Finite Group Databasebeta

← C3×#80597 #11865745

Subgroups — C3×#80597 #11865745

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic, complemented
2C2×C3×#916C211yesmaximal, characteristic, complemented
3C3×#5668C211yesmaximal, characteristic, complemented
4C3×C4×#239C211yesmaximal, characteristic, complemented
5C32×#464C211yesmaximal, characteristic, complemented
6C3×#5182C211yesmaximal, characteristic, complemented
7C3×#5163C211yesmaximal, characteristic, complemented
8C3×#5057C211yesmaximal, characteristic, complemented
9C3×#5028C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
12C3×#4818C211yesmaximal, characteristic, complemented
13C3×#4804C211yesmaximal, characteristic, complemented
14C3×#4786C211yesmaximal, characteristic, complemented
15C3×#4772C211yesmaximal, characteristic, complemented
16C3×#3035—31nomaximal
17#80597C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C32×#124C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C3×#940C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#919—24no—
33C3×#916—24no—
34C2×C3×D24C2211yescharacteristic
35C2×C3×#204C2211yescharacteristic
36C2×C3×D3×C8C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic
38C3×#893—21no—
39C3×#893C2211yescharacteristic
40C3×#892—21no—
41C3×#892C2211yescharacteristic
42C3×#884—21no—
43C3×#884—21no—
44C3×#67⋊C4—21no—
45C3×#67⋊C4—21no—
46C3×#875C2211yescharacteristic
47C3×C4×D12—21no—
48C3×C4×D12C2211yescharacteristic
49C3×C42×D3—21no—
50C3×C42×D3C2211yescharacteristic
51C32×C4⋊C8C2211yescharacteristic
52C32×#103C2211yescharacteristic
53C32×#102C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#832C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×Dic3⋊C8C2211yescharacteristic
59C3×Dic3⋊C8C2211yescharacteristic
60C3×#810C2211yescharacteristic
61C3×#809C2211yescharacteristic
62C3×C4⋊(C3⋊C8)C2211yescharacteristic
63C2×C3×#135—31no—
64C2×C3×#135—31no—
65C3×#532—31no—
66C3×C4×#41—31no—
67C2×#919C2×C311yescharacteristic, complemented
68C2×#916C2×C311yescharacteristic, complemented
69#5668C2×C311yescharacteristic, complemented
70C4×#239C2×C311yescharacteristic, complemented
71C3×#464—21no—
72C3×#464—31no—
73C3×#464D311yescharacteristic, complemented
74C3×#464C2×C311yescharacteristic, complemented
75C3×#463—31no—
76C3×#463—31no—
77C3×#462—31no—
78C3×#461—31no—
79C3×#460—31no—
80C3×#459—31no—
81C2×C3×C4⋊C8—31no—
82C3×#416—31no—
83C3×#416—31no—
84#5182C2×C311yescharacteristic, complemented
85#5163C2×C311yescharacteristic, complemented
86#5057C2×C311yescharacteristic, complemented
87#5028C2×C311yescharacteristic, complemented
88#4844C2×C311yescharacteristic, complemented
89D3×C4⋊C8C2×C311yescharacteristic, complemented
90#4818C2×C311yescharacteristic, complemented
91#4804C2×C311yescharacteristic, complemented
92#4786C2×C311yescharacteristic, complemented
93#4772C2×C311yescharacteristic, complemented
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#239—22no—
102C3×#239—22no—
103C3×#239—22no—
104C3×#239D414yescomplemented
105C3×#237—22no—
106C3×#237—22no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3D411yescharacteristic
116C2×C3×C4×D3D411yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C32×Q16—22no—
120C32×SD16—22no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2311yescharacteristic
125C32×C22⋊C4—21no—
126C32×C22⋊C4—21no—
127C32×C42—21no—
128C32×C42C2311yescharacteristic
129C3×#216—22no—
130C3×#215—22no—
