Finite Group Databasebeta

← C3×#10594834 #13174593

Subgroups — C3×#10594834 #13174593

Order 1728.

1554 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C3×#3799C211yesmaximal, characteristic, complemented
3C32×C4×#67C211yesmaximal, characteristic, complemented
4C32×#924C211yesmaximal, characteristic, complemented
5C3×#63975C212yesmaximal, complemented
6C3×#63958C212yesmaximal, complemented
7C3×#63894C211yesmaximal, characteristic, complemented
8C3×#63883C212yesmaximal, complemented
9C3×#63866C211yesmaximal, characteristic, complemented
10C3×#63857C211yesmaximal, characteristic, complemented
11C3×#63853C212yesmaximal, complemented
12C3×#5631—31nomaximal
13C3×#5551—31nomaximal
14#10594834C311yesmaximal, characteristic, direct product factor
15C22×C33×C4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C3×#3828—24no—
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2212yes—
20C2×C3×#634C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C2×C3×#626C2212yes—
25C2×C3×#624C2212yes—
26C2×C3×#624C2212yes—
27C3×#3799—24no—
28C32×#217C2212yes—
29C32×#217C2211yescharacteristic
30C32×(C2×D3)⋊C4C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×Dic3⋊C4C2212yes—
33C32×Dic3⋊C4C2211yescharacteristic
34C32×C4×Dic3C2211yescharacteristic
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×Dic3⋊Dic3C2212yes—
38C3×#3722C2212yes—
39C3×(C2×D3)⋊Dic3C2212yes—
40C2×#3828C2×C311yescharacteristic, complemented
41C2×C3×#239—31no—
42C2×C3×#235—31no—
43C2×C3×#235—31no—
44C2×C3×#235—31no—
45C2×C3×#235—61no—
46C2×#3799C2×C311yescharacteristic, complemented
47C32×C22⋊Q8—31no—
48C32×C4×D4—31no—
49C3×#944—31no—
50C3×#938—32no—
51C3×C4×#67—21no—
52C3×C4×#67D311yescharacteristic, complemented
53C3×C4×#67C2×C311yescharacteristic, complemented
54C3×#924—21no—
55C3×#924—31no—
56C3×#924D311yescharacteristic, complemented
57C3×#924C2×C311yescharacteristic, complemented
58C3×#897—31no—
59C3×#894—32no—
60C3×#893—31no—
61C3×D3×C4⋊C4—32no—
62C3×D3×C4⋊C4—32no—
63C3×#884—32no—
64C3×#883—32no—
65C3×#883—32no—
66C3×#883—32no—
67C3×C4×D12—31no—
68C3×#869—31no—
69#63975C2×C312yescomplemented
70#63958C2×C312yescomplemented
71#63894C2×C311yescharacteristic, complemented
72#63883C2×C312yescomplemented
73#63866C2×C311yescharacteristic, complemented
74#63857C2×C311yescharacteristic, complemented
75#63853C2×C312yescomplemented
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3C2312yes—
78C22×C32×D3C2311yescharacteristic
79C2×C33×C4—22no—
80C2×C33×C4C2311yescharacteristic
81C2×C33×C4C2311yescharacteristic
82C3×#638—24no—
83C2×C3×C3⋊Dic3C2312yes—
84C3×C4⋊(C3⋊D3)D414yescomplemented
85C3×C4×C3⋊D3—24no—
86C3×#634—22no—
87C32×#67—22no—
