Finite Group Databasebeta

← C3×#81499 #11873269

Subgroups — C3×#81499 #11873269

Order 1152.

764 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5625C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic
3C32×#485C211yesmaximal, characteristic
4C3×#5050C211yesmaximal, characteristic
5C3×#4996C211yesmaximal, characteristic
6C3×#4877C211yesmaximal, characteristic, complemented
7C3×#4873C211yesmaximal, characteristic, complemented
8C3×#4857C211yesmaximal, characteristic, complemented
9C3×#4853C211yesmaximal, characteristic, complemented
10C3×#4795C211yesmaximal, characteristic, complemented
11C3×#4795C211yesmaximal, characteristic, complemented
12C3×#4790C211yesmaximal, characteristic, complemented
13C3×#4789C211yesmaximal, characteristic, complemented
14C3×#4739C211yesmaximal, characteristic
15C3×#4720C211yesmaximal, characteristic
16C3×#3127—31nomaximal
17#81499C311yesmaximal, characteristic, direct product factor
18C22×C3×Dic6C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C32×#117C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic
28C2×C3×Dic12C2211yescharacteristic
29C3×#890—21no—
30C3×#890C2211yescharacteristic
31C3×#889—21no—
32C3×#887C2211yescharacteristic
33C3×#887C2211yescharacteristic
34C3×#887C2211yescharacteristic
35C3×#887C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×#879—21no—
38C3×#879—21no—
39C3×#877—21no—
40C3×#877—21no—
41C3×C4×Dic6—21no—
42C3×C4×Dic6—21no—
43C32×#107C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#815C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#541—31no—
62C3×#519—31no—
63#5625C2×C311yescharacteristic
64#5516C2×C311yescharacteristic
65C3×#485—21no—
66C3×#485—31no—
67C3×#485D311yescharacteristic
68C3×#485C2×C311yescharacteristic
69C3×#479—31no—
70C3×#479—31no—
71C3×#462—31no—
72C3×#462—31no—
73C3×#451—31no—
74C3×#451—31no—
75C3×#441—31no—
76C3×#441—31no—
77C3×C4×Q16—31no—
78C3×C4×Q16—31no—
79C3×#433—31no—
80#5050C2×C311yescharacteristic
81#4996C2×C311yescharacteristic
82#4877C2×C311yescharacteristic, complemented
83#4873C2×C311yescharacteristic, complemented
84#4857C2×C311yescharacteristic, complemented
85#4853C2×C311yescharacteristic, complemented
86#4795C2×C311yescharacteristic, complemented
87#4795C2×C311yescharacteristic, complemented
88#4790C2×C311yescharacteristic, complemented
89#4789C2×C311yescharacteristic, complemented
90#4739C2×C311yescharacteristic
91#4720C2×C311yescharacteristic
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3×Dic3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—22no—
97C2×C3×Dic6—22no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4—21no—
104C32×C4⋊C4C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108C32×C22⋊C4—21no—
109C32×C42—21no—
110C3×#217—21no—
111C3×#217D411yescharacteristic
112C3×#217D411yescharacteristic
113C3×#216—22no—
114C3×#216—22no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3D411yescharacteristic
118C3×C4⋊Dic3D411yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×Dic12—22no—
140C3×Dic12—22no—
141#3127—31noSylow
142C22×C3×Q8—31no—
143C22×Dic6C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C2×C3×Q16—31no—
147C2×C3×Q16—31no—
148C3×C4⋊Q8—31no—
149C3×#126—61no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#125—61no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8C2×D311yescharacteristic
157C3×C22⋊Q8C22×C311yescharacteristic
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—61no—
165C3×C4×Q8—61no—
166C3×#117—21no—
167C3×#117—31no—
168C3×#117—61no—
169C3×#117—61no—
170C3×#117C2×D311yescharacteristic
171C3×#117C22×C311yescharacteristic
172Q8×Dic3C22×C311yescharacteristic
173#944C22×C311yescharacteristic
174C2×#216C22×C311yescharacteristic
175C2×#216C22×C311yescharacteristic
176#926C22×C311yescharacteristic
177#924C22×C311yescharacteristic
178C2×Dic12C22×C311yescharacteristic
179C2×Dic12C22×C311yescharacteristic
180#890—21no—
181#890C22×C311yescharacteristic
182#889—21no—
183#887C22×C311yescharacteristic
184#887C22×C311yescharacteristic
185#887C22×C311yescharacteristic
186#887C22×C311yescharacteristic
187#887C22×C311yescharacteristic
188#879—21no—
189#879—21no—
190#877—21no—
191#877—21no—
192C4×Dic6—21no—
193C4×Dic6—21no—
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic
197C3×#107C22×C311yescharacteristic
