Finite Group Databasebeta

← C3×#10594524 #13173941

Subgroups — C3×#10594524 #13173941

Order 1728.

1532 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3799C211yesmaximal, characteristic, complemented
2C2×C3×#3796C211yesmaximal, characteristic, complemented
3C3×#64104C211yesmaximal, characteristic, complemented
4C32×#895C211yesmaximal, characteristic, complemented
5C32×#887C211yesmaximal, characteristic, complemented
6C3×#63911C211yesmaximal, characteristic, complemented
7C3×#63911C212yesmaximal, complemented
8C3×#63910C212yesmaximal, complemented
9C3×C4×#626C211yesmaximal, characteristic, complemented
10C3×#63886C212yesmaximal, complemented
11C3×#63880C212yesmaximal, complemented
12C3×#5599—31nomaximal
13C3×#5577—31nomaximal
14#10594524C311yesmaximal, characteristic, direct product factor
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×D12C2211yescharacteristic
19C2×C32×D12C2212yes—
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×Dic6C2211yescharacteristic
22C2×C3×#626C2212yes—
23C2×C3×#626C2212yes—
24C2×C3×#626C2211yescharacteristic
25C2×C3×#626C2212yes—
26C2×C3×#626C2212yes—
27C2×C3×#624C2212yes—
28C2×C3×D3×Dic3C2212yes—
29C3×#3799—24no—
30C3×#3796—24no—
31C33×C4⋊C4C2211yescharacteristic
32C3×#3752C2212yes—
33C32×(C2×D3)⋊C4C2212yes—
34C32×Dic3⋊C4C2212yes—
35C32×C4×Dic3C2212yes—
36C32×C4×Dic3C2211yescharacteristic
37C3×Dic3⋊Dic3C2211yescharacteristic
38C3×#3722C2211yescharacteristic
39C3×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×C3×#239—31no—
41C2×C3×#239—31no—
42C2×C3×#237—31no—
43C2×C3×#235—31no—
44C2×#3799C2×C311yescharacteristic, complemented
45C2×#3796C2×C311yescharacteristic, complemented
46C32×#121—31no—
47C32×C4×Q8—31no—
48#64104C2×C311yescharacteristic, complemented
49C3×#940—32no—
50C3×#940—31no—
51C3×#939—32no—
52C3×C4×#67—31no—
53C3×#895—21no—
54C3×#895—32no—
55C3×#895—31no—
56C3×#895—31no—
57C3×#895—32no—
58C3×#895—61no—
59C3×#895D311yescharacteristic, complemented
60C3×#895C2×C311yescharacteristic, complemented
61C3×#887—21no—
62C3×#887D311yescharacteristic, complemented
63C3×#887C2×C311yescharacteristic, complemented
64C3×#884—32no—
65C3×#67⋊C4—32no—
66C3×#874—32no—
67C3×#874—31no—
68C3×C4×D12—31no—
69C3×C4×D12—32no—
70#63911C2×C312yescomplemented
71#63911C2×C311yescharacteristic, complemented
72#63910C2×C312yescomplemented
73C4×#626C2×C311yescharacteristic, complemented
74#63886C2×C312yescomplemented
75#63880C2×C312yescomplemented
76C22×C3×C3⋊D3C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3C2312yes—
79C22×C32×D3C2311yescharacteristic
80C2×C33×C4C2312yes—
81C2×C33×C4C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4⋊(C3⋊D3)—22no—
84C3×C4⋊(C3⋊D3)—42no—
85C3×C4×C3⋊D3—22no—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2311yescharacteristic
90C32×D12—22no—
91C32×D12—42no—
92C32×C4×D3—22no—
