Finite Group Databasebeta

← C3×#80604 #11878944

Subgroups — C3×#80604 #11878944

Order 1152.

844 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5668C211yesmaximal, characteristic
2C3×#5578C211yesmaximal, characteristic, complemented
3C32×#464C211yesmaximal, characteristic, complemented
4C3×#5187C211yesmaximal, characteristic, complemented
5C3×#5183C211yesmaximal, characteristic, complemented
6C3×#5175C211yesmaximal, characteristic, complemented
7C3×#5173C211yesmaximal, characteristic, complemented
8C3×#5054C211yesmaximal, characteristic, complemented
9C3×#5028C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4833C211yesmaximal, characteristic, complemented
12C3×#4808C211yesmaximal, characteristic, complemented
13C3×#4792C211yesmaximal, characteristic, complemented
14C3×#4783C211yesmaximal, characteristic, complemented
15C3×#4760C211yesmaximal, characteristic, complemented
16C3×#3210—31nomaximal
17#80604C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C32×#124C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C3×#940C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C2×C3×Dic12C2211yescharacteristic
33C2×C3×#204C2211yescharacteristic
34C3×#897C2211yescharacteristic
35C3×#896—21no—
36C3×#889—21no—
37C3×#888C2211yescharacteristic
38C3×#884—21no—
39C3×#884—21no—
40C3×#67⋊C4—21no—
41C3×#67⋊C4—21no—
42C3×#875C2211yescharacteristic
43C3×#872—21no—
44C3×C42×D3C2211yescharacteristic
45C3×C4×Dic6—21no—
46C3×C4×Dic6C2211yescharacteristic
47C32×C4⋊C8C2211yescharacteristic
48C32×#103C2211yescharacteristic
49C32×#102C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#809C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#533—31no—
62C3×#532—31no—
63#5668C2×C311yescharacteristic
64#5578C2×C311yescharacteristic, complemented
65C3×#494—31no—
66C3×#492—31no—
67C3×#487—31no—
68C3×#486—31no—
69C3×#464—21no—
70C3×#464—31no—
71C3×#464—31no—
72C3×#464—31no—
73C3×#464D311yescharacteristic, complemented
74C3×#464C2×C311yescharacteristic, complemented
75C3×#452—31no—
76C3×#452—31no—
77C3×#452—31no—
78C3×#452—31no—
79C3×#431—31no—
80#5187C2×C311yescharacteristic, complemented
81#5183C2×C311yescharacteristic, complemented
82#5175C2×C311yescharacteristic, complemented
83#5173C2×C311yescharacteristic, complemented
84#5054C2×C311yescharacteristic, complemented
85#5028C2×C311yescharacteristic, complemented
86#4845C2×C311yescharacteristic, complemented
87#4833C2×C311yescharacteristic, complemented
88#4808C2×C311yescharacteristic, complemented
89#4792C2×C311yescharacteristic, complemented
90#4783C2×C311yescharacteristic, complemented
91#4760C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#239—41no—
100C3×#239—41no—
101C3×#237—41no—
102C3×#237—41no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C32×Q16—41no—
113C32×SD16—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C22⋊C4—21no—
120C32×C42—21no—
121C32×C42C2311yescharacteristic
122C3×#216—41no—
123C3×#216—41no—
124C3×#215—41no—
125C3×#214—41no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3D411yescharacteristic
141C3×C4×Dic3D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C3×Dic12—41no—
146C3×#204—41no—
147#3210—31noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×#239C22×C311yescharacteristic
151C2×#237C22×C311yescharacteristic
152C2×C3×Q16—21no—
153C2×C3×Q16—31no—
154C2×C3×Q16—31no—
155C2×C3×Q16—31no—
156C2×C3×Q16C2×D311yescharacteristic
157C2×C3×Q16C22×C311yescharacteristic
158C2×C3×SD16—21no—
159C2×C3×SD16—31no—
160C2×C3×SD16—31no—
161C2×C3×SD16—31no—
162C2×C3×SD16C2×D311yescharacteristic
163C2×C3×SD16C22×C311yescharacteristic
164C3×C4⋊Q8—31no—
165C3×C4⋊Q8—31no—
166C3×C4⋊Q8—31no—
167C3×#127—31no—
168C3×#125—61no—
169C3×#124—21no—
170C3×#124—31no—
171C3×#124C2×D311yescharacteristic
172C3×#124C22×C311yescharacteristic
173C3×C22⋊Q8—31no—
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—61no—
176C3×#121—61no—
177C3×#121—61no—
178C3×C4×Q8—21no—
179C3×C4×Q8—31no—
180C3×C4×Q8—61no—
181C3×C4×Q8C2×D311yescharacteristic
182C3×C4×Q8C22×C311yescharacteristic
183C3×C4×D4—61no—
184C3×C4×D4—61no—
185C3×#117—61no—
186C2×C3×C42—31no—
187#946C22×C311yescharacteristic
188#944C22×C311yescharacteristic
189#944C22×C311yescharacteristic
190C2×#216C22×C311yescharacteristic
191C2×#216C22×C311yescharacteristic
192C2×#215C22×C311yescharacteristic
193#940C22×C311yescharacteristic
194C2×#214C22×C311yescharacteristic
195C2×Dic12C22×C311yescharacteristic
196C2×#204C22×C311yescharacteristic
197#897C22×C311yescharacteristic
198#896—21no—
199#889—21no—
200#888C22×C311yescharacteristic
201#884—21no—
202#884—21no—
203#67⋊C4—21no—
204#67⋊C4—21no—
205#875C22×C311yescharacteristic