198C3×#106—21no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic
201C3×#106C22×C311yescharacteristic
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103C2×D311yescharacteristic
213C3×#103C2×D311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×#103C22×C311yescharacteristic
216C3×C22⋊C8—21no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C22×C311yescharacteristic
220C3×#97—31no—
221C3×C4×C8—31no—
222#830C22×C311yescharacteristic
223#816C22×C311yescharacteristic
224#816C22×C311yescharacteristic
225#815C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227Dic3⋊C8C22×C311yescharacteristic
228C8×Dic3C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C23×C32C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3×Dic3—24no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×Dic6—24no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6#4112yes—
261C3×Dic6#4112yes—
262C32×C8—21no—
263C32×C8—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—31no—
267#519—31no—
268#485—31no—
269#485C3×D311yescharacteristic
270#479—31no—
271#479—31no—
272#462—31no—
273#462—31no—
274#451—31no—
275#451—31no—
276#441—31no—
277#441—31no—
278C4×Q16—31no—
279C4×Q16—31no—
280#433—31no—
281C2×C3×Q8—21no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—62no—
286C2×C3×Q8—62no—
287C2×C3×Q8—61no—
288C2×C3×Q8C22×D311yescharacteristic
289C2×C3×Q8C23×C311yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4—61no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C23×C311yescharacteristic
294C22×Dic3—21no—
295C2×Dic6—21no—
296C2×Dic6—22no—
297C2×Dic6—22no—
298C2×Dic6C23×C311yescharacteristic
299C2×Dic6C23×C311yescharacteristic
300C2×Dic6C23×C311yescharacteristic
301C3×Q16—62no—
302C3×Q16—62no—
303C3×Q16—62no—
304C3×Q16—62no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C2×C3×C8C23×C311yescharacteristic
312C2×C3×C8C23×C311yescharacteristic
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—41no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C23×C311yescharacteristic
337C3×C4⋊C4C23×C311yescharacteristic
338C3×C4⋊C4C23×C311yescharacteristic
339C3×C22⋊C4—21no—
340C3×C22⋊C4—21no—
341C3×C22⋊C4—21no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—41no—
346C3×C22⋊C4—41no—
347C3×C22⋊C4—61no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—31no—
351C3×C42—31no—
352C3×C42—41no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42—61no—
359#217—21no—
360#217C3×D411yescharacteristic
361#217C3×D411yescharacteristic
362#216—22no—
363#216—22no—
364C4⋊Dic3—21no—
365C4⋊Dic3—21no—
366C4⋊Dic3C3×D411yescharacteristic
367C4⋊Dic3C3×D411yescharacteristic
368C4⋊Dic3C23×C311yescharacteristic
369Dic3⋊C4—21no—
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378C4×Dic3—21no—
379C4×Dic3—21no—
380C4×Dic3—21no—
381C4×Dic3—21no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3C23×C311yescharacteristic
385C4×Dic3C23×C311yescharacteristic
386C2×C3⋊C8C23×C311yescharacteristic
387C2×C3⋊C8C23×C311yescharacteristic
388Dic12—22no—
389Dic12—22no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32C22×D411yescharacteristic
394C32×C4—21no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4—41no—
398C32×C4—41no—
399C32×C4C2×#4111yescharacteristic
400C32×C4C2×#4111yescharacteristic
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—31no—
410C2×Q16—31no—
411C2×Q16—31no—
412C2×Q16—31no—
413C2×Q16—31no—
414C4⋊Q8—31no—
415#126—61no—
416#126—61no—
417#125—31no—
418#125—61no—
419#125—61no—
420C22⋊Q8—31no—
421C22⋊Q8C2×C3×D311yescharacteristic
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—61no—
429C4×Q8—61no—
430#117—31no—
431#117—61no—
432#117—61no—
433#117C2×C3×D311yescharacteristic
434#107—31no—
435#107C2×C3×D311yescharacteristic
436#106—31no—
437#106C2×C3×D311yescharacteristic
438C4⋊C8—31no—
439C4⋊C8—31no—
440#103—31no—
441#103—31no—
442#103—31no—
443#103—31no—
444#103—31no—
445#103—31no—
446#103C2×C3×D311yescharacteristic
447#103C2×C3×D311yescharacteristic
448C22⋊C8—31no—
449C22⋊C8C2×C3×D311yescharacteristic
450#97—31no—
451C4×C8—31no—
452C23×C3—21no—
453C23×C3D3×D411yescharacteristic
454C23×C3C2×C3×D411yescharacteristic
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—32no—
460C3×Q8—32no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—64no—