93C32×Dic6D414yescomplemented
94C3×#626—24no—
95C3×#626—24no—
96C3×#626—24no—
97C3×#626—22no—
98C3×#626—42no—
99C3×#624—24no—
100C3×D3×Dic3—24no—
101C3×#550—91no—
102#5599—31no—
103#5577—31no—
104C2×C32×Q8—31no—
105C2×C32×D4—31no—
106C2×C32×D4—32no—
107C22×C32×C4—31no—
108C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
109C2×C4⋊(C3⋊D3)C22×C312yes—
110C2×C4×C3⋊D3C22×C311yescharacteristic
111C2×C3×#67—32no—
112C2×C3×#67—32no—
113C2×C3×#67—31no—
114C2×C3×#67—32no—
115C2×C3×#67—32no—
116C22×C3×Dic3—32no—
117C3×#239—64no—
118C3×#239—64no—
119C3×#237—64no—
120C3×#235—64no—
121C2×C3×D12—21no—
122C2×C3×D12—22no—
123C2×C3×D12—32no—
124C2×C3×D12—32no—
125C2×C3×D12—31no—
126C2×C3×D12—32no—
127C2×C3×D12—31no—
128C2×C3×D12—31no—
129C2×C3×D12—32no—
130C2×C3×D12—32no—
131C2×C3×D12—32no—
132C2×C3×D12—61no—
133C2×C3×D12—62no—
134C2×C3×D12C2×D311yescharacteristic
135C2×C3×D12C2×D312yes—
136C2×C3×D12C22×C311yescharacteristic
137C2×C3×D12C22×C312yes—
138C2×C3×C4×D3—21no—
139C2×C3×C4×D3—32no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—32no—
143C2×C3×C4×D3—32no—
144C2×C3×C4×D3—61no—
145C2×C3×C4×D3C2×D311yescharacteristic
146C2×C3×C4×D3C22×C311yescharacteristic
147C2×C3×Dic6—21no—
148C2×C3×Dic6C2×D311yescharacteristic
149C2×C3×Dic6C22×C311yescharacteristic
150C2×#626C22×C312yes—
151C2×#626C22×C312yes—
152C2×#626C22×C312yes—
153C2×#626C22×C311yescharacteristic
154C2×#626C22×C312yes—
155C2×#624C22×C312yes—
156C2×D3×Dic3C22×C312yes—
157#3799—24no—
158#3796—24no—
159C32×C4⋊C4—21no—
160C32×C4⋊C4—21no—
161C32×C4⋊C4—21no—
162C32×C4⋊C4—32no—
163C32×C4⋊C4—41no—
164C32×C4⋊C4C2×D311yescharacteristic
165C32×C4⋊C4C2×D311yescharacteristic
166C32×C4⋊C4C22×C311yescharacteristic
167C32×C22⋊C4—32no—
168C32×C42—32no—
169C32×C42—31no—
170#3752C22×C312yes—
171C3×#217—31no—
172C3×(C2×D3)⋊C4—22no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—32no—
175C3×(C2×D3)⋊C4—32no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—62no—
179C3×(C2×D3)⋊C4C2×D312yes—
180C3×(C2×D3)⋊C4C22×C312yes—
181C3×C4⋊Dic3—31no—
182C3×Dic3⋊C4—22no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4C2×D312yes—
185C3×Dic3⋊C4C22×C312yes—
186C3×C4×Dic3—22no—
187C3×C4×Dic3—21no—
188C3×C4×Dic3C2×D312yes—
189C3×C4×Dic3C2×D311yescharacteristic
190C3×C4×Dic3C22×C312yes—
191C3×C4×Dic3C22×C311yescharacteristic
192Dic3⋊Dic3C22×C311yescharacteristic
193#3722C22×C311yescharacteristic
194(C2×D3)⋊Dic3C22×C311yescharacteristic
195C22×C33C2411yescharacteristic
196C2×C3×C3⋊D3—22no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—22no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—22no—
202C2×C32×D3—22no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—22no—
206C2×C32×D3—21no—
207C2×C32×D3—22no—
208C33×C4—22no—
209C33×C4C2×D412yes—
210C3×C3⋊Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3C2×D414yes—