131C3×#215—22no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×C4×Dic3—21no—
143C3×C4×Dic3—21no—
144C3×C4×Dic3D411yescharacteristic
145C3×C4×Dic3D411yescharacteristic
146C3×C4×Dic3C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149C3×D24—22no—
150C3×#204—22no—
151C3×D3×C8—22no—
152C3×D3×C8—22no—
153#3035—31noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C2×C3×#41—31no—
157C2×#239C22×C311yescharacteristic
158C2×#239C22×C311yescharacteristic
159C2×#237C22×C311yescharacteristic
160C3×#135—64no—
161C3×#135—64no—
162C2×C3×Q16—21no—
163C2×C3×Q16—31no—
164C2×C3×Q16C2×D311yescharacteristic
165C2×C3×Q16C22×C311yescharacteristic
166C2×C3×SD16—21no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16C2×D311yescharacteristic
171C2×C3×SD16C22×C311yescharacteristic
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C22×C3×C8—31no—
176C3×C4⋊Q8—31no—
177C3×#127—31no—
178C3×#124—21no—
179C3×#124—31no—
180C3×#124C2×D311yescharacteristic
181C3×#124C22×C311yescharacteristic
182C3×#121—61no—
183C3×#121—61no—
184C3×C4×Q8—21no—
185C3×C4×Q8—31no—
186C3×C4×Q8C2×D311yescharacteristic
187C3×C4×Q8C22×C311yescharacteristic
188C3×C4×D4—31no—
189C3×C4×D4—31no—
190C3×C4×D4—61no—
191C3×C4×D4—61no—
192C3×C4×D4—61no—
193C3×C4×D4—61no—
194C3×#117—31no—
195C3×#117—61no—
196C2×C3×C42—31no—
197C2×C3×C42—61no—
198Q8×Dic3C22×C311yescharacteristic
199#944C22×C311yescharacteristic
200C2×#216C22×C311yescharacteristic
201C2×#215C22×C311yescharacteristic
202C2×#215C22×C311yescharacteristic
203#940C22×C311yescharacteristic
204C2×#213C22×C311yescharacteristic
205#919—24no—
206#916—24no—
207C2×D24C22×C311yescharacteristic
208C2×#204C22×C311yescharacteristic
209C2×D3×C8C22×C311yescharacteristic
210C2×D3×C8C22×C311yescharacteristic
211#893—21no—
212#893C22×C311yescharacteristic
213#892—21no—
214#892C22×C311yescharacteristic
215#884—21no—
216#884—21no—
217#67⋊C4—21no—
218#67⋊C4—21no—
219#875C22×C311yescharacteristic
220C4×D12—21no—
221C4×D12C22×C311yescharacteristic
222C42×D3—21no—
223C42×D3C22×C311yescharacteristic
224C3×C4⋊C8—21no—
225C3×C4⋊C8—31no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8C2×D311yescharacteristic
229C3×C4⋊C8C22×C311yescharacteristic
230C3×#103—21no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103C2×D311yescharacteristic
235C3×#103C22×C311yescharacteristic
236C3×#102—21no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102C2×D311yescharacteristic
241C3×#102C22×C311yescharacteristic
242#835C22×C311yescharacteristic
243#832C22×C311yescharacteristic
244#821C22×C311yescharacteristic
245#816C22×C311yescharacteristic
246Dic3⋊C8C22×C311yescharacteristic
247Dic3⋊C8C22×C311yescharacteristic
248#810C22×C311yescharacteristic
249#809C22×C311yescharacteristic
250C4⋊(C3⋊C8)C22×C311yescharacteristic
251C23×C32—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C32×Q8—21no—
256C32×Q8—21no—
257C32×Q8—21no—
258C32×Q8C2×D412yes—
259C32×D4—21no—
260C32×D4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267C3×#67—42no—
268C3×#67—42no—
269C3×#67—42no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—42no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—24no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—42no—
281C3×D12C2×D412yes—
282C3×C4×D3—24no—
283C3×C4×D3—22no—
284C3×C4×D3—41no—
285C3×C4×D3—42no—
286C3×C4×D3—42no—
287C3×C4×D3—42no—
288C3×C4×D3C2×D412yes—
289C3×C4×D3#4112yes—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C32×C8—21no—
293C32×C8—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#135—31no—