464C3×Q8—61no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—61no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—64no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4C2×C3×D411yescharacteristic
499C2×C3×C4C23×D311yescharacteristic
500C2×C3×C4C24×C311yescharacteristic
501C2×Dic3—24no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3C2×C3×D411yescharacteristic
507C2×Dic3C2×C3×D411yescharacteristic
508C2×Dic3C2×C3×D411yescharacteristic
509C2×Dic3C2×C3×D411yescharacteristic
510Dic6—24no—
511Dic6—21no—
512Dic6—21no—
513Dic6—21no—
514Dic6—21no—
515Dic6C3×#4112yes—
516Dic6C3×#4112yes—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—41no—
522C3×C8—41no—
523C3×C8—61no—
524C3×C8—61no—
525C3⋊C8—21no—
526C3⋊C8—21no—
527C2×C32—41no—
528C2×C32#52511yescharacteristic
529C2×C32#57811yescharacteristic
530C2×C32#57811yescharacteristic
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—62no—
535C2×Q8—62no—
536C2×Q8—61no—
537C2×Q8C22×C3×D311yescharacteristic
538C22×C4—61no—
539C22×C4C22×C3×D311yescharacteristic
540Q16—62no—
541Q16—62no—
542Q16—62no—
543Q16—62no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8C22×C3×D311yescharacteristic
547C2×C8C22×C3×D311yescharacteristic
548C4⋊C4—21no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4C22×C3×D311yescharacteristic
564C4⋊C4C22×C3×D311yescharacteristic
565C4⋊C4C22×C3×D311yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—31no—
569C22⋊C4—31no—
570C22⋊C4—61no—
571C42—21no—
572C42—31no—
573C42—31no—
574C42—61no—
575C42—61no—
576C42—61no—
577C42—61no—
578C42—61no—
579C42—61no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3C2×D3×D411yescharacteristic
591C22×C3C22×C3×D411yescharacteristic
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—62no—
606C3×C4—62no—
607C3×C4—61no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—81no—
612C3×C4—81no—
613C3×C4—81no—
614C3×C4—81no—
615C3×C4—121no—
616C3×C4—121no—
617C3×C4D3×#4111yescharacteristic
618C3×C4D3×#4111yescharacteristic
619C3×C4C2×C3×#4111yescharacteristic
620C3×C4C2×C3×#4111yescharacteristic
621Dic3—21no—
622Dic3—21no—
623Dic3—21no—
624Dic3—21no—
625Dic3—22no—
626Dic3—22no—
627Dic3—41no—
628Dic3—41no—
629C32#312711yescharacteristic, complemented, Sylow
630C23C3×D3×D411yescharacteristic
631Q8—21no—
632Q8—21no—
633Q8—32no—
634Q8—32no—
635Q8—64no—
636Q8—61no—
637Q8—61no—
638Q8—61no—
639Q8—61no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—64no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4C3×D3×D411yescharacteristic
656C2×C4C23×C3×D311yescharacteristic
657C8—21no—
658C8—21no—
659C8—61no—
660C8—61no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—41no—
665C2×C3—41no—
666C2×C3—81no—
667C2×C3#565611yescharacteristic
668C2×C3#577111yescharacteristic
669C2×C3#577911yescharacteristic
670C2×C3C3×#52511yescharacteristic
671C2×C3C3×#57811yescharacteristic
672C2×C3C3×#57811yescharacteristic
673C22—21no—
674C22—21no—
675C22—21no—
676C22C2×C3×D3×D411yescharacteristic
677C4—21no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—61no—
683C4—61no—
684C4—61no—
685C4—61no—
686C4—62no—
687C4—62no—
688C4—121no—
689C4—121no—
690C4C3×D3×#4111yescharacteristic
691C4C3×D3×#4111yescharacteristic
692C3—21no—
693C3#8149911yescharacteristic, direct product factor
694C3C3×#312711yescharacteristic, complemented
695C2—41no—
696C2C3×#565611yescharacteristic
697C2C3×#577111yescharacteristic
698C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC3×#485D3
hypocenterC3C3×#3127
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#485

Complements

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

NH ≅ G/Ntype
6. C3×#4877C2semidirect
7. C3×#4873C2semidirect
8. C3×#4857C2semidirect
9. C3×#4853C2semidirect
10. C3×#4795C2semidirect
11. C3×#4795C2semidirect
12. C3×#4790C2semidirect
13. C3×#4789C2semidirect
17. #81499C3direct (N × H)
82. #4877C2×C3semidirect
83. #4873C2×C3semidirect
84. #4857C2×C3semidirect
85. #4853C2×C3semidirect
86. #4795C2×C3semidirect
87. #4795C2×C3semidirect
88. #4790C2×C3semidirect
89. #4789C2×C3semidirect
629. C32#3127semidirect
693. C3#81499direct (N × H)
694. C3C3×#3127semidirect

Maximal subgroups

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

subgroupindex
C3×#56252
C3×#55162
C32×#4852
C3×#50502
C3×#49962
C3×#48772
C3×#48732
C3×#48572
C3×#48532
C3×#47952
C3×#47902
C3×#47892
C3×#47392
C3×#47202
C3×#31273
#814993