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93C32×C4×D3—22no—
94C32×Dic6—22no—
95C3×#626—24no—
96C3×#624—24no—
97C3×#624—24no—
98C3×#547—91no—
99#5631—31no—
100#5551—31no—
101C2×C32×Q8—31no—
102C2×C32×D4—31no—
103C22×C32×C4—21no—
104C22×C32×C4—21no—
105C22×C32×C4—21no—
106C22×C32×C4—31no—
107C22×C32×C4—41no—
108C22×C32×C4C2×D311yescharacteristic
109C22×C32×C4C2×D311yescharacteristic
110C22×C32×C4C22×C311yescharacteristic
111C2×#638C22×C312yes—
112#3828—24no—
113C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
114C2×C4×C3⋊D3C22×C312yes—
115C2×#634C22×C311yescharacteristic
116C2×C3×#67—21no—
117C2×C3×#67—32no—
118C2×C3×#67—32no—
119C2×C3×#67—32no—
120C2×C3×#67—62no—
121C2×C3×#67C2×D311yescharacteristic
122C2×C3×#67C22×C311yescharacteristic
123C3×#239—64no—
124C3×#235—64no—
125C3×#235—64no—
126C3×#235—64no—
127C3×#235—68no—
128C2×C3×D12—31no—
129C2×C3×D12—31no—
130C2×C3×D12—32no—
131C2×C3×D12—61no—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3—32no—
134C2×C3×C4×D3—32no—
135C2×C3×C4×D3—32no—
136C2×C3×C4×D3—32no—
137C2×C3×C4×D3—32no—
138C2×C3×C4×D3—32no—
139C2×C3×C4×D3—62no—
140C2×C3×C4×D3C2×D311yescharacteristic
141C2×C3×C4×D3C22×C311yescharacteristic
142C2×C3×Dic6—21no—
143C2×C3×Dic6—31no—
144C2×C3×Dic6—31no—
145C2×C3×Dic6—61no—
146C2×C3×Dic6C2×D311yescharacteristic
147C2×C3×Dic6C22×C311yescharacteristic
148C2×#626C22×C312yes—
149C2×#624C22×C312yes—
150C2×#624C22×C312yes—
151#3799—24no—
152C32×C4⋊C4—31no—
153C32×C4⋊C4—32no—
154C32×C4⋊C4—31no—
155C32×C22⋊C4—31no—
156C32×C22⋊C4—32no—
157C32×C22⋊C4—31no—
158C32×C42—31no—
159C3×#217—22no—
160C3×#217—21no—
161C3×#217—32no—
162C3×#217C2×D311yescharacteristic
163C3×#217C2×D312yes—
164C3×#217C22×C312yes—
165C3×#217C22×C311yescharacteristic
166C3×(C2×D3)⋊C4—21no—
167C3×(C2×D3)⋊C4—32no—
168C3×(C2×D3)⋊C4—32no—
169C3×(C2×D3)⋊C4—32no—
170C3×(C2×D3)⋊C4C2×D311yescharacteristic
171C3×(C2×D3)⋊C4C22×C311yescharacteristic
172C3×C4⋊Dic3—21no—
173C3×C4⋊Dic3—32no—
174C3×C4⋊Dic3—32no—
175C3×C4⋊Dic3—32no—
176C3×C4⋊Dic3C2×D311yescharacteristic
177C3×C4⋊Dic3C22×C311yescharacteristic
178C3×Dic3⋊C4—22no—
179C3×Dic3⋊C4—21no—
180C3×Dic3⋊C4—32no—
181C3×Dic3⋊C4—32no—
182C3×Dic3⋊C4—32no—
183C3×Dic3⋊C4C2×D312yes—
184C3×Dic3⋊C4C2×D311yescharacteristic
185C3×Dic3⋊C4C22×C312yes—
186C3×Dic3⋊C4C22×C311yescharacteristic
187C3×C4×Dic3—21no—
188C3×C4×Dic3C2×D311yescharacteristic
189C3×C4×Dic3C22×C311yescharacteristic
190Dic3⋊Dic3C22×C312yes—
191Dic3⋊Dic3C22×C312yes—
192Dic3⋊Dic3C22×C312yes—
193#3722C22×C312yes—
194(C2×D3)⋊Dic3C22×C312yes—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33C2411yescharacteristic
199C2×C3×C3⋊D3—22no—
200C2×C3×C3⋊D3—22no—
201C2×C3×C3⋊D3C2×D414yes—