297C2×#135—31no—
298#532—31no—
299C4×#41—31no—
300#464—31no—
301#464C3×D311yescharacteristic, complemented
302#463—31no—
303#463—31no—
304#462—31no—
305#461—31no—
306#460—31no—
307#459—31no—
308C2×C4⋊C8—31no—
309#416—31no—
310#416—31no—
311C3×#41—34no—
312C3×#41—62no—
313C3×#41—62no—
314C3×#41—62no—
315C3×#41—62no—
316C3×#41—62no—
317C2×C3×Q8—21no—
318C2×C3×Q8—21no—
319C2×C3×Q8—31no—
320C2×C3×Q8C22×D311yescharacteristic
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C23×C311yescharacteristic
323C2×C3×Q8C23×C311yescharacteristic
324C2×C3×D4—21no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C23×C311yescharacteristic
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—21no—
345C22×Dic3—21no—
346#239—22no—
347#239—22no—
348#239—22no—
349#239C3×D414yescomplemented
350#237—22no—
351#237—22no—
352C2×D12—21no—
353C2×D12—21no—
354C2×D12C23×C311yescharacteristic
355C2×D12C23×C311yescharacteristic
356C2×C4×D3—21no—
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3C3×D411yescharacteristic
361C2×C4×D3C3×D411yescharacteristic
362C2×C4×D3C23×C311yescharacteristic
363C2×Dic6C23×C311yescharacteristic
364C3×Q16—22no—
365C3×Q16—22no—
366C3×Q16—42no—
367C3×Q16—62no—
368C3×SD16—22no—
369C3×SD16—22no—
370C3×SD16—42no—
371C3×SD16—62no—
372C3×SD16—62no—
373C3×SD16—62no—
374C3×D8—62no—
375C3×D8—62no—
376C2×C3×C8—21no—
377C2×C3×C8—21no—
378C2×C3×C8—31no—
379C2×C3×C8—31no—
380C2×C3×C8—62no—
381C2×C3×C8—62no—
382C2×C3×C8C22×D311yescharacteristic
383C2×C3×C8C22×D311yescharacteristic
384C2×C3×C8C23×C311yescharacteristic
385C2×C3×C8C23×C311yescharacteristic
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—41no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4C22×D311yescharacteristic
395C3×C4⋊C4C23×C311yescharacteristic
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—41no—
401C3×C22⋊C4—41no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C42—21no—
408C3×C42—21no—
409C3×C42—21no—
410C3×C42—31no—
411C3×C42—31no—
412C3×C42—31no—
413C3×C42—41no—
414C3×C42—61no—
415C3×C42—61no—
416C3×C42C22×D311yescharacteristic
417C3×C42C23×C311yescharacteristic
418#216—22no—
419#215—22no—
420#215—22no—
421#213—22no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427C4⋊Dic3—21no—
428C4⋊Dic3C23×C311yescharacteristic
429Dic3⋊C4—21no—
430Dic3⋊C4—21no—
431C4×Dic3—21no—
432C4×Dic3—21no—
433C4×Dic3C3×D411yescharacteristic
434C4×Dic3C3×D411yescharacteristic
435C4×Dic3C23×C311yescharacteristic
436C2×C3⋊C8C23×C311yescharacteristic
437C2×C3⋊C8C23×C311yescharacteristic
438D24—22no—
439#204—22no—
440D3×C8—22no—
441D3×C8—22no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—22no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455C32×C4—22no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4—41no—
459C32×C4—41no—
460C32×C4C22×D411yescharacteristic
461C32×C4C2×#4111yescharacteristic
462C3×Dic3—21no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C3×Dic3#13512yescomplemented
467C2×#41—31no—
468C2×#41—31no—
469C2×#41—31no—
470#135—64no—
471#135—64no—
472C2×Q16—31no—
473C2×Q16C2×C3×D311yescharacteristic
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16C2×C3×D311yescharacteristic
478C2×D8—31no—
479C2×D8—31no—
480C22×C8—31no—
481C22×C8—31no—
482C4⋊Q8—31no—
483#127—31no—
484#124—31no—
485#124C2×C3×D311yescharacteristic
486#121—61no—
487#121—61no—
488C4×Q8—31no—
489C4×Q8C2×C3×D311yescharacteristic
490C4×D4—31no—
491C4×D4—31no—
492C4×D4—61no—