214C32×Dic3#4112yescomplemented
215C2×C3×#41—91no—
216C2×C3×#41—91no—
217C2×#239—31no—
218C2×#239—31no—
219C2×#237—31no—
220C2×#235—31no—
221C3×#127—91no—
222C3×#127—92no—
223C3×#121—31no—
224C3×#121—31no—
225C3×#121—61no—
226C3×#121—92no—
227C3×#121—92no—
228C3×#121—91no—
229C3×C4×Q8—31no—
230C3×C4×Q8—31no—
231C3×C4×Q8—61no—
232C3×C4×D4—92no—
233C3×C4×D4—91no—
234#940—32no—
235#940—31no—
236#939—32no—
237C4×#67—31no—
238#895—32no—
239#895—31no—
240#895—31no—
241#895—32no—
242#895—61no—
243#895C3×D311yescharacteristic, complemented
244#887C3×D311yescharacteristic, complemented
245#884—32no—
246#67⋊C4—32no—
247#874—32no—
248#874—31no—
249C4×D12—31no—
250C4×D12—32no—
251C23×C32—31no—
252C23×C32—32no—
253C22×C3⋊D3C23×C311yescharacteristic
254C22×C3⋊D3C23×C312yes—
255C22×C3×D3—21no—
256C22×C3×D3—22no—
257C22×C3×D3—32no—
258C22×C3×D3—31no—
259C22×C3×D3—32no—
260C22×C3×D3—31no—
261C22×C3×D3—61no—
262C22×C3×D3—62no—
263C22×C3×D3C22×D311yescharacteristic
264C22×C3×D3C22×D312yes—
265C22×C3×D3C23×C311yescharacteristic
266C22×C3×D3C23×C312yes—
267C32×Q8—34no—
268C32×D4—62no—
269C32×D4—122no—
270C2×C32×C4—21no—
271C2×C32×C4—22no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—22no—
275C2×C32×C4—22no—
276C2×C32×C4—31no—
277C2×C32×C4—32no—
278C2×C32×C4—31no—
279C2×C32×C4—31no—
280C2×C32×C4—41no—
281C2×C32×C4—42no—
282C2×C32×C4—62no—
283C2×C32×C4C22×D312yes—
284C2×C32×C4C22×D312yes—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C23×C312yes—
288C2×C32×C4C23×C311yescharacteristic
289C2×C3⋊Dic3C23×C311yescharacteristic
290C4⋊(C3⋊D3)—22no—
291C4⋊(C3⋊D3)—42no—
292C4×C3⋊D3—22no—
293C3×#67—64no—
294C3×#67—64no—
295C3×#67—64no—
296C3×#67—62no—
297C3×#67—122no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—61no—
305C2×C3×Dic3—64no—
306C2×C3×Dic3C22×D311yescharacteristic
307C2×C3×Dic3C22×D311yescharacteristic
308C2×C3×Dic3C22×D312yes—
309C2×C3×Dic3C22×D311yescharacteristic
310C2×C3×Dic3C23×C311yescharacteristic
311C2×C3×Dic3C23×C311yescharacteristic
312C2×C3×Dic3C23×C312yes—
313C2×C3×Dic3C23×C311yescharacteristic
314C3×D12—22no—
315C3×D12—22no—
316C3×D12—42no—
317C3×D12—42no—
318C3×D12—42no—
319C3×D12—44no—
320C3×D12—62no—
321C3×D12—64no—
322C3×D12—64no—
323C3×D12—64no—
324C3×D12—62no—
325C3×D12—62no—
326C3×D12—122no—
327C3×D12—122no—
328C3×D12—122no—
329C3×D12—124no—
330C3×D12—122no—
331C3×C4×D3—22no—
332C3×C4×D3—22no—
333C3×C4×D3—42no—
334C3×C4×D3—64no—
335C3×C4×D3—64no—
336C3×C4×D3—62no—
337C3×C4×D3—62no—
338C3×C4×D3—64no—
339C3×C4×D3—122no—
340C3×Dic6—24no—
341C3×Dic6D1214yescomplemented
342C3×Dic6C3×D414yescomplemented
343#626—24no—
344#626—24no—
345#626—24no—
346#626—22no—
347#626—42no—
348#624—24no—
349D3×Dic3—24no—
350#550—91noSylow
351C2×C33C22×D411yescharacteristic
352C2×C33C2×#4111yescharacteristic
353C2×C33H(5,𝔽2)11yescharacteristic
354C3×C3⋊D3—41no—