202C2×C32×D3—21no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C33×C4—21no—
206C33×C4C2×D412yes—
207C3×C3⋊Dic3—22no—
208C32×Dic3—21no—
209C32×Dic3—22no—
210C32×Dic3—22no—
211C32×Dic3—21no—
212C32×Dic3#4112yescomplemented
213C2×C3×#41—91no—
214C2×C3×#41—91no—
215C2×#239—31no—
216C2×#235—31no—
217C2×#235—31no—
218C2×#235—31no—
219C2×#235—61no—
220C3×C4⋊Q8—91no—
221C3×#123—92no—
222C3×#123—92no—
223C3×C22⋊Q8—31no—
224C3×C22⋊Q8—31no—
225C3×C22⋊Q8—61no—
226C3×C22⋊Q8—91no—
227C3×#121—92no—
228C3×C4×D4—31no—
229C3×C4×D4—31no—
230C3×C4×D4—61no—
231C3×C4×D4—91no—
232C2×C3×C4⋊C4—92no—
233#944—31no—
234#938—32no—
235C4×#67C3×D311yescharacteristic, complemented
236#924—31no—
237#924C3×D311yescharacteristic, complemented
238#897—31no—
239#894—32no—
240#893—31no—
241D3×C4⋊C4—32no—
242D3×C4⋊C4—32no—
243#884—32no—
244#883—32no—
245#883—32no—
246#883—32no—
247C4×D12—31no—
248#869—31no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—31no—
253C23×C32—41no—
254C23×C32C22×D311yescharacteristic
255C23×C32C22×D311yescharacteristic
256C23×C32C23×C311yescharacteristic
257C22×C3⋊D3C23×C312yes—
258C22×C3×D3—21no—
259C22×C3×D3—32no—
260C22×C3×D3—32no—
261C22×C3×D3—62no—
262C22×C3×D3C22×D311yescharacteristic
263C22×C3×D3C23×C311yescharacteristic
264C32×Q8—62no—
265C32×D4—62no—
266C2×C32×C4—22no—
267C2×C32×C4—24no—
268C2×C32×C4—22no—
269C2×C32×C4—22no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—31no—
277C2×C32×C4—31no—
278C2×C32×C4—32no—
279C2×C32×C4—31no—
280C2×C32×C4—32no—
281C2×C32×C4—41no—
282C2×C32×C4—41no—
283C2×C32×C4—42no—
284C2×C32×C4—42no—
285C2×C32×C4—44no—
286C2×C32×C4—62no—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C23×C311yescharacteristic
292C2×C32×C4C23×C311yescharacteristic
293#638—24no—
294C2×C3⋊Dic3C23×C312yes—
295C4⋊(C3⋊D3)C3×D414yescomplemented
296C4×C3⋊D3—24no—
297#634—22no—
298C3×#67—24no—
299C3×#67—22no—
300C3×#67—22no—
301C3×#67—64no—
302C3×#67—64no—
303C3×#67—64no—
304C3×#67—68no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—32no—
311C2×C3×Dic3—32no—
312C2×C3×Dic3—62no—
313C2×C3×Dic3C22×D311yescharacteristic
314C2×C3×Dic3C22×D312yes—
315C2×C3×Dic3C22×D312yes—
316C2×C3×Dic3C22×D311yescharacteristic
317C2×C3×Dic3C22×D311yescharacteristic
318C2×C3×Dic3C23×C312yes—
319C2×C3×Dic3C23×C311yescharacteristic
320C2×C3×Dic3C23×C311yescharacteristic
321C2×C3×Dic3C23×C312yes—
322C2×C3×Dic3C23×C311yescharacteristic
323C3×D12—34no—
324C3×D12—34no—
325C3×D12—64no—
326C3×D12—64no—
327C3×C4×D3—22no—
328C3×C4×D3—22no—
329C3×C4×D3—42no—
330C3×C4×D3—64no—
331C3×C4×D3—64no—
332C3×C4×D3—64no—
333C3×C4×D3—64no—
334C3×C4×D3—64no—
335C3×C4×D3—68no—
336C3×C4×D3—64no—
337C3×Dic6—22no—
338C3×Dic6—22no—
339C3×Dic6—42no—
340C3×Dic6—64no—
341C3×Dic6—62no—