493C4×D4—61no—
494C4×D4—61no—
495C4×D4—61no—
496#117—31no—
497#117—61no—
498C2×C42—31no—
499C2×C42—61no—
500C4⋊C8—31no—
501C4⋊C8—31no—
502C4⋊C8—31no—
503C4⋊C8C2×C3×D311yescharacteristic
504#103—31no—
505#103—31no—
506#103—31no—
507#103C2×C3×D311yescharacteristic
508#102—31no—
509#102—31no—
510#102—31no—
511#102C2×C3×D311yescharacteristic
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—31no—
515C23×C3—41no—
516C23×C3—61no—
517C23×C3—61no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3C2×C3×D411yescharacteristic
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—22no—
528C3×Q8—41no—
529C3×Q8—41no—
530C3×Q8—41no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×Q8D3×D412yes—
534C3×Q8C2×C3×D412yes—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—21no—
539C3×D4—32no—
540C3×D4—41no—
541C3×D4—41no—
542C3×D4—64no—
543C3×D4—61no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—122no—
547C3×D4—122no—
548C3×D4—122no—
549C3×D4—122no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—31no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—62no—
568C2×C3×C4—64no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—121no—
572C2×C3×C4—122no—
573C2×C3×C4—122no—
574C2×C3×C4—122no—
575C2×C3×C4—122no—
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4D3×D411yescharacteristic
578C2×C3×C4C2×C3×D411yescharacteristic
579C2×C3×C4C2×C3×D411yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C24×C311yescharacteristic
582#67—42no—
583#67—42no—
584#67—42no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—42no—
588C2×Dic3C2×C3×D411yescharacteristic
589C2×Dic3C2×C3×D411yescharacteristic
590C2×Dic3C2×C3×D411yescharacteristic
591D12—24no—
592D12—21no—
593D12—21no—
594D12—21no—
595D12—42no—
596D12C2×C3×D412yes—
597C4×D3—24no—
598C4×D3—22no—
599C4×D3—41no—
600C4×D3—42no—
601C4×D3—42no—
602C4×D3—42no—
603C4×D3C2×C3×D412yes—
604C4×D3C3×#4112yes—
605Dic6—21no—
606Dic6—21no—
607C3×C8—21no—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—41no—
612C3×C8—41no—
613C3×C8—61no—
614C3×C8—61no—
615C3⋊C8—21no—
616C3⋊C8—21no—
617C2×C32—81no—
618C2×C32C2×#12111yescharacteristic
619C2×C32C2×#13511yescharacteristic
620C2×C32#57511yescharacteristic
621C3×D3—22no—
622C3×D3—42no—
623C3×D3—81no—
624#41—34no—
625#41—62no—
626#41—62no—
627#41—62no—
628#41—62no—
629#41—62no—
630C2×Q8—31no—
631C2×Q8C22×C3×D311yescharacteristic
632C2×Q8C22×C3×D311yescharacteristic
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4C22×C3×D311yescharacteristic
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649Q16—22no—
650Q16—62no—
651SD16—22no—
652SD16—62no—
653SD16—62no—
654SD16—62no—
655D8—62no—
656D8—62no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—62no—
660C2×C8—62no—
661C2×C8C22×C3×D311yescharacteristic
662C2×C8C22×C3×D311yescharacteristic
663C4⋊C4—21no—
664C4⋊C4—31no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4C22×C3×D311yescharacteristic
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C42—21no—
677C42—31no—
678C42—31no—
679C42—31no—
680C42—61no—
681C42—61no—
682C42C22×C3×D311yescharacteristic
683C22×C3—21no—
684C22×C3—32no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—62no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C22×C3×D411yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3C3×#12112yes—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—32no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—42no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—61no—