206#872—21no—
207C42×D3C22×C311yescharacteristic
208C4×Dic6—21no—
209C4×Dic6C22×C311yescharacteristic
210C3×C4⋊C8—21no—
211C3×C4⋊C8—31no—
212C3×C4⋊C8C2×D311yescharacteristic
213C3×C4⋊C8C22×C311yescharacteristic
214C3×#103—21no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103C2×D311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×#102—21no—
221C3×#102—31no—
222C3×#102—31no—
223C3×#102—31no—
224C3×#102C2×D311yescharacteristic
225C3×#102C22×C311yescharacteristic
226C3×C22⋊C8—31no—
227C3×C22⋊C8—31no—
228C3×C4×C8—31no—
229C3×C4×C8—31no—
230#835C22×C311yescharacteristic
231#832C22×C311yescharacteristic
232#821C22×C311yescharacteristic
233(C2×D3)⋊C8C22×C311yescharacteristic
234(C2×D3)⋊C8C22×C311yescharacteristic
235#816C22×C311yescharacteristic
236C8×Dic3C22×C311yescharacteristic
237C8×Dic3C22×C311yescharacteristic
238#810C22×C311yescharacteristic
239#809C22×C311yescharacteristic
240C4⋊(C3⋊C8)C22×C311yescharacteristic
241C23×C32—21no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67—42no—
257C3×#67—42no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—22no—
272C3×C4×D3—22no—
273C3×C4×D3—42no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278C3×Dic6—42no—
279C32×C8—21no—
280C32×C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#533—31no—
284#532—31no—
285#494—31no—
286#492—31no—
287#487—31no—
288#486—31no—
289#464—31no—
290#464—31no—
291#464—31no—
292#464C3×D311yescharacteristic, complemented
293#452—31no—
294#452—31no—
295#452—31no—
296#452—31no—
297#431—31no—
298C3×#41—121no—
299C3×#41—121no—
300C3×#41—121no—
301C3×#41—121no—
302C2×C3×Q8—21no—
303C2×C3×Q8—21no—
304C2×C3×Q8—31no—
305C2×C3×Q8—31no—
306C2×C3×Q8—61no—
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C23×C311yescharacteristic
310C2×C3×Q8C23×C311yescharacteristic
311C2×C3×D4—21no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C23×C311yescharacteristic
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C2×#67—21no—
325C2×#67—21no—
326C2×#67—21no—
327C22×Dic3—21no—
328#239—41no—
329#239—41no—
330#237—41no—
331#237—41no—
332C2×D12—21no—
333C2×D12C23×C311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3C3×D411yescharacteristic
336C2×C4×D3C3×D411yescharacteristic
337C2×C4×D3C23×C311yescharacteristic
338C2×Dic6—21no—
339C2×Dic6C23×C311yescharacteristic
340C2×Dic6C23×C311yescharacteristic
341C3×Q16—41no—
342C3×Q16—41no—
343C3×Q16—42no—
344C3×Q16—121no—
345C3×Q16—121no—
346C3×Q16—121no—
347C3×SD16—41no—
348C3×SD16—41no—
349C3×SD16—42no—
350C3×SD16—121no—
351C3×SD16—121no—
352C3×SD16—121no—
353C2×C3×C8—21no—
354C2×C3×C8—21no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C23×C311yescharacteristic
360C2×C3×C8C23×C311yescharacteristic
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—41no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C23×C311yescharacteristic
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—21no—
380C3×C22⋊C4—41no—
381C3×C22⋊C4—41no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C42—21no—
387C3×C42—21no—
388C3×C42—21no—
389C3×C42—31no—
390C3×C42—31no—
391C3×C42—31no—
392C3×C42—41no—
393C3×C42—61no—
394C3×C42C22×D311yescharacteristic
395C3×C42C23×C311yescharacteristic
396#216—41no—
397#216—41no—
398#215—41no—
399#214—41no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404C4⋊Dic3—21no—
405C4⋊Dic3C23×C311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—21no—
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413C4×Dic3—21no—
414C4×Dic3C3×D411yescharacteristic
415C4×Dic3C3×D411yescharacteristic
416C4×Dic3C23×C311yescharacteristic
417C2×C3⋊C8C23×C311yescharacteristic
418C2×C3⋊C8C23×C311yescharacteristic
419Dic12—41no—
420#204—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32C22×D411yescharacteristic
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4—41no—
435C32×C4—41no—
436C32×C4H(5,𝔽2)11yescharacteristic
437C32×C4H(5,𝔽2)11yescharacteristic
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3#13512yes—
443C3×Dic3#13712yes—
444C2×#41—31no—
445C2×#41—31no—
446C2×Q16—31no—
447C2×Q16—31no—
448C2×Q16—31no—
449C2×Q16C2×C3×D311yescharacteristic
450C2×SD16—31no—
451C2×SD16—31no—
452C2×SD16—31no—
453C2×SD16C2×C3×D311yescharacteristic
454C4⋊Q8—31no—
455C4⋊Q8—31no—
456C4⋊Q8—31no—
457#127—31no—
458#125—61no—
459#124—31no—
460#124C2×C3×D311yescharacteristic
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463C22⋊Q8—61no—
464#121—61no—
465#121—61no—
466C4×Q8—31no—
467C4×Q8—61no—
468C4×Q8C2×C3×D311yescharacteristic
469C4×D4—61no—
470C4×D4—61no—
471#117—61no—
472C2×C42—31no—
473C4⋊C8—31no—
474C4⋊C8C2×C3×D311yescharacteristic
475#103—31no—
476#103—31no—
477#103—31no—