342C3×Dic6—62no—
343#626—24no—
344#624—24no—
345#624—24no—
346#547—91noSylow
347C2×C33—41no—
348C2×C33C22×D411yescharacteristic
349C2×C33C2×#4111yescharacteristic
350C2×C332−1+411yescharacteristic
351C3×C3⋊D3—24no—
352C32×D3—41no—
353C3×#41—184no—
354C3×#41—184no—
355C2×C3×Q8—31no—
356C2×C3×Q8—31no—
357C2×C3×Q8—61no—
358C2×C3×Q8—91no—
359C2×C3×D4—31no—
360C2×C3×D4—31no—
361C2×C3×D4—61no—
362C2×C3×D4—92no—
363C2×C3×D4—92no—
364C2×C3×D4—91no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—41no—
371C22×C3×C4—61no—
372C22×C3×C4—92no—
373C22×C3×C4—92no—
374C22×C3×C4—92no—
375C22×C3×C4D3211yescharacteristic
376C22×C3×C4C2×C3×D311yescharacteristic
377C22×C3×C4C2×C3×D311yescharacteristic
378C2×#67—32no—
379C2×#67—32no—
380C2×#67—32no—
381C2×#67—62no—
382C2×#67C2×C3×D311yescharacteristic
383#239—64no—
384#235—64no—
385#235—64no—
386#235—64no—
387#235—68no—
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—32no—
391C2×D12—61no—
392C2×C4×D3—32no—
393C2×C4×D3—32no—
394C2×C4×D3—32no—
395C2×C4×D3—32no—
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3—62no—
399C2×C4×D3C2×C3×D311yescharacteristic
400C2×Dic6—31no—
401C2×Dic6—31no—
402C2×Dic6—61no—
403C2×Dic6C2×C3×D311yescharacteristic
404C3×C4⋊C4—31no—
405C3×C4⋊C4—32no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—32no—
409C3×C4⋊C4—31no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4—62no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4—92no—
414C3×C4⋊C4—92no—
415C3×C4⋊C4—92no—
416C3×C22⋊C4—31no—
417C3×C22⋊C4—32no—
418C3×C22⋊C4—31no—
419C3×C22⋊C4—32no—
420C3×C22⋊C4—31no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—92no—
426C3×C22⋊C4—92no—
427C3×C42—31no—
428C3×C42—31no—
429C3×C42—61no—
430#217—32no—
431#217C2×C3×D311yescharacteristic
432#217C2×C3×D312yes—
433(C2×D3)⋊C4—32no—
434(C2×D3)⋊C4—32no—
435(C2×D3)⋊C4—32no—
436(C2×D3)⋊C4C2×C3×D311yescharacteristic
437C4⋊Dic3—32no—
438C4⋊Dic3—32no—
439C4⋊Dic3—32no—
440C4⋊Dic3C2×C3×D311yescharacteristic
441Dic3⋊C4—32no—
442Dic3⋊C4—32no—
443Dic3⋊C4—32no—
444Dic3⋊C4C2×C3×D312yes—
445Dic3⋊C4C2×C3×D311yescharacteristic
446C4×Dic3C2×C3×D311yescharacteristic
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—22no—
451C22×C32—22no—
452C22×C32—22no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—42no—
470C22×C32—42no—
471C22×C32—42no—
472C22×C32—61no—
473C22×C32—61no—
474C22×C32—61no—
475C22×C32C23×D311yescharacteristic
476C22×C32C23×D311yescharacteristic
477C22×C32C24×C311yescharacteristic
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3C2×C3×D414yes—
481C2×C3×D3—22no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—21no—
488C2×C3×D3—34no—
489C2×C3×D3—34no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—64no—