731C3×C4—81no—
732C3×C4—81no—
733C3×C4—121no—
734C3×C4—121no—
735C3×C4C2×D3×D411yescharacteristic
736C3×C4D3×#4111yescharacteristic
737C3×C4C22×C3×D411yescharacteristic
738C3×C4C2×C3×#4111yescharacteristic
739Dic3—21no—
740Dic3—41no—
741Dic3—41no—
742Dic3C3×#12112yes—
743Dic3C3×#13512yescomplemented
744C32#303511yescharacteristic, complemented, Sylow
745C23—21no—
746C23—31no—
747C23—61no—
748C23—61no—
749Q8—21no—
750Q8—21no—
751Q8—21no—
752Q8—61no—
753Q8—61no—
754Q8C3×D3×D412yes—
755D4—21no—
756D4—21no—
757D4—32no—
758D4—64no—
759D4—61no—
760D4—61no—
761D4—61no—
762D4—122no—
763D4—122no—
764D4—122no—
765D4—122no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—31no—
774C2×C4—62no—
775C2×C4—64no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—121no—
779C2×C4—122no—
780C2×C4—122no—
781C2×C4—122no—
782C2×C4—122no—
783C2×C4C3×D3×D411yescharacteristic
784C2×C4C3×D3×D411yescharacteristic
785C2×C4C23×C3×D311yescharacteristic
786C8—21no—
787C8—21no—
788C8—61no—
789C8—61no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—62no—
794C2×C3—81no—
795C2×C3—81no—
796C2×C3—122no—
797C2×C3—161no—
798C2×C3—241no—
799C2×C3D3×#12111yescharacteristic
800C2×C3D3×#13511yescharacteristic
801C2×C3#577711yescharacteristic
802C2×C3C2×C3×#12111yescharacteristic
803C2×C3C2×C3×#13511yescharacteristic
804C2×C3C3×#57511yescharacteristic
805D3—22no—
806D3—42no—
807D3—81no—
808C22—32no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—61no—
813C22—61no—
814C22—62no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22C2×C3×D3×D411yescharacteristic
821C4—21no—
822C4—21no—
823C4—22no—
824C4—32no—
825C4—32no—
826C4—41no—
827C4—41no—
828C4—61no—
829C4—121no—
830C4—121no—
831C4C2×C3×D3×D411yescharacteristic
832C4C3×D3×#4111yescharacteristic
833C3—21no—
834C3#8059711yescharacteristic, direct product factor
835C3C3×#303511yescharacteristic, complemented
836C2—62no—
837C2—81no—
838C2—122no—
839C2—241no—
840C2C3×D3×#12111yescharacteristic
841C2C3×D3×#13511yescharacteristic
842C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#464C2
socleC22×C32C22×D4
hypercenterC3×#464D3
hypocenterC3C3×#3035
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
1. C2×C3×#919C2semidirect
2. C2×C3×#916C2semidirect
3. C3×#5668C2semidirect
4. C3×C4×#239C2semidirect
5. C32×#464C2semidirect
6. C3×#5182C2semidirect
7. C3×#5163C2semidirect
8. C3×#5057C2semidirect
9. C3×#5028C2semidirect
10. C3×#4844C2semidirect
11. C3×D3×C4⋊C8C2semidirect
12. C3×#4818C2semidirect
13. C3×#4804C2semidirect
14. C3×#4786C2semidirect
15. C3×#4772C2semidirect
17. #80597C3direct (N × H)
67. C2×#919C2×C3semidirect
68. C2×#916C2×C3semidirect
69. #5668C2×C3semidirect
70. C4×#239C2×C3semidirect
73. C3×#464D3semidirect
74. C3×#464C2×C3semidirect
84. #5182C2×C3semidirect
85. #5163C2×C3semidirect
86. #5057C2×C3semidirect
87. #5028C2×C3semidirect
88. #4844C2×C3semidirect
89. D3×C4⋊C8C2×C3semidirect
90. #4818C2×C3semidirect
91. #4804C2×C3semidirect
92. #4786C2×C3semidirect
93. #4772C2×C3semidirect
104. C3×#239D4semidirect
301. #464C3×D3semidirect
349. #239C3×D4semidirect
466. C3×Dic3#135semidirect
743. Dic3C3×#135semidirect
744. C32#3035semidirect
834. C3#80597direct (N × H)
835. C3C3×#3035semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
C2×C3×#9162
C3×#56682
C3×C4×#2392
C32×#4642
C3×#51822
C3×#51632
C3×#50572
C3×#50282
C3×#48442
C3×D3×C4⋊C82
C3×#48182
C3×#48042
C3×#47862
C3×#47722
C3×#30353
#805973