355C3×C3⋊D3—42no—
356C32×D3—41no—
357C32×D3—42no—
358C3×#41—184no—
359C3×#41—184no—
360C2×C3×Q8—31no—
361C2×C3×Q8—31no—
362C2×C3×Q8—61no—
363C2×C3×D4—31no—
364C2×C3×D4—32no—
365C2×C3×D4—31no—
366C2×C3×D4—32no—
367C2×C3×D4—61no—
368C2×C3×D4—62no—
369C2×C3×D4—92no—
370C2×C3×D4—91no—
371C2×C3×D4—92no—
372C2×C3×D4—92no—
373C2×C3×D4—92no—
374C2×C3×D4—91no—
375C2×C3×D4—92no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—61no—
379C22×C3×C4—92no—
380C22×C3×C4—92no—
381C22×C3×C4—91no—
382C2×#67—32no—
383C2×#67—32no—
384C2×#67—31no—
385C2×#67—32no—
386C2×#67—32no—
387C22×Dic3—32no—
388#239—64no—
389#239—64no—
390#237—64no—
391#235—64no—
392C2×D12—31no—
393C2×D12—32no—
394C2×D12—32no—
395C2×D12—32no—
396C2×D12—31no—
397C2×D12—31no—
398C2×D12—32no—
399C2×D12—32no—
400C2×D12—32no—
401C2×D12—61no—
402C2×D12—62no—
403C2×D12C2×C3×D311yescharacteristic
404C2×D12C2×C3×D312yes—
405C2×C4×D3—32no—
406C2×C4×D3—31no—
407C2×C4×D3—31no—
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—61no—
411C2×C4×D3C2×C3×D311yescharacteristic
412C2×Dic6C2×C3×D311yescharacteristic
413C3×C4⋊C4—21no—
414C3×C4⋊C4—21no—
415C3×C4⋊C4—21no—
416C3×C4⋊C4—32no—
417C3×C4⋊C4—32no—
418C3×C4⋊C4—41no—
419C3×C4⋊C4—62no—
420C3×C4⋊C4—91no—
421C3×C4⋊C4D3211yescharacteristic
422C3×C4⋊C4C2×C3×D311yescharacteristic
423C3×C4⋊C4C2×C3×D311yescharacteristic
424C3×C22⋊C4—32no—
425C3×C22⋊C4—32no—
426C3×C22⋊C4—62no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4—91no—
429C3×C22⋊C4—92no—
430C3×C42—32no—
431C3×C42—31no—
432C3×C42—32no—
433C3×C42—31no—
434C3×C42—61no—
435C3×C42—62no—
436#217—31no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—32no—
439(C2×D3)⋊C4—32no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—31no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4C2×C3×D312yes—
444C4⋊Dic3—31no—
445Dic3⋊C4—31no—
446Dic3⋊C4C2×C3×D312yes—
447C4×Dic3C2×C3×D312yes—
448C4×Dic3C2×C3×D311yescharacteristic
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—41no—
453C22×C32—61no—
454C22×C32—62no—
455C22×C32—61no—
456C22×C32—61no—
457C22×C32—62no—
458C22×C32—62no—
459C22×C32C23×D311yescharacteristic
460C22×C32C23×D311yescharacteristic
461C22×C32C24×C311yescharacteristic
462C2×C3⋊D3—21no—
463C2×C3⋊D3—22no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—21no—
470C2×C3×D3—22no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—21no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—21no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—42no—
484C2×C3×D3—42no—
485C2×C3×D3—42no—
486C2×C3×D3—62no—
487C2×C3×D3—62no—
488C2×C3×D3—61no—
489C2×C3×D3—62no—
490C2×C3×D3—61no—
491C2×C3×D3—61no—
492C2×C3×D3—62no—
493C2×C3×D3—61no—
494C2×C3×D3—62no—
495C2×C3×D3—61no—
496C2×C3×D3—62no—
497C2×C3×D3—61no—
498C2×C3×D3—62no—
499C2×C3×D3—121no—
500C2×C3×D3—121no—
501C2×C3×D3—122no—
502C2×C3×D3—122no—
503C2×C3×D3—122no—
