Finite Group Databasebeta

← C3×#80212 #11870566

Subgroups — C3×#80212 #11870566

Order 1152.

868 conjugacy classes of subgroups.

The subgroup lattice has 761 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Dic3×#41C211yesmaximal, characteristic, complemented
2C3×#5624C211yesmaximal, characteristic, complemented
3C32×#452C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic
5C3×#5185C211yesmaximal, characteristic, complemented
6C3×Dic3×Q16C211yesmaximal, characteristic, complemented
7C3×#5165C211yesmaximal, characteristic, complemented
8C3×Dic3×SD16C211yesmaximal, characteristic, complemented
9C3×#5045C211yesmaximal, characteristic, complemented
10C3×#4799C211yesmaximal, characteristic, complemented
11C3×#4788C211yesmaximal, characteristic, complemented
12C3×#4766C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4737C211yesmaximal, characteristic, complemented
15C3×#4718C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#80212C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×D4×Dic3—21no—
28C3×D4×Dic3—21no—
29C3×D4×Dic3C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#930C2211yescharacteristic
33C3×#926—21no—
34C3×#926C2211yescharacteristic
35C2×C3×C4×Dic3—21no—
36C2×C3×C4×Dic3C2211yescharacteristic
37C3×#898—21no—
38C3×#893C2211yescharacteristic
39C3×#892—21no—
40C3×#890C2211yescharacteristic
41C3×#886—21no—
42C3×#67⋊C4—21no—
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#818C2211yescharacteristic
54C3×#817C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×C8×Dic3C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63Dic3×#41C2×C311yescharacteristic, complemented
64#5624C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#479—31no—
68C3×#478—31no—
69C3×#464—31no—
70C3×#463—31no—
71C3×#452—21no—
72C3×#452D311yescharacteristic, complemented
73C3×#452C2×C311yescharacteristic, complemented
74C3×#449—31no—
75C3×C4×Q16—31no—
76C3×C4×SD16—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#431—31no—
80#5238C2×C311yescharacteristic
81#5185C2×C311yescharacteristic, complemented
82Dic3×Q16C2×C311yescharacteristic, complemented
83#5165C2×C311yescharacteristic, complemented
84Dic3×SD16C2×C311yescharacteristic, complemented
85#5045C2×C311yescharacteristic, complemented
86#4799C2×C311yescharacteristic, complemented
87#4788C2×C311yescharacteristic, complemented
88#4766C2×C311yescharacteristic, complemented
89#4756C2×C311yescharacteristic, complemented
90#4737C2×C311yescharacteristic, complemented
91#4718C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—22no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3D411yescharacteristic
104C22×C3×Dic3D411yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C32×Q16—22no—
108C32×SD16—22no—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#215—22no—
118C3×#213—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
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×Dic3D411yescharacteristic
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3102—31noSylow
142C2×C3×#41—21no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C22×C311yescharacteristic
145C2×C3×Q16—21no—
146C2×C3×Q16C2×D311yescharacteristic
147C2×C3×Q16C22×C311yescharacteristic
148C2×C3×SD16—21no—
149C2×C3×SD16—31no—
150C2×C3×SD16C2×D311yescharacteristic
151C2×C3×SD16C22×C311yescharacteristic
152C2×C3×D8—31no—
153C3×#126—61no—
154C3×#125—31no—
155C3×#124—31no—
156C3×#123—61no—
157C3×C22⋊Q8—21no—
158C3×C22⋊Q8C2×D311yescharacteristic
159C3×C22⋊Q8C22×C311yescharacteristic
160C3×#121—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—61no—
168C3×C4×D4—61no—
169C3×C4×D4—61no—
170C3×#117—31no—
171C3×#117—61no—
172C3×#117—61no—
173C2×C3×C42—31no—
174C2×C3×C42—61no—
175#947C22×C311yescharacteristic
176Q8×Dic3C22×C311yescharacteristic
177Q8×Dic3C22×C311yescharacteristic
178Q8×Dic3C22×C311yescharacteristic
179C2×#215C22×C311yescharacteristic
180D4×Dic3—21no—
181D4×Dic3—21no—
182D4×Dic3C22×C311yescharacteristic
183D4×Dic3C22×C311yescharacteristic
184C2×#213C22×C311yescharacteristic
185#930C22×C311yescharacteristic
186#926—21no—
187#926C22×C311yescharacteristic
188C2×C4×Dic3—21no—
189C2×C4×Dic3C22×C311yescharacteristic
190#898—21no—
191#893C22×C311yescharacteristic
192#892—21no—
193#890C22×C311yescharacteristic
194#886—21no—
195#67⋊C4—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—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic
207C3×#103C22×C311yescharacteristic
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×C22⋊C8—21no—
215C3×C22⋊C8—31no—
216C3×C22⋊C8C2×D311yescharacteristic
217C3×C22⋊C8C22×C311yescharacteristic
218C3×C4×C8—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic
