Finite Group Databasebeta

← C3×#80177 #11873263

Subgroups — C3×#80177 #11873263

Order 1152.

790 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5812C211yesmaximal, characteristic
2C3×#5625C211yesmaximal, characteristic
3C32×#451C211yesmaximal, characteristic
4C3×#5228C211yesmaximal, characteristic
5C3×#5184C211yesmaximal, characteristic, complemented
6C3×#5182C211yesmaximal, characteristic, complemented
7C3×#5182C211yesmaximal, characteristic, complemented
8C3×Dic3×Q16C211yesmaximal, characteristic, complemented
9C3×#5045C211yesmaximal, characteristic
10C3×#4799C211yesmaximal, characteristic, complemented
11C3×#4796C211yesmaximal, characteristic, complemented
12C3×#4790C211yesmaximal, characteristic, complemented
13C3×#4789C211yesmaximal, characteristic, complemented
14C3×#4723C211yesmaximal, characteristic
15C3×#4720C211yesmaximal, characteristic
16C3×#3127—31nomaximal
17#80177C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C3×Q8×Dic3—21no—
23C3×Q8×Dic3—21no—
24C3×Q8×Dic3C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×#944C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic
32C3×#926—21no—
33C3×#926—21no—
34C3×#926C2211yescharacteristic
35C3×#926C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C3×#890—21no—
38C3×#890C2211yescharacteristic
39C3×#889—21no—
40C3×#887C2211yescharacteristic
41C3×#879—21no—
42C3×#879—21no—
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#815C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic
58C3×C8×Dic3C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#541—31no—
62C3×#519—31no—
63#5812C2×C311yescharacteristic
64#5625C2×C311yescharacteristic
65C3×#485—31no—
66C3×#485—31no—
67C3×#479—31no—
68C3×#479—31no—
69C3×#462—31no—
70C3×#462—31no—
71C3×#451—21no—
72C3×#451—31no—
73C3×#451D311yescharacteristic
74C3×#451C2×C311yescharacteristic
75C3×#441—31no—
76C3×#441—31no—
77C3×C4×Q16—31no—
78C3×C4×Q16—31no—
79C3×#433—31no—
80#5228C2×C311yescharacteristic
81#5184C2×C311yescharacteristic, complemented
82#5182C2×C311yescharacteristic, complemented
83#5182C2×C311yescharacteristic, complemented
84Dic3×Q16C2×C311yescharacteristic, complemented
85#5045C2×C311yescharacteristic
86#4799C2×C311yescharacteristic, complemented
87#4796C2×C311yescharacteristic, complemented
88#4790C2×C311yescharacteristic, complemented
89#4789C2×C311yescharacteristic, complemented
90#4723C2×C311yescharacteristic
91#4720C2×C311yescharacteristic
92C2×C32×Q8—22no—
93C2×C32×Q8—22no—
94C2×C32×Q8—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C32×Q16—22no—
102C32×Q16—22no—
103C2×C32×C8C2311yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108C3×#217—21no—
109C3×#217—21no—
110C3×#217D411yescharacteristic
111C3×#217D411yescharacteristic
112C3×#216—22no—
113C3×#216—22no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3D411yescharacteristic
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3127—31noSylow
142C22×C3×Q8—21no—
143C22×C3×Q8C2×D311yescharacteristic
144C22×C3×Q8C22×C311yescharacteristic
145C2×C3×Q16—21no—
146C2×C3×Q16—21no—
147C2×C3×Q16—31no—
148C2×C3×Q16—31no—
149C2×C3×Q16C2×D311yescharacteristic
150C2×C3×Q16C2×D311yescharacteristic
151C2×C3×Q16C22×C311yescharacteristic
152C2×C3×Q16C22×C311yescharacteristic
153C3×C4⋊Q8—31no—
154C3×#126—61no—
155C3×#126—61no—
156C3×#125—31no—
157C3×#125—61no—
158C3×#125—61no—
159C3×C22⋊Q8—21no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8C2×D311yescharacteristic
162C3×C22⋊Q8C22×C311yescharacteristic
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—31no—
166C3×C4×Q8—31no—
167C3×C4×Q8—31no—
168C3×C4×Q8—31no—
169C3×C4×Q8—61no—
170C3×C4×Q8—61no—
171C3×#117—31no—
172C3×#117—31no—
173C3×#117—61no—
174C3×#117—61no—
175Q8×Dic3—21no—
176Q8×Dic3—21no—
177Q8×Dic3C22×C311yescharacteristic
178Q8×Dic3C22×C311yescharacteristic
179Q8×Dic3C22×C311yescharacteristic
180Q8×Dic3C22×C311yescharacteristic
181Q8×Dic3C22×C311yescharacteristic
182#944C22×C311yescharacteristic
183C2×#216C22×C311yescharacteristic
184C2×#216C22×C311yescharacteristic
185#926—21no—
186#926—21no—
187#926C22×C311yescharacteristic
188#926C22×C311yescharacteristic
189#924C22×C311yescharacteristic
190#890—21no—
191#890C22×C311yescharacteristic
192#889—21no—
193#887C22×C311yescharacteristic
194#879—21no—
195#879—21no—
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—31no—
201C3×C4⋊C8—31no—
202C3×#103—21no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#103C22×C311yescharacteristic