504C32×C4—22no—
505C32×C4—22no—
506C32×C4—22no—
507C32×C4—22no—
508C32×C4—22no—
509C32×C4—22no—
510C32×C4—34no—
511C32×C4—32no—
512C32×C4—42no—
513C32×C4—42no—
514C32×C4—42no—
515C32×C4—42no—
516C32×C4—61no—
517C32×C4—61no—
518C32×C4—82no—
519C32×C4C2×D1212yes—
520C32×C4D3×D412yes—
521C32×C4C2×C3×D412yes—
522C3⋊Dic3—21no—
523C3×Dic3—21no—
524C3×Dic3—21no—
525C3×Dic3—21no—
526C3×Dic3—21no—
527C3×Dic3—24no—
528C3×Dic3—22no—
529C3×Dic3—41no—
530C3×Dic3—41no—
531C3×Dic3—61no—
532C3×Dic3—61no—
533C3×Dic3—121no—
534C3×Dic3C2×D1214yes—
535C3×Dic3#23912yescomplemented
536C3×Dic3C2×C3×D414yes—
537C3×Dic3C3×#4112yescomplemented
538C2×#41—91no—
539C2×#41—91no—
540#127—91no—
541#127—92no—
542#121—31no—
543#121—92no—
544#121—92no—
545#121—91no—
546C4×Q8—31no—
547C4×D4—92no—
548C4×D4—91no—
549C33#55011yescharacteristic, complemented, Sylow
550C23×C3—32no—
551C23×C3—31no—
552C23×C3—31no—
553C23×C3—32no—
554C23×C3—61no—
555C23×C3—62no—
556C23×C3—91no—
557C23×C3—92no—
558C22×D3—31no—
559C22×D3—32no—
560C22×D3—32no—
561C22×D3—31no—
562C22×D3—61no—
563C22×D3—62no—
564C22×D3C22×C3×D311yescharacteristic
565C22×D3C22×C3×D312yes—
566C3×Q8—34no—
567C3×Q8—34no—
568C3×Q8—64no—
569C3×D4—62no—
570C3×D4—62no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—124no—
575C3×D4—184no—
576C3×D4—182no—
577C3×D4—184no—
578C3×D4—184no—
579C3×D4—182no—
580C3×D4—362no—
581C3×D4—362no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—31no—
589C2×C3×C4—32no—
590C2×C3×C4—31no—
591C2×C3×C4—32no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—41no—
597C2×C3×C4—42no—
598C2×C3×C4—61no—
599C2×C3×C4—62no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—62no—
603C2×C3×C4—62no—
604C2×C3×C4—91no—
605C2×C3×C4—122no—
606C2×C3×C4—184no—
607C2×C3×C4—184no—
608C2×C3×C4—182no—
609C2×C3×C4C2×D3212yes—
610C2×C3×C4C2×D3211yescharacteristic
611C2×C3×C4C22×C3×D312yes—
612C2×C3×C4C22×C3×D312yes—
613C2×C3×C4C22×C3×D311yescharacteristic
614C2×C3×C4C22×C3×D311yescharacteristic
615#67—64no—
616#67—64no—
617#67—64no—
618#67—62no—
619#67—122no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—61no—
623C2×Dic3—64no—
624C2×Dic3C22×C3×D311yescharacteristic
625C2×Dic3C22×C3×D311yescharacteristic
626C2×Dic3C22×C3×D312yes—
627C2×Dic3C22×C3×D311yescharacteristic
628D12—22no—
629D12—42no—
630D12—62no—
631D12—64no—
632D12—64no—
633D12—64no—
634D12—62no—
635D12—62no—
636D12—122no—
637D12—122no—
638D12—122no—
639D12—124no—
640D12—122no—
641C4×D3—22no—
642C4×D3—64no—
643C4×D3—64no—
644C4×D3—62no—
645C4×D3—62no—
646C4×D3—64no—
647C4×D3—122no—
648Dic6C3×D1214yescomplemented
649C2×C32—21no—
650C2×C32—21no—
651C2×C32—21no—
652C2×C32—21no—
653C2×C32—21no—
654C2×C32—21no—
655C2×C32—21no—
656C2×C32—21no—
657C2×C32—21no—
658C2×C32—41no—
659C2×C32—41no—
660C2×C32—41no—
661C2×C32—121no—
662C2×C32—122no—
663C2×C32C22×D1211yescharacteristic