493C2×C3×D3—62no—
494C2×C3×D3—62no—
495C2×C3×D3—62no—
496C2×C3×D3—62no—
497C2×C3×D3—122no—
498C2×C3×D3—122no—
499C32×C4—21no—
500C32×C4—22no—
501C32×C4—21no—
502C32×C4—21no—
503C32×C4—22no—
504C32×C4—22no—
505C32×C4—22no—
506C32×C4—32no—
507C32×C4—42no—
508C32×C4—41no—
509C32×C4—41no—
510C32×C4—42no—
511C32×C4—62no—
512C32×C4—61no—
513C32×C4—62no—
514C32×C4—61no—
515C32×C4D3×D412yes—
516C32×C4D3×D412yes—
517C32×C4C2×C3×D412yes—
518C3⋊Dic3—22no—
519C3×Dic3—22no—
520C3×Dic3—21no—
521C3×Dic3—22no—
522C3×Dic3—21no—
523C3×Dic3—21no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—21no—
527C3×Dic3—22no—
528C3×Dic3—42no—
529C3×Dic3—41no—
530C3×Dic3—42no—
531C3×Dic3—41no—
532C3×Dic3—64no—
533C3×Dic3—62no—
534C3×Dic3—62no—
535C3×Dic3#23512yescomplemented
536C3×Dic3C3×#4112yescomplemented
537C2×#41—91no—
538C2×#41—91no—
539C4⋊Q8—91no—
540#123—92no—
541#123—92no—
542C22⋊Q8—31no—
543C22⋊Q8—91no—
544#121—92no—
545C4×D4—31no—
546C4×D4—91no—
547C2×C4⋊C4—92no—
548C33#54711yescharacteristic, complemented, Sylow
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—31no—
553C23×C3—31no—
554C23×C3—41no—
555C23×C3—61no—
556C23×C3—92no—
557C23×C3C2×D3211yescharacteristic
558C23×C3C22×C3×D311yescharacteristic
559C23×C3C22×C3×D311yescharacteristic
560C22×D3—32no—
561C22×D3—32no—
562C22×D3—62no—
563C22×D3C22×C3×D311yescharacteristic
564C3×Q8—62no—
565C3×Q8—62no—
566C3×Q8—122no—
567C3×Q8—182no—
568C3×D4—62no—
569C3×D4—62no—
570C3×D4—64no—
571C3×D4—94no—
572C3×D4—184no—
573C3×D4—184no—
574C2×C3×C4—24no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—32no—
588C2×C3×C4—31no—
589C2×C3×C4—32no—
590C2×C3×C4—31no—
591C2×C3×C4—32no—
592C2×C3×C4—31no—
593C2×C3×C4—32no—
594C2×C3×C4—42no—
595C2×C3×C4—42no—
596C2×C3×C4—44no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—62no—
602C2×C3×C4—61no—
603C2×C3×C4—62no—
604C2×C3×C4—62no—
605C2×C3×C4—62no—
606C2×C3×C4—92no—
607C2×C3×C4—122no—
608C2×C3×C4—184no—
609C2×C3×C4—184no—
610C2×C3×C4—184no—
611C2×C3×C4C2×D3211yescharacteristic
612C2×C3×C4C2×D3211yescharacteristic
613C2×C3×C4C22×C3×D311yescharacteristic
614C2×C3×C4C22×C3×D311yescharacteristic
615C2×C3×C4C22×C3×D311yescharacteristic
616C2×C3×C4C22×C3×D311yescharacteristic
617#67—22no—
618#67—64no—
619#67—64no—
620#67—64no—
621#67—68no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—62no—
625C2×Dic3C22×C3×D311yescharacteristic
626C2×Dic3C22×C3×D312yes—
627C2×Dic3C22×C3×D312yes—
628C2×Dic3C22×C3×D311yescharacteristic
629C2×Dic3C22×C3×D311yescharacteristic
630D12—34no—
631D12—34no—
632D12—64no—
633D12—64no—
634C4×D3—22no—
635C4×D3—64no—
636C4×D3—64no—
637C4×D3—64no—
638C4×D3—64no—
639C4×D3—64no—
640C4×D3—68no—
641C4×D3—64no—