213C3×#103C22×C311yescharacteristic
214C3×C22⋊C8—21no—
215C3×C22⋊C8—31no—
216C3×C22⋊C8C2×D311yescharacteristic
217C3×C22⋊C8C22×C311yescharacteristic
218C3×#97—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic
221#835C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223#835C22×C311yescharacteristic
224#830C22×C311yescharacteristic
225#818C22×C311yescharacteristic
226#817C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229#815C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231Dic3⋊C8C22×C311yescharacteristic
232C8×Dic3C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C23×C32C2×D411yescharacteristic
236C32×Q8—24no—
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8—21no—
240C32×Q8—21no—
241C32×Q8#4112yes—
242C32×Q8#4112yes—
243C2×C32×C4—24no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×Dic6—21no—
261C3×Dic6—21no—
262C32×C8—21no—
263C32×C8—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—31no—
267#519—31no—
268#485—31no—
269#485—31no—
270#479—31no—
271#479—31no—
272#462—31no—
273#462—31no—
274#451—31no—
275#451C3×D311yescharacteristic
276#441—31no—
277#441—31no—
278C4×Q16—31no—
279C4×Q16—31no—
280#433—31no—
281C2×C3×Q8—22no—
282C2×C3×Q8—22no—
283C2×C3×Q8—22no—
284C2×C3×Q8—22no—
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8—21no—
288C2×C3×Q8—21no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8—41no—
292C2×C3×Q8—42no—
293C2×C3×Q8—42no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C23×C311yescharacteristic
298C2×C3×Q8C23×C311yescharacteristic
299C2×C3×Q8C23×C311yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—41no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C23×C311yescharacteristic
306C2×Dic6C23×C311yescharacteristic
307C3×Q16—22no—
308C3×Q16—22no—
309C3×Q16—22no—
310C3×Q16—22no—
311C3×Q16—42no—
312C3×Q16—42no—
313C3×Q16—62no—
314C3×Q16—62no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C2×C3×C8C22×D311yescharacteristic
320C2×C3×C8C22×D311yescharacteristic
321C2×C3×C8C23×C311yescharacteristic
322C2×C3×C8C23×C311yescharacteristic
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—41no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
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⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C23×C311yescharacteristic
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—31no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42—61no—
361#217—21no—
362#217—21no—
363#217C3×D411yescharacteristic
364#217C3×D411yescharacteristic
365#216—22no—
366#216—22no—
367C4⋊Dic3—21no—
368C4⋊Dic3—21no—
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3C3×D411yescharacteristic
374C4⋊Dic3C3×D411yescharacteristic
375C4⋊Dic3C23×C311yescharacteristic
376C4⋊Dic3C23×C311yescharacteristic
377C4⋊Dic3C23×C311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3C23×C311yescharacteristic
391C4×Dic3C23×C311yescharacteristic
392C2×C3⋊C8C23×C311yescharacteristic
393C2×C3⋊C8C23×C311yescharacteristic
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32C22×D411yescharacteristic
398C32×C4—22no—
399C32×C4—22no—
400C32×C4—21no—
401C32×C4—41no—
402C32×C4—41no—
403C32×C4C2×#4111yescharacteristic
404C32×C4C2×#4111yescharacteristic
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—21no—
408C3×Dic3—21no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C22×Q8C2×C3×D311yescharacteristic
414C2×Q16—31no—
415C2×Q16—31no—
416C2×Q16C2×C3×D311yescharacteristic
417C2×Q16C2×C3×D311yescharacteristic
418C4⋊Q8—31no—
419#126—61no—
420#126—61no—
421#125—31no—
422#125—61no—
423#125—61no—
424C22⋊Q8—31no—
425C22⋊Q8C2×C3×D311yescharacteristic
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×Q8—31no—
430C4×Q8—31no—
431C4×Q8—31no—
432C4×Q8—61no—
433C4×Q8—61no—
434#117—31no—
435#117—31no—
436#117—61no—
437#117—61no—
438#107—31no—
439#107—31no—
440#106—31no—
441#106—31no—
442C4⋊C8—31no—
443C4⋊C8—31no—
444#103—31no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103—31no—
450#103C2×C3×D311yescharacteristic
451#103C2×C3×D311yescharacteristic
452C22⋊C8—31no—
453C22⋊C8C2×C3×D311yescharacteristic
454#97—31no—
455C4×C8—31no—
456C23×C3—21no—
457C23×C3D3×D411yescharacteristic
458C23×C3C2×C3×D411yescharacteristic
459C3×Q8—24no—
460C3×Q8—24no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—21no—
467C3×Q8—21no—
468C3×Q8—21no—
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×Q8—44no—
476C3×Q8—61no—
477C3×Q8—61no—
478C3×Q8#23712yes—