478#103C2×C3×D311yescharacteristic
479#102—31no—
480#102—31no—
481#102—31no—
482#102C2×C3×D311yescharacteristic
483C22⋊C8—31no—
484C22⋊C8—31no—
485C4×C8—31no—
486C4×C8—31no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—61no—
492C22×D3—21no—
493C22×D3C2×C3×D411yescharacteristic
494C3×Q8—22no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—41no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×Q8—61no—
507C3×Q8—61no—
508C3×Q8—61no—
509C3×Q8—61no—
510C3×Q8—122no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—122no—
520C3×D4—122no—
521C3×D4—122no—
522C3×D4—122no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—62no—
539C2×C3×C4—62no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—122no—
546C2×C3×C4—122no—
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4C2×C3×D411yescharacteristic
550C2×C3×C4C2×C3×D411yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C24×C311yescharacteristic
553#67—42no—
554#67—42no—
555#67—42no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—42no—
560C2×Dic3C2×C3×D411yescharacteristic
561C2×Dic3C2×C3×D411yescharacteristic
562C2×Dic3C2×C3×D411yescharacteristic
563D12—21no—
564D12—21no—
565D12—42no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—22no—
569C4×D3—22no—
570C4×D3—42no—
571Dic6—21no—
572Dic6—21no—
573Dic6—21no—
574Dic6—21no—
575Dic6—42no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—21no—
580C3×C8—41no—
581C3×C8—41no—
582C3×C8—61no—
583C3×C8—61no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C2×C32—81no—
587C2×C32#53511yescharacteristic
588C2×C32C2×#13511yescharacteristic
589C2×C32C2×#13711yescharacteristic
590C3×D3—41no—
591C3×D3—81no—
592#41—121no—
593#41—121no—
594#41—121no—
595#41—121no—
596C2×Q8—31no—
597C2×Q8—31no—
598C2×Q8—61no—
599C2×Q8C22×C3×D311yescharacteristic
600C2×Q8C22×C3×D311yescharacteristic
601C2×D4—31no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4C22×C3×D311yescharacteristic
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—61no—
611C22×C4—61no—
612Q16—41no—
613Q16—121no—
614Q16—121no—
615Q16—121no—
616SD16—41no—
617SD16—121no—
618SD16—121no—
619SD16—121no—
620C2×C8—31no—
621C2×C8—31no—
622C2×C8C22×C3×D311yescharacteristic
623C2×C8C22×C3×D311yescharacteristic
624C4⋊C4—21no—
625C4⋊C4—31no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4C22×C3×D311yescharacteristic
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C42—21no—
642C42—31no—
643C42—31no—
644C42—31no—
645C42—61no—
646C42C22×C3×D311yescharacteristic
647C22×C3—21no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C22×C3×D411yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—32no—
678C3×C4—32no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—42no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—81no—
690C3×C4—81no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4#100411yescharacteristic
695C3×C4#100911yescharacteristic
696C3×C4C3×H(5,𝔽2)11yescharacteristic
697C3×C4C3×H(5,𝔽2)11yescharacteristic
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3C3×#13512yes—
703Dic3C3×#13712yes—
704C32#321011yescharacteristic, complemented, Sylow
705C23—21no—
706C23—31no—
707C23—61no—
708Q8—21no—
709Q8—21no—
710Q8—21no—
711Q8—21no—
712Q8—61no—
713Q8—61no—
714Q8—61no—
715Q8—61no—
716Q8—122no—
717D4—21no—
718D4—21no—
719D4—61no—
720D4—61no—
721D4—122no—
722D4—122no—
723D4—122no—
724D4—122no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4C3×D3×D411yescharacteristic
741C2×C4C3×D3×D411yescharacteristic
742C2×C4C23×C3×D311yescharacteristic
743C8—21no—
744C8—21no—
745C8—61no—
746C8—61no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—81no—
751C2×C3—81no—
752C2×C3—121no—
753C2×C3—161no—
754C2×C3—241no—
755C2×C3#560711yescharacteristic
756C2×C3D3×#13511yescharacteristic
757C2×C3D3×#13711yescharacteristic
758C2×C3C3×#53511yescharacteristic
759C2×C3C2×C3×#13511yescharacteristic
760C2×C3C2×C3×#13711yescharacteristic
761D3—41no—
762D3—81no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22C2×C3×D3×D411yescharacteristic
773C4—21no—
774C4—21no—
775C4—32no—
776C4—32no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—61no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4C3×#100411yescharacteristic
785C4C3×#100911yescharacteristic
786C3—21no—
787C3#8060411yescharacteristic, direct product factor
788C3C3×#321011yescharacteristic, complemented
789C2—81no—
790C2—121no—
791C2—241no—
792C2C3×#560711yescharacteristic
793C2C3×D3×#13511yescharacteristic
794C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#464C2
socleC22×C32C22×D4
prime radicalC3×#5668C2
hypercenterC3×#464D3
hypocenterC3C3×#3210
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#464

