Finite Group Databasebeta

← C3×#80176 #11872567

Subgroups — C3×#80176 #11872567

Order 1152.

814 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5812C211yesmaximal, characteristic, complemented
2C3×#5643C211yesmaximal, characteristic
3C32×#451C211yesmaximal, characteristic, complemented
4C3×#5227C211yesmaximal, characteristic
5C3×#5185C211yesmaximal, characteristic, complemented
6C3×#5185C211yesmaximal, characteristic, complemented
7C3×#5184C211yesmaximal, characteristic, complemented
8C3×Dic3×Q16C211yesmaximal, characteristic, complemented
9C3×#5045C211yesmaximal, characteristic, complemented
10C3×#4817C211yesmaximal, characteristic, complemented
11C3×#4793C211yesmaximal, characteristic, complemented
12C3×#4791C211yesmaximal, characteristic, complemented
13C3×#4788C211yesmaximal, characteristic, complemented
14C3×#4737C211yesmaximal, characteristic
15C3×#4720C211yesmaximal, characteristic, complemented
16C3×#3121—31nomaximal
17#80176C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3—21no—
24C3×Q8×Dic3—21no—
25C3×Q8×Dic3C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×#930C2211yescharacteristic
33C3×#926—21no—
34C3×#926—21no—
35C3×#926C2211yescharacteristic
36C3×#926C2211yescharacteristic
37C3×#898—21no—
38C3×#897—21no—
39C3×#893C2211yescharacteristic
40C3×#888C2211yescharacteristic
41C3×#885—21no—
42C3×#883—21no—
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#818C2211yescharacteristic
54C3×#817C2211yescharacteristic
55C3×#815C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic
58C3×C8×Dic3C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#542—31no—
62C3×#519—31no—
63#5812C2×C311yescharacteristic, complemented
64#5643C2×C311yescharacteristic
65C3×#485—31no—
66C3×#482—31no—
67C3×#477—31no—
68C3×#475—31no—
69C3×#464—31no—
70C3×#464—31no—
71C3×#451—21no—
72C3×#451D311yescharacteristic, complemented
73C3×#451C2×C311yescharacteristic, complemented
74C3×#448—31no—
75C3×#441—31no—
76C3×#440—31no—
77C3×C4×Q16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5227C2×C311yescharacteristic
81#5185C2×C311yescharacteristic, complemented
82#5185C2×C311yescharacteristic, complemented
83#5184C2×C311yescharacteristic, complemented
84Dic3×Q16C2×C311yescharacteristic, complemented
85#5045C2×C311yescharacteristic, complemented
86#4817C2×C311yescharacteristic, complemented
87#4793C2×C311yescharacteristic, complemented
88#4791C2×C311yescharacteristic, complemented
89#4788C2×C311yescharacteristic, complemented
90#4737C2×C311yescharacteristic
91#4720C2×C311yescharacteristic, complemented
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×#67—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6—21no—
104C32×Q16—22no—
105C32×Q16—22no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C3×#217—21no—
112C3×#217D411yescharacteristic
113C3×#217D411yescharacteristic
114C3×#215—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×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—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#3121—31noSylow
142C22×C3×Q8—21no—
143C22×C3×Q8C2×D311yescharacteristic
144C22×C3×Q8C22×C311yescharacteristic
145C2×C3×Q16—21no—
146C2×C3×Q16—21no—
147C2×C3×Q16C2×D311yescharacteristic
148C2×C3×Q16C2×D311yescharacteristic
149C2×C3×Q16C22×C311yescharacteristic
150C2×C3×Q16C22×C311yescharacteristic
151C2×C3×SD16—31no—
152C2×C3×SD16—31no—
153C3×C4⋊Q8—31no—
154C3×#126—61no—
155C3×#124—31no—
156C3×#124—61no—
157C3×#123—61no—
158C3×C22⋊Q8—21no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C22⋊Q8C22×C311yescharacteristic
162C3×#121—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—31no—
166C3×C4×Q8—31no—
167C3×C4×Q8—31no—
168C3×C4×Q8—61no—
169C3×C4×Q8—61no—
170C3×C4×D4—31no—
171C3×#117—31no—
172C3×#117—31no—
173C3×#117—61no—
174C3×#117—61no—
175#947C22×C311yescharacteristic
176Q8×Dic3—21no—
177Q8×Dic3—21no—
178Q8×Dic3C22×C311yescharacteristic
179Q8×Dic3C22×C311yescharacteristic
180Q8×Dic3C22×C311yescharacteristic
181Q8×Dic3C22×C311yescharacteristic
182Q8×Dic3C22×C311yescharacteristic
183C2×#215C22×C311yescharacteristic
184C2×#215C22×C311yescharacteristic
185#930C22×C311yescharacteristic
186#926—21no—
187#926—21no—
188#926C22×C311yescharacteristic
189#926C22×C311yescharacteristic
190#898—21no—
191#897—21no—
192#893C22×C311yescharacteristic
193#888C22×C311yescharacteristic
194#885—21no—
195#883—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×#103C2×D311yescharacteristic
209C3×#103C2×D311yescharacteristic
210C3×#103C22×C311yescharacteristic
211C3×#103C22×C311yescharacteristic