479C3×Q8#23712yes—
480C3×Q8C3×#4112yes—
481C3×Q8C3×#4112yes—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
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—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—44no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C2×C3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C24×C311yescharacteristic
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3C2×C3×D411yescharacteristic
522C2×Dic3C2×C3×D411yescharacteristic
523C2×Dic3C2×C3×D411yescharacteristic
524C2×Dic3C2×C3×D411yescharacteristic
525Dic6—21no—
526Dic6—21no—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—21no—
531C3×C8—41no—
532C3×C8—41no—
533C3×C8—61no—
534C3×C8—61no—
535C3⋊C8—21no—
536C3⋊C8—21no—
537C2×C32—41no—
538C2×C32#52511yescharacteristic
539C2×C32#57811yescharacteristic
540C2×C32#57811yescharacteristic
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—21no—
544C2×Q8—31no—
545C2×Q8C22×C3×D311yescharacteristic
546C2×Q8C22×C3×D311yescharacteristic
547C2×Q8C22×C3×D311yescharacteristic
548C22×C4—21no—
549C22×C4C22×C3×D311yescharacteristic
550Q16—22no—
551Q16—22no—
552Q16—62no—
553Q16—62no—
554C2×C8—31no—
555C2×C8—31no—
556C2×C8C22×C3×D311yescharacteristic
557C2×C8C22×C3×D311yescharacteristic
558C4⋊C4—21no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—31no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4C22×C3×D311yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—31no—
578C22⋊C4—31no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C42—31no—
582C42—31no—
583C42—61no—
584C42—61no—
585C42—61no—
586C42—61no—
587C42—61no—
588C42—61no—
589C42—61no—
590C22×C3—22no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3C2×D3×D411yescharacteristic
601C22×C3C22×C3×D411yescharacteristic
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—21no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—41no—
611C3×C4—42no—
612C3×C4—42no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—61no—
620C3×C4—61no—
621C3×C4—81no—
622C3×C4—81no—
623C3×C4—121no—
624C3×C4—121no—
625C3×C4—121no—
626C3×C4—121no—
627C3×C4C2×#23711yescharacteristic
628C3×C4C2×#23711yescharacteristic
629C3×C4C2×C3×#4111yescharacteristic
630C3×C4C2×C3×#4111yescharacteristic
631Dic3—21no—
632Dic3—21no—
633Dic3—21no—
634Dic3—21no—
635Dic3—41no—
636Dic3—41no—
637Dic3—41no—
638Dic3—41no—
639C32#312711yescharacteristic, complemented, Sylow
640C23C3×D3×D411yescharacteristic
641Q8—24no—
642Q8—21no—
643Q8—21no—
644Q8—21no—
645Q8—21no—
646Q8—61no—
647Q8—61no—
648Q8C3×#23712yes—
649Q8C3×#23712yes—
650C2×C4—24no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4C3×D3×D411yescharacteristic
666C2×C4C23×C3×D311yescharacteristic
667C8—21no—
668C8—21no—
669C8—61no—
670C8—61no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—42no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3#558611yescharacteristic
678C2×C3#576611yescharacteristic
679C2×C3#577911yescharacteristic
680C2×C3C3×#52511yescharacteristic
681C2×C3C3×#57811yescharacteristic
682C2×C3C3×#57811yescharacteristic
683C22—21no—
684C22—21no—
685C22—21no—
686C22C2×C3×D3×D411yescharacteristic
687C4—22no—
688C4—22no—
689C4—21no—
690C4—41no—
691C4—41no—
692C4—61no—
693C4—61no—
694C4—61no—
695C4—61no—
696C4—121no—
697C4—121no—
698C4—121no—
699C4—121no—
700C4C2×C3×#23711yescharacteristic
701C4C2×C3×#23711yescharacteristic
702C3—21no—
703C3#8017711yescharacteristic, direct product factor
704C3C3×#312711yescharacteristic, complemented
705C2—41no—
706C2C3×#558611yescharacteristic
707C2C3×#576611yescharacteristic
708C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC3×#451D3
hypocenterC3C3×#3127
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
5. C3×#5184C2semidirect
6. C3×#5182C2semidirect
7. C3×#5182C2semidirect
8. C3×Dic3×Q16C2semidirect
10. C3×#4799C2semidirect
11. C3×#4796C2semidirect
12. C3×#4790C2semidirect
13. C3×#4789C2semidirect
17. #80177C3direct (N × H)
81. #5184C2×C3semidirect
82. #5182C2×C3semidirect
83. #5182C2×C3semidirect
84. Dic3×Q16C2×C3semidirect
86. #4799C2×C3semidirect
87. #4796C2×C3semidirect
88. #4790C2×C3semidirect
89. #4789C2×C3semidirect
639. C32#3127semidirect
703. C3#80177direct (N × H)
704. C3C3×#3127semidirect

Maximal subgroups

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

subgroupindex
C3×#58122
C3×#56252
C32×#4512
C3×#52282
C3×#51842
C3×#51822
C3×Dic3×Q162
C3×#50452
C3×#47992
C3×#47962
C3×#47902
C3×#47892
C3×#47232
C3×#47202
C3×#31273
#801773