664C2×C32C2×D3×D411yescharacteristic
665C2×C32#100411yescharacteristic
666C2×C32C2×#23911yescharacteristic
667C2×C32D3×#4111yescharacteristic
668C2×C32#100911yescharacteristic
669C2×C32C22×C3×D411yescharacteristic
670C2×C32C2×C3×#4111yescharacteristic
671C2×C32C3×H(5,𝔽2)11yescharacteristic
672C3⋊D3—41no—
673C3⋊D3—42no—
674C3×D3—42no—
675C3×D3—41no—
676C3×D3—42no—
677C3×D3—41no—
678C3×D3—42no—
679C3×D3—82no—
680C3×D3—122no—
681C3×D3—121no—
682C3×D3—122no—
683C3×D3—121no—
684C3×D3—122no—
685C3×D3—242no—
686#41—184no—
687#41—184no—
688C2×Q8—31no—
689C2×D4—31no—
690C2×D4—32no—
691C2×D4—92no—
692C2×D4—91no—
693C2×D4—92no—
694C2×D4—92no—
695C2×D4—92no—
696C2×D4—91no—
697C2×D4—92no—
698C22×C4—31no—
699C22×C4—92no—
700C22×C4—92no—
701C22×C4—91no—
702C4⋊C4—32no—
703C4⋊C4—91no—
704C4⋊C4C3×D3211yescharacteristic
705C22⋊C4—32no—
706C22⋊C4—91no—
707C22⋊C4—91no—
708C22⋊C4—92no—
709C42—32no—
710C42—31no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—41no—
715C22×C3—62no—
716C22×C3—61no—
717C22×C3—62no—
718C22×C3—61no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—61no—
722C22×C3—62no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—61no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—122no—
731C22×C3—122no—
732C22×C3—122no—
733C22×C3—181no—
734C22×C3—182no—
735C22×C3—181no—
736C22×C3—182no—
737C22×C3—181no—
738C22×C3—182no—
739C22×C3C22×D3211yescharacteristic
740C22×C3C23×C3×D311yescharacteristic
741C22×C3C23×C3×D311yescharacteristic
742C2×D3—21no—
743C2×D3—22no—
744C2×D3—21no—
745C2×D3—22no—
746C2×D3—21no—
747C2×D3—22no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—61no—
751C2×D3—62no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—62no—
755C2×D3—61no—
756C2×D3—62no—
757C2×D3—61no—
758C2×D3—62no—
759C2×D3—61no—
760C2×D3—62no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—122no—
764C2×D3—122no—
765C2×D3—122no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—34no—
773C3×C4—32no—
774C3×C4—34no—
775C3×C4—32no—
776C3×C4—42no—
777C3×C4—42no—
778C3×C4—42no—
779C3×C4—42no—
780C3×C4—64no—
781C3×C4—62no—
782C3×C4—61no—
783C3×C4—61no—
784C3×C4—61no—
785C3×C4—61no—
786C3×C4—82no—
787C3×C4—121no—
788C3×C4—121no—
789C3×C4—181no—
790C3×C4D3×D1212yes—
791C3×C4C2×C3×D1212yes—
792C3×C4C3×D3×D412yes—
793Dic3—21no—
794Dic3—21no—
795Dic3—61no—
796Dic3—61no—
797Dic3—121no—
798Dic3C2×C3×D1214yes—
799Dic3C3×#23912yescomplemented
800C32—21no—
801C32—21no—
802C32—21no—
803C32—41no—
804C32#557711yescharacteristic, complemented
805C32#559911yescharacteristic, complemented
806C32C3×#55011yescharacteristic, complemented
807C23—32no—
808C23—31no—
809C23—91no—
810C23—92no—
811Q8—34no—
812D4—62no—
813D4—122no—
814D4—184no—
815D4—184no—
816D4—182no—
817D4—184no—
818D4—182no—
819D4—362no—
820D4—362no—
821C2×C4—31no—
822C2×C4—32no—
823C2×C4—31no—