642Dic6—22no—
643Dic6—64no—
644Dic6—62no—
645Dic6—62no—
646C2×C32—21no—
647C2×C32—21no—
648C2×C32—21no—
649C2×C32—21no—
650C2×C32—21no—
651C2×C32—21no—
652C2×C32—21no—
653C2×C32—21no—
654C2×C32—21no—
655C2×C32—41no—
656C2×C32—41no—
657C2×C32—41no—
658C2×C32—42no—
659C2×C32—42no—
660C2×C32—42no—
661C2×C32—44no—
662C2×C32—41no—
663C2×C32—41no—
664C2×C32—41no—
665C2×C32—121no—
666C2×C32C2×#23511yescharacteristic
667C2×C32C2×D3×D411yescharacteristic
668C2×C32C2×D3×D411yescharacteristic
669C2×C32#100711yescharacteristic
670C2×C32D3×#4111yescharacteristic
671C2×C32#101011yescharacteristic
672C2×C32C22×C3×D411yescharacteristic
673C2×C32C2×C3×#4111yescharacteristic
674C2×C32C3×2−1+411yescharacteristic
675C3⋊D3—24no—
676C3×D3—42no—
677C3×D3—41no—
678C3×D3—41no—
679C3×D3—64no—
680C3×D3—64no—
681C3×D3—124no—
682#41—184no—
683#41—184no—
684C2×Q8—31no—
685C2×Q8—91no—
686C2×D4—31no—
687C2×D4—92no—
688C2×D4—92no—
689C2×D4—91no—
690C22×C4—31no—
691C22×C4—92no—
692C22×C4—92no—
693C22×C4—92no—
694C22×C4C3×D3211yescharacteristic
695C4⋊C4—31no—
696C4⋊C4—32no—
697C4⋊C4—31no—
698C4⋊C4—92no—
699C4⋊C4—92no—
700C4⋊C4—92no—
701C22⋊C4—31no—
702C22⋊C4—32no—
703C22⋊C4—31no—
704C22⋊C4—92no—
705C22⋊C4—92no—
706C42—31no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—41no—
732C22×C3—62no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—94no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—182no—
743C22×C3—182no—
744C22×C3C22×D3211yescharacteristic
745C22×C3C23×C3×D311yescharacteristic
746C22×C3C23×C3×D311yescharacteristic
747C2×D3—21no—
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—34no—
751C2×D3—34no—
752C2×D3—64no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—122no—
758C2×D3—122no—
759C3×C4—22no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—32no—
767C3×C4—32no—
768C3×C4—41no—
769C3×C4—41no—
770C3×C4—42no—
771C3×C4—42no—
772C3×C4—62no—
773C3×C4—61no—
774C3×C4—62no—
775C3×C4—61no—
776C3×C4—62no—
777C3×C4—62no—
778C3×C4—61no—
779C3×C4—62no—
780C3×C4—61no—
781C3×C4—121no—
782C3×C4—122no—
783C3×C4—121no—
784C3×C4—122no—
785C3×C4—182no—
786C3×C4#381112yes—
787C3×C4C3×D3×D412yes—
788C3×C4C3×D3×D412yes—
789Dic3—22no—
790Dic3—21no—
791Dic3—22no—
792Dic3—21no—
793Dic3—64no—
794Dic3—62no—
795Dic3—62no—
796Dic3C3×#23512yescomplemented
797C32—21no—
798C32—21no—
799C32—21no—
800C32—41no—
801C32#555111yescharacteristic, complemented
802C32#563111yescharacteristic, complemented
803C32C3×#54711yescharacteristic, complemented
804C23—31no—
805C23—92no—
806C23C2×C3×D3211yescharacteristic
807Q8—62no—
808Q8—182no—
809D4—62no—
810D4—94no—
811D4—184no—
812D4—184no—
813C2×C4—22no—
814C2×C4—31no—
815C2×C4—31no—
816C2×C4—32no—
817C2×C4—31no—