Complements

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

NH ≅ G/Ntype
2. C3×#5578C2semidirect
3. C32×#464C2semidirect
4. C3×#5187C2semidirect
5. C3×#5183C2semidirect
6. C3×#5175C2semidirect
7. C3×#5173C2semidirect
8. C3×#5054C2semidirect
9. C3×#5028C2semidirect
10. C3×#4845C2semidirect
11. C3×#4833C2semidirect
12. C3×#4808C2semidirect
13. C3×#4792C2semidirect
14. C3×#4783C2semidirect
15. C3×#4760C2semidirect
17. #80604C3direct (N × H)
64. #5578C2×C3semidirect
73. C3×#464D3semidirect
74. C3×#464C2×C3semidirect
80. #5187C2×C3semidirect
81. #5183C2×C3semidirect
82. #5175C2×C3semidirect
83. #5173C2×C3semidirect
84. #5054C2×C3semidirect
85. #5028C2×C3semidirect
86. #4845C2×C3semidirect
87. #4833C2×C3semidirect
88. #4808C2×C3semidirect
89. #4792C2×C3semidirect
90. #4783C2×C3semidirect
91. #4760C2×C3semidirect
292. #464C3×D3semidirect
704. C32#3210semidirect
787. C3#80604direct (N × H)
788. C3C3×#3210semidirect

Maximal subgroups

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

subgroupindex
C3×#56682
C3×#55782
C32×#4642
C3×#51872
C3×#51832
C3×#51752
C3×#51732
C3×#50542
C3×#50282
C3×#48452
C3×#48332
C3×#48082
C3×#47922
C3×#47832
C3×#47602
C3×#32103
#806043