212C3×#102—31no—
213C3×#102—31no—
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#821C22×C311yescharacteristic
226#821C22×C311yescharacteristic
227#818C22×C311yescharacteristic
228#817C22×C311yescharacteristic
229#815C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231Dic3⋊C8C22×C311yescharacteristic
232C8×Dic3C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C32×Q8—24no—
238C32×Q8—21no—
239C32×Q8—21no—
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8#4112yes—
243C32×Q8#4112yes—
244C2×C32×C4—24no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C3×#67—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×C4×D3—81no—
264C3×Dic6—81no—
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#451C3×D311yescharacteristic, complemented
278#448—31no—
279#441—31no—
280#440—31no—
281C4×Q16—31no—
282C4×SD16—31no—
283#433—31no—
284C2×C3×Q8—22no—
285C2×C3×Q8—22no—
286C2×C3×Q8—22no—
287C2×C3×Q8—22no—
288C2×C3×Q8—21no—
289C2×C3×Q8—21no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—21no—
293C2×C3×Q8—41no—
294C2×C3×Q8—42no—
295C2×C3×Q8—42no—
296C2×C3×Q8—61no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C23×C311yescharacteristic
301C2×C3×Q8C23×C311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—41no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C2×#67—21no—
313C2×D12C23×C311yescharacteristic
314C2×C4×D3—21no—
315C2×Dic6—21no—
316C3×Q16—22no—
317C3×Q16—22no—
318C3×Q16—22no—
319C3×Q16—22no—
320C3×Q16—42no—
321C3×Q16—42no—
322C3×SD16—62no—
323C3×SD16—62no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C23×C311yescharacteristic
331C2×C3×C8C23×C311yescharacteristic
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C23×C311yescharacteristic
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—31no—
360C3×C42—31no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42—61no—
365C3×C42—61no—
366C3×C42—61no—
367#217—21no—
368#217C3×D411yescharacteristic
369#217C3×D411yescharacteristic
370#215—22no—
371#215—22no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3C3×D411yescharacteristic
382C4⋊Dic3C3×D411yescharacteristic
383C4⋊Dic3C23×C311yescharacteristic
384C4⋊Dic3C23×C311yescharacteristic
385C4⋊Dic3C23×C311yescharacteristic
386Dic3⋊C4—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3C23×C311yescharacteristic
394C4×Dic3C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32C22×D411yescharacteristic
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C32×C4—22no—
405C32×C4—22no—
406C32×C4—21no—
407C32×C4—41no—
408C32×C4—41no—
409C32×C4C2×#4111yescharacteristic
410C32×C4C2×#4111yescharacteristic
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C22×Q8C2×C3×D311yescharacteristic
419C2×Q16C2×C3×D311yescharacteristic
420C2×Q16C2×C3×D311yescharacteristic
421C2×SD16—31no—
422C2×SD16—31no—
423C4⋊Q8—31no—
424#126—61no—
425#124—31no—
426#124—61no—
427#123—61no—
428C22⋊Q8—61no—
429C22⋊Q8C2×C3×D311yescharacteristic
430#121—31no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×Q8—31no—
434C4×Q8—31no—
435C4×Q8—31no—
436C4×Q8—61no—
437C4×Q8—61no—
438C4×D4—31no—
439#117—31no—
440#117—31no—
441#117—61no—
442#117—61no—
443#107—31no—
444#107—31no—
445#106—31no—
446#106—31no—
447C4⋊C8—31no—
448C4⋊C8—31no—
449#103—31no—
450#103—31no—
451#103—31no—
452#103—31no—
453#103C2×C3×D311yescharacteristic
454#103C2×C3×D311yescharacteristic
455#102—31no—
456#102—31no—
457C22⋊C8—31no—
458C22⋊C8C2×C3×D311yescharacteristic
459#97—31no—
460C4×C8—31no—
461C23×C3—21no—
462C23×C3—61no—
463C23×C3D3×D411yescharacteristic
464C23×C3C2×C3×D411yescharacteristic
465C22×D3—21no—
466C3×Q8—24no—
467C3×Q8—24no—
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—21no—
471C3×Q8—21no—
472C3×Q8—21no—
473C3×Q8—21no—
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—22no—
477C3×Q8—22no—
478C3×Q8—41no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×Q8—44no—
483C3×Q8—241no—
484C3×Q8#23712yes—
485C3×Q8#23712yes—
486C3×Q8C3×#4112yes—
487C3×Q8C3×#4112yes—
488C3×D4—61no—
489C3×D4—61no—
490C3×D4—241no—
491C2×C3×C4—24no—
492C2×C3×C4—24no—
493C2×C3×C4—21no—
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—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—44no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—241no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C2×C3×D411yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C24×C311yescharacteristic
526#67—81no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3C2×C3×D411yescharacteristic
531C2×Dic3C2×C3×D411yescharacteristic
532C2×Dic3C2×C3×D411yescharacteristic