818C2×C4—32no—
819C2×C4—62no—
820C2×C4—92no—
821C2×C4—184no—
822C2×C4—184no—
823C2×C4—184no—
824C2×C4C2×C3×D3211yescharacteristic
825C2×C4C2×C3×D3211yescharacteristic
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—42no—
836C2×C3—42no—
837C2×C3—42no—
838C2×C3—44no—
839C2×C3—41no—
840C2×C3—41no—
841C2×C3—41no—
842C2×C3—41no—
843C2×C3—41no—
844C2×C3—41no—
845C2×C3—122no—
846C2×C3—121no—
847C2×C3—121no—
848C2×C3—184no—
849C2×C3#6429711yescharacteristic
850C2×C3D3×#23511yescharacteristic
851C2×C3C2×#381111yescharacteristic
852C2×C3C2×C3×#23511yescharacteristic
853C2×C3C2×C3×D3×D411yescharacteristic
854C2×C3C2×C3×D3×D411yescharacteristic
855C2×C3C3×#100711yescharacteristic
856C2×C3C3×D3×#4111yescharacteristic
857C2×C3C3×#101011yescharacteristic
858D3—41no—
859D3—64no—
860D3—64no—
861D3—124no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—61no—
866C22—61no—
867C22—61no—
868C22—94no—
869C22—182no—
870C22—182no—
871C22C22×C3×D3211yescharacteristic
872C4—21no—
873C4—32no—
874C4—61no—
875C4—62no—
876C4—61no—
877C4—62no—
878C4—182no—
879C4C3×#381112yes—
880C3—21no—
881C3—21no—
882C3—21no—
883C3—41no—
884C3#1059483411yescharacteristic, direct product factor
885C3C3×#555111yescharacteristic, complemented
886C3C3×#563111yescharacteristic, complemented
887C2—41no—
888C2—121no—
889C2—184no—
890C2C3×#6429711yescharacteristic
891C2C3×D3×#23511yescharacteristic
892C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3828C2semidirect
2. C2×C3×#3799C2semidirect
3. C32×C4×#67C2semidirect
4. C32×#924C2semidirect
5. C3×#63975C2semidirect
6. C3×#63958C2semidirect
7. C3×#63894C2semidirect
8. C3×#63883C2semidirect
9. C3×#63866C2semidirect
10. C3×#63857C2semidirect
11. C3×#63853C2semidirect
14. #10594834C3direct (N × H)
40. C2×#3828C2×C3semidirect
46. C2×#3799C2×C3semidirect
52. C3×C4×#67D3semidirect
53. C3×C4×#67C2×C3semidirect
56. C3×#924D3semidirect
57. C3×#924C2×C3semidirect
69. #63975C2×C3semidirect
70. #63958C2×C3semidirect
71. #63894C2×C3semidirect
72. #63883C2×C3semidirect
73. #63866C2×C3semidirect
74. #63857C2×C3semidirect
75. #63853C2×C3semidirect
84. C3×C4⋊(C3⋊D3)D4semidirect
212. C32×Dic3#41semidirect
235. C4×#67C3×D3semidirect
237. #924C3×D3semidirect
295. C4⋊(C3⋊D3)C3×D4semidirect
535. C3×Dic3#235semidirect
536. C3×Dic3C3×#41semidirect
548. C33#547semidirect
796. Dic3C3×#235semidirect
801. C32#5551semidirect
802. C32#5631semidirect
803. C32C3×#547semidirect
884. C3#10594834direct (N × H)
885. C3C3×#5551semidirect
886. C3C3×#5631semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×C3×#37992
C32×C4×#672
C32×#9242
C3×#639752
C3×#639582
C3×#638942
C3×#638832
C3×#638662
C3×#638572
C3×#638532
C3×#56313
C3×#55513
#105948343