221#835C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#830C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226#821C22×C311yescharacteristic
227#818C22×C311yescharacteristic
228#817C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231C8×Dic3C22×C311yescharacteristic
232C8×Dic3C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C23×C32—21no—
236C23×C32C2×D411yescharacteristic
237C22×C3×D3—21no—
238C32×Q8—21no—
239C32×Q8—21no—
240C32×Q8—21no—
241C32×Q8#4112yes—
242C32×D4—24no—
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—24no—
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—42no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—41no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×C4×D3—42no—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#529—31no—
273C4×#41—31no—
274#485—31no—
275#482—31no—
276#479—31no—
277#478—31no—
278#464—31no—
279#463—31no—
280#452C3×D311yescharacteristic, complemented
281#449—31no—
282C4×Q16—31no—
283C4×SD16—31no—
284C4×SD16—31no—
285C4×D8—31no—
286#431—31no—
287C3×#41—22no—
288C3×#41—22no—
289C3×#41—22no—
290C3×#41—22no—
291C3×#41—42no—
292C3×#41—42no—
293C2×C3×Q8—21no—
294C2×C3×Q8—21no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C23×C311yescharacteristic
298C2×C3×Q8C23×C311yescharacteristic
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—41no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C23×C311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—41no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C23×C311yescharacteristic
318C2×#67—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3C3×D411yescharacteristic
322C22×Dic3C3×D411yescharacteristic
323C2×D12C23×C311yescharacteristic
324C2×C4×D3—21no—
325C3×Q16—22no—
326C3×Q16—22no—
327C3×Q16—42no—
328C3×SD16—22no—
329C3×SD16—22no—
330C3×SD16—42no—
331C3×SD16—62no—
332C3×D8—62no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C23×C311yescharacteristic
340C2×C3×C8C23×C311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—41no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C23×C311yescharacteristic
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—41no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—31no—
368C3×C42—31no—
369C3×C42—61no—
370C3×C42—61no—
371C3×C42—61no—
372C3×C42—61no—
373#217—21no—
374#217—21no—
375#217—21no—
376#215—22no—
377#213—22no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3—21no—
385C4⋊Dic3—21no—
386C4⋊Dic3C23×C311yescharacteristic
387C4⋊Dic3C23×C311yescharacteristic
388C4⋊Dic3C23×C311yescharacteristic
389Dic3⋊C4—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3C3×D411yescharacteristic
395C4×Dic3C3×D411yescharacteristic
396C4×Dic3C23×C311yescharacteristic
397C4×Dic3C23×C311yescharacteristic
398C2×C3⋊C8C23×C311yescharacteristic
399C2×C3⋊C8C23×C311yescharacteristic
400C22×C32—21no—
401C22×C32—22no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C32×C4—21no—
411C32×C4—22no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3#13512yes—
423C2×#41C2×C3×D311yescharacteristic
424C2×Q16C2×C3×D311yescharacteristic
425C2×SD16—31no—
426C2×SD16C2×C3×D311yescharacteristic
427C2×D8—31no—
428#126—61no—
429#125—31no—
430#124—31no—
431#123—61no—
432C22⋊Q8C2×C3×D311yescharacteristic
433#121—31no—
434C4×Q8—31no—
435C4×Q8—31no—
436C4×Q8—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—61no—
441C4×D4—61no—
442C4×D4—61no—
443#117—31no—
444#117—61no—
445#117—61no—
446C2×C42—31no—
447C2×C42—61no—
448#107—31no—
449#107—31no—
450#106—31no—
451#106—31no—
452C4⋊C8—31no—
453C4⋊C8—31no—
454#103—31no—
455#103—31no—
456#103—31no—
457#103C2×C3×D311yescharacteristic
458#102—31no—
459#102—31no—
460#102—31no—
461#102C2×C3×D311yescharacteristic
462C22⋊C8—31no—
463C22⋊C8C2×C3×D311yescharacteristic
464C4×C8—31no—
465C4×C8—31no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—41no—
470C23×C3—61no—
471C23×C3D3×D411yescharacteristic
472C23×C3C2×C3×D411yescharacteristic
473C22×D3—21no—
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—22no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×Q8#23712yes—
485C3×Q8C3×#4112yes—
486C3×D4—24no—
487C3×D4—24no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—22no—
491C3×D4—41no—
492C3×D4—44no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—122no—
496C3×D4#23712yes—
497C3×D4C3×#4112yes—
498C2×C3×C4—24no—
499C2×C3×C4—24no—
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—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—44no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—62no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—122no—
527C2×C3×C4—122no—
528C2×C3×C4—121no—
529C2×C3×C4—122no—
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4C2×C3×D411yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C24×C311yescharacteristic
534#67—42no—