533C2×Dic3C2×C3×D411yescharacteristic
534D12—21no—
535D12—21no—
536C4×D3—81no—
537Dic6—81no—
538C3×C8—21no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—41no—
543C3×C8—41no—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C2×C32—41no—
549C2×C32#52511yescharacteristic
550C2×C32#57711yescharacteristic
551C2×C32#57811yescharacteristic
552C3×D3—81no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—21no—
556C2×Q8—61no—
557C2×Q8C22×C3×D311yescharacteristic
558C2×Q8C22×C3×D311yescharacteristic
559C2×Q8C22×C3×D311yescharacteristic
560C2×D4—31no—
561C2×D4—61no—
562C22×C4—21no—
563C22×C4—61no—
564C22×C4C22×C3×D311yescharacteristic
565Q16—22no—
566Q16—22no—
567SD16—62no—
568SD16—62no—
569C2×C8—31no—
570C2×C8—31no—
571C2×C8C22×C3×D311yescharacteristic
572C2×C8C22×C3×D311yescharacteristic
573C4⋊C4—21no—
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—31no—
577C4⋊C4—31no—
578C4⋊C4—31no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4C22×C3×D311yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—31no—
588C22⋊C4—31no—
589C22⋊C4—61no—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C42—31no—
595C42—31no—
596C42—61no—
597C42—61no—
598C42—61no—
599C42—61no—
600C42—61no—
601C42—61no—
602C22×C3—22no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3C2×D3×D411yescharacteristic
616C22×C3C22×C3×D411yescharacteristic
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—21no—
623C3×C4—22no—
624C3×C4—22no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—41no—
629C3×C4—42no—
630C3×C4—42no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—61no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—61no—
639C3×C4—81no—
640C3×C4—81no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4C2×#23711yescharacteristic
645C3×C4C2×#23711yescharacteristic
646C3×C4C2×C3×#4111yescharacteristic
647C3×C4C2×C3×#4111yescharacteristic
648Dic3—21no—
649Dic3—21no—
650Dic3—21no—
651Dic3—21no—
652Dic3—41no—
653Dic3—41no—
654Dic3—41no—
655C32#312111yescharacteristic, complemented, Sylow
656C23—61no—
657C23C3×D3×D411yescharacteristic
658Q8—24no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—21no—
663Q8—241no—
664Q8C3×#23712yes—
665Q8C3×#23712yes—
666D4—61no—
667D4—61no—
668D4—241no—
669C2×C4—24no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—31no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—241no—
684C2×C4C3×D3×D411yescharacteristic
685C2×C4C23×C3×D311yescharacteristic
686C8—21no—
687C8—21no—
688C8—61no—
689C8—61no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—42no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—241no—
697C2×C3#558611yescharacteristic
698C2×C3#576611yescharacteristic
699C2×C3#577811yescharacteristic
700C2×C3C3×#52511yescharacteristic
701C2×C3C3×#57711yescharacteristic
702C2×C3C3×#57811yescharacteristic
703D3—81no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—121no—
708C22—121no—
709C22—121no—
710C22C2×C3×D3×D411yescharacteristic
711C4—22no—
712C4—22no—
713C4—21no—
714C4—41no—
715C4—41no—
716C4—61no—
717C4—61no—
718C4—61no—
719C4—61no—
720C4—121no—
721C4—121no—
722C4—121no—
723C4C2×C3×#23711yescharacteristic
724C4C2×C3×#23711yescharacteristic
725C3—21no—
726C3#8017611yescharacteristic, direct product factor
727C3C3×#312111yescharacteristic, complemented
728C2—41no—
729C2—241no—
730C2C3×#558611yescharacteristic
731C2C3×#576611yescharacteristic
732C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC3×#930C22
hypercenterC3×#451D3
hypocenterC3C3×#3121
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
1. C3×#5812C2semidirect
3. C32×#451C2semidirect
5. C3×#5185C2semidirect
6. C3×#5185C2semidirect
7. C3×#5184C2semidirect
8. C3×Dic3×Q16C2semidirect
9. C3×#5045C2semidirect
10. C3×#4817C2semidirect
11. C3×#4793C2semidirect
12. C3×#4791C2semidirect
13. C3×#4788C2semidirect
15. C3×#4720C2semidirect
17. #80176C3direct (N × H)
63. #5812C2×C3semidirect
72. C3×#451D3semidirect
73. C3×#451C2×C3semidirect
81. #5185C2×C3semidirect
82. #5185C2×C3semidirect
83. #5184C2×C3semidirect
84. Dic3×Q16C2×C3semidirect
85. #5045C2×C3semidirect
86. #4817C2×C3semidirect
87. #4793C2×C3semidirect
88. #4791C2×C3semidirect
89. #4788C2×C3semidirect
91. #4720C2×C3semidirect
277. #451C3×D3semidirect
655. C32#3121semidirect
726. C3#80176direct (N × H)
727. C3C3×#3121semidirect

Maximal subgroups

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

subgroupindex
C3×#58122
C3×#56432
C32×#4512
C3×#52272
C3×#51852
C3×#51842
C3×Dic3×Q162
C3×#50452
C3×#48172
C3×#47932
C3×#47912
C3×#47882
C3×#47372
C3×#47202
C3×#31213
#801763