824C2×C4—31no—
825C2×C4—62no—
826C2×C4—91no—
827C2×C4—184no—
828C2×C4—184no—
829C2×C4—182no—
830C2×C4C2×C3×D3212yes—
831C2×C4C2×C3×D3211yescharacteristic
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—41no—
842C2×C3—41no—
843C2×C3—41no—
844C2×C3—122no—
845C2×C3—121no—
846C2×C3—122no—
847C2×C3—121no—
848C2×C3—122no—
849C2×C3—242no—
850C2×C3—361no—
851C2×C3—362no—
852C2×C3C2×D3×D1211yescharacteristic
853C2×C3#6431411yescharacteristic
854C2×C3D3×#23911yescharacteristic
855C2×C3C22×C3×D1211yescharacteristic
856C2×C3C2×C3×D3×D411yescharacteristic
857C2×C3C3×#100411yescharacteristic
858C2×C3C2×C3×#23911yescharacteristic
859C2×C3C3×D3×#4111yescharacteristic
860C2×C3C3×#100911yescharacteristic
861D3—41no—
862D3—42no—
863D3—122no—
864D3—121no—
865D3—122no—
866D3—121no—
867D3—122no—
868D3—242no—
869C22—61no—
870C22—62no—
871C22—61no—
872C22—62no—
873C22—61no—
874C22—62no—
875C22—181no—
876C22—182no—
877C22—181no—
878C22—182no—
879C22—181no—
880C22—182no—
881C22C22×C3×D3211yescharacteristic
882C4—22no—
883C4—32no—
884C4—34no—
885C4—61no—
886C4—61no—
887C4—181no—
888C4C3×D3×D1212yes—
889C3—21no—
890C3—21no—
891C3—21no—
892C3—41no—
893C3#1059452411yescharacteristic, direct product factor
894C3C3×#557711yescharacteristic, complemented
895C3C3×#559911yescharacteristic, complemented
896C2—121no—
897C2—122no—
898C2—361no—
899C2—362no—
900C2C2×C3×D3×D1211yescharacteristic
901C2C3×#6431411yescharacteristic
902C2C3×D3×#23911yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#550
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3799C2semidirect
2. C2×C3×#3796C2semidirect
3. C3×#64104C2semidirect
4. C32×#895C2semidirect
5. C32×#887C2semidirect
6. C3×#63911C2semidirect
7. C3×#63911C2semidirect
8. C3×#63910C2semidirect
9. C3×C4×#626C2semidirect
10. C3×#63886C2semidirect
11. C3×#63880C2semidirect
14. #10594524C3direct (N × H)
44. C2×#3799C2×C3semidirect
45. C2×#3796C2×C3semidirect
48. #64104C2×C3semidirect
59. C3×#895D3semidirect
60. C3×#895C2×C3semidirect
62. C3×#887D3semidirect
63. C3×#887C2×C3semidirect
70. #63911C2×C3semidirect
71. #63911C2×C3semidirect
72. #63910C2×C3semidirect
73. C4×#626C2×C3semidirect
74. #63886C2×C3semidirect
75. #63880C2×C3semidirect
93. C32×Dic6D4semidirect
214. C32×Dic3#41semidirect
243. #895C3×D3semidirect
244. #887C3×D3semidirect
341. C3×Dic6D12semidirect
342. C3×Dic6C3×D4semidirect
535. C3×Dic3#239semidirect
537. C3×Dic3C3×#41semidirect
549. C33#550semidirect
648. Dic6C3×D12semidirect
799. Dic3C3×#239semidirect
804. C32#5577semidirect
805. C32#5599semidirect
806. C32C3×#550semidirect
893. C3#10594524direct (N × H)
894. C3C3×#5577semidirect
895. C3C3×#5599semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37992
C2×C3×#37962
C3×#641042
C32×#8952
C32×#8872
C3×#639112
C3×#639102
C3×C4×#6262
C3×#638862
C3×#638802
C3×#55993
C3×#55773
#105945243