535C2×Dic3—22no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—41no—
540C2×Dic3—42no—
541C2×Dic3—42no—
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544C2×Dic3C2×C3×D411yescharacteristic
545C2×Dic3C2×C3×D411yescharacteristic
546D12—21no—
547D12—21no—
548C4×D3—42no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—41no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C2×C32—41no—
560C2×C32—42no—
561C2×C32#52511yescharacteristic
562C2×C32C2×#13511yescharacteristic
563C2×C32#57511yescharacteristic
564C3×D3—81no—
565#41—22no—
566#41—22no—
567C2×Q8C22×C3×D311yescharacteristic
568C2×Q8C22×C3×D311yescharacteristic
569C2×D4—21no—
570C2×D4—31no—
571C2×D4—61no—
572C2×D4C22×C3×D311yescharacteristic
573C22×C4—21no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4C22×C3×D311yescharacteristic
580Q16—22no—
581SD16—22no—
582SD16—62no—
583D8—62no—
584C2×C8—31no—
585C2×C8—31no—
586C2×C8C22×C3×D311yescharacteristic
587C2×C8C22×C3×D311yescharacteristic
588C4⋊C4—21no—
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4C22×C3×D311yescharacteristic
598C22⋊C4—21no—
599C22⋊C4—61no—
600C22⋊C4—61no—
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C42—31no—
607C42—31no—
608C42—31no—
609C42—31no—
610C42—61no—
611C42—61no—
612C42—61no—
613C42—61no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—22no—
622C22×C3—21no—
623C22×C3—42no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C22×C3×D411yescharacteristic
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C3×C4—21no—
642C3×C4—22no—
643C3×C4—21no—
644C3×C4—22no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—32no—
648C3×C4—41no—
649C3×C4—42no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—81no—
658C3×C4—81no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4C2×#23711yescharacteristic
663C3×C4C2×#23711yescharacteristic
664C3×C4C2×C3×#4111yescharacteristic
665C3×C4C2×C3×#4111yescharacteristic
666Dic3—21no—
667Dic3—21no—
668Dic3—21no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3C3×#13512yes—
673C32#310211yescharacteristic, complemented, Sylow
674C23—21no—
675C23—61no—
676C23C3×D3×D411yescharacteristic
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8C3×#23712yes—
681D4—24no—
682D4—21no—
683D4—61no—
684D4—61no—
685D4—122no—
686D4C3×#23712yes—
687C2×C4—24no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—62no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—121no—
704C2×C4—122no—
705C2×C4C3×D3×D411yescharacteristic
706C2×C4C23×C3×D311yescharacteristic
707C8—21no—
708C8—21no—
709C8—61no—
710C8—61no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—41no—
715C2×C3—42no—
716C2×C3—41no—
717C2×C3—42no—
718C2×C3—81no—
719C2×C3—82no—
720C2×C3—241no—
721C2×C3#558611yescharacteristic
722C2×C3D3×#13511yescharacteristic
723C2×C3#577711yescharacteristic
724C2×C3C3×#52511yescharacteristic
725C2×C3C2×C3×#13511yescharacteristic
726C2×C3C3×#57511yescharacteristic
727D3—81no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—121no—
735C22—121no—
736C22—121no—
737C22C2×C3×D3×D411yescharacteristic
738C4—21no—
739C4—22no—
740C4—32no—
741C4—41no—
742C4—41no—
743C4—61no—
744C4—61no—
745C4—61no—
746C4—121no—
747C4—121no—
748C4—121no—
749C4C2×C3×#23711yescharacteristic
750C4C2×C3×#23711yescharacteristic
751C3—21no—
752C3#8021211yescharacteristic, direct product factor
753C3C3×#310211yescharacteristic, complemented
754C2—41no—
755C2—42no—
756C2—241no—
757C2C3×#558611yescharacteristic
758C2C3×D3×#13511yescharacteristic
759C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#452C2
socleC22×C32C22×D4
prime radicalC3×#5238C2
hypercenterC3×#452D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
1. C3×Dic3×#41C2semidirect
2. C3×#5624C2semidirect
3. C32×#452C2semidirect
5. C3×#5185C2semidirect
6. C3×Dic3×Q16C2semidirect
7. C3×#5165C2semidirect
8. C3×Dic3×SD16C2semidirect
9. C3×#5045C2semidirect
10. C3×#4799C2semidirect
11. C3×#4788C2semidirect
12. C3×#4766C2semidirect
13. C3×#4756C2semidirect
14. C3×#4737C2semidirect
15. C3×#4718C2semidirect
17. #80212C3direct (N × H)
63. Dic3×#41C2×C3semidirect
64. #5624C2×C3semidirect
72. C3×#452D3semidirect
73. C3×#452C2×C3semidirect
81. #5185C2×C3semidirect
82. Dic3×Q16C2×C3semidirect
83. #5165C2×C3semidirect
84. Dic3×SD16C2×C3semidirect
85. #5045C2×C3semidirect
86. #4799C2×C3semidirect
87. #4788C2×C3semidirect
88. #4766C2×C3semidirect
89. #4756C2×C3semidirect
90. #4737C2×C3semidirect
91. #4718C2×C3semidirect
280. #452C3×D3semidirect
673. C32#3102semidirect
752. C3#80212direct (N × H)
753. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
C3×#56242
C32×#4522
C3×#52382
C3×#51852
C3×Dic3×Q162
C3×#51652
C3×Dic3×SD162
C3×#50452
C3×#47992
C3×#47882
C3×#47662
C3×#47562
C3×#47372
C3×#47182
C3×#31023
#802123