacteristic
521C2×Dic3C2×C3×D411yescharacteristic
522C2×Dic3C2×C3×D411yescharacteristic
523C4×D3—21no—
524C4×D3—21no—
525C4×D3—81no—
526Dic6—21no—
527Dic6—21no—
528Dic6—21no—
529Dic6C3×#4112yes—
530C3×C8—22no—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—21no—
535C3×C8—41no—
536C3×C8—61no—
537C3×C8—61no—
538C3⋊C8—21no—
539C3⋊C8—21no—
540C2×C32—42no—
541C2×C32#52511yescharacteristic
542C2×C32#57711yescharacteristic
543C2×C32#57811yescharacteristic
544C3×D3—41no—
545#41—62no—
546#41—62no—
547C2×Q8—31no—
548C2×Q8—31no—
549C2×Q8C22×C3×D311yescharacteristic
550C2×D4—61no—
551C2×D4C22×C3×D311yescharacteristic
552C22×C4—21no—
553C22×C4—31no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557Q16—62no—
558Q16—62no—
559SD16—22no—
560SD16—62no—
561C2×C8—31no—
562C2×C8—31no—
563C2×C8C22×C3×D311yescharacteristic
564C2×C8C22×C3×D311yescharacteristic
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⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4C22×C3×D311yescharacteristic
581C4⋊C4C22×C3×D311yescharacteristic
582C22⋊C4—21no—
583C22⋊C4—31no—
584C22⋊C4—31no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C22⋊C4—61no—
588C42—21no—
589C42—31no—
590C42—61no—
591C42—61no—
592C42—61no—
593C42C22×C3×D311yescharacteristic
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—21no—
597C22×C3—42no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3—61no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3C2×D3×D411yescharacteristic
608C22×C3C22×C3×D411yescharacteristic
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—21no—
612C3×C4—22no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—41no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—61no—
630C3×C4—62no—
631C3×C4—81no—
632C3×C4—81no—
633C3×C4—121no—
634C3×C4—121no—
635C3×C4—121no—
636C3×C4C2×#23511yescharacteristic
637C3×C4D3×#4111yescharacteristic
638C3×C4C2×C3×#4111yescharacteristic
639C3×C4C2×C3×#4111yescharacteristic
640Dic3—21no—
641Dic3—21no—
642Dic3—22no—
643Dic3—21no—
644Dic3—41no—
645Dic3—41no—
646Dic3—41no—
647C32#312011yescharacteristic, complemented, Sylow
648C23—21no—
649C23—31no—
650Q8—21no—
651Q8—21no—
652Q8—32no—
653Q8—61no—
654Q8—61no—
655Q8—61no—
656D4—21no—
657D4—64no—
658D4C3×#23512yes—
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—61no—
672C2×C4—81no—
673C2×C4—241no—
674C2×C4—241no—
675C2×C4C3×D3×D411yescharacteristic
676C2×C4C3×D3×D411yescharacteristic
677C2×C4C23×C3×D311yescharacteristic
678C8—21no—
679C8—21no—
680C8—61no—
681C8—61no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—42no—
686C2×C3—42no—
687C2×C3—82no—
688C2×C3—121no—
689C2×C3#554711yescharacteristic
690C2×C3#576211yescharacteristic
691C2×C3#577111yescharacteristic
692C2×C3C3×#52511yescharacteristic
693C2×C3C3×#57711yescharacteristic
694C2×C3C3×#57811yescharacteristic
695D3—41no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—61no—
700C22—61no—
701C22—61no—
702C22C2×C3×D3×D411yescharacteristic
703C4—21no—
704C4—21no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—61no—
709C4—61no—
710C4—61no—
711C4—62no—
712C4—121no—
713C4—121no—
714C4—121no—
715C4C2×C3×#23511yescharacteristic
716C4C3×D3×#4111yescharacteristic
717C3—21no—
718C3#7965711yescharacteristic, direct product factor
719C3C3×#312011yescharacteristic, complemented
720C2—42no—
721C2—121no—
722C2C3×#554711yescharacteristic
723C2C3×#576211yescharacteristic
724C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×C3×#237C22
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3120
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C3×#5583C2semidirect
3. C32×C4×SD16C2semidirect
5. C3×#5162C2semidirect
6. C3×#5030C2semidirect
7. C3×#5018C2semidirect
8. C3×#4862C2semidirect
9. C3×#4857C2semidirect
10. C3×#4811C2semidirect
11. C3×#4795C2semidirect
13. C3×#4766C2semidirect
14. C3×C4×Dic12C2semidirect
15. C3×#4690C2semidirect
17. #79657C3direct (N × H)
63. #5583C2×C3semidirect
77. C3×C4×SD16D3semidirect
78. C3×C4×SD16C2×C3semidirect
81. #5162C2×C3semidirect
82. #5030C2×C3semidirect
83. #5018C2×C3semidirect
84. #4862C2×C3semidirect
85. #4857C2×C3semidirect
86. #4811C2×C3semidirect
87. #4795C2×C3semidirect
89. #4766C2×C3semidirect
90. C4×Dic12C2×C3semidirect
91. #4690C2×C3semidirect
282. C4×SD16C3×D3semidirect
647. C32#3120semidirect
718. C3#79657direct (N × H)
719. C3C3×#3120semidirect

Maximal subgroups

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

subgroupindex
C3×#55832
C3×#55462
C32×C4×SD162
C3×#51732
C3×#51622
C3×#50302
C3×#50182
C3×#48622
C3×#48572
C3×#48112
C3×#47952
C3×#47832
C3×#47662
C3×C4×Dic122
C3×#46902
C3×#31203
#796573