Finite Group Databasebeta

← C3×#10595067 #13174664

Subgroups — C3×#10595067 #13174664

Order 1728.

1742 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3C3×#64139C211yesmaximal, characteristic, complemented
4C32×C4×#67C211yesmaximal, characteristic, complemented
5C3×#63983C212yesmaximal, complemented
6C3×#63971C212yesmaximal, complemented
7C3×D3×(C2×D3)⋊C4C212yesmaximal, complemented
8C3×Dic3×D12C211yesmaximal, characteristic, complemented
9C3×#63864C211yesmaximal, characteristic, complemented
10C3×#63856C211yesmaximal, characteristic, complemented
11C3×#63850C212yesmaximal, complemented
12C3×#5829—31nomaximal
13C3×#5550—31nomaximal
14#10595067C311yesmaximal, characteristic, direct product factor
15C22×C3×D32C2212yes—
16C22×C33×C4C2211yescharacteristic, complemented
17C2×C3×#638C2212yescomplemented
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C32×#67C2211yescharacteristic
20C2×C32×#67C2212yescomplemented
21C32×#235—24no—
22C2×C32×D12C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2212yescomplemented
25C2×C32×Dic6C2211yescharacteristic, complemented
26C2×C3×#626C2212yes—
27C2×C3×D3×Dic3C2212yescomplemented
28C3×D3×D12—24no—
29C3×#3752C2212yescomplemented
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C32×#217C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×Dic3⋊C4C2211yescharacteristic, complemented
34C32×C4×Dic3C2211yescharacteristic, complemented
35C3×#3724C2212yescomplemented
36C3×#3722C2212yescomplemented
37C3×#3722C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yes—
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×C32×#41—31no—
41C2×C3×D3×D4—31no—
42C2×C3×#235—21no—
43C2×C3×#235D311yescharacteristic, complemented
44C2×C3×#235C2×C311yescharacteristic, complemented
45C22×C3×D12—31no—
46C2×D3×D12C2×C311yescharacteristic, complemented
47C32×C4×D4—31no—
48#64139C2×C311yescharacteristic, complemented
49C3×#947—31no—
50C3×#946—31no—
51C3×#939—32no—
52C3×#937—32no—
53C3×#937—32no—
54C3×D4×Dic3—31no—
55C3×#930—31no—
56C3×#930—31no—
57C3×#930—61no—
58C3×#929—32no—
59C3×C4×#67—21no—
60C3×C4×#67D311yescharacteristic, complemented
61C3×C4×#67C2×C311yescharacteristic, complemented
62C2×C3×(C2×D3)⋊C4—32no—
63C3×#924—31no—
64C3×#894—32no—
65C3×#884—32no—
66C3×D3×C22⋊C4—32no—
67C3×#875—31no—
68C3×C4×D12—31no—
69#63983C2×C312yescomplemented
70#63971C2×C312yescomplemented
71D3×(C2×D3)⋊C4C2×C312yescomplemented
72Dic3×D12C2×C311yescharacteristic, complemented
73#63864C2×C311yescharacteristic, complemented
74#63856C2×C311yescharacteristic, complemented
75#63850C2×C312yescomplemented
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3C2312yes—
78C22×C32×D3C2312yes—
79C22×C32×D3C2311yescharacteristic
80C2×C3×D32—24no—
81C2×C3×D32—24no—
82C2×C3×D32—42no—
83C2×C33×C4—22no—
84C2×C33×C4C2311yescharacteristic
85C2×C33×C4C2311yescharacteristic
86C3×#638—42no—
87C2×C3×C3⋊Dic3C2312yes—
88C3×C4⋊(C3⋊D3)—22no—
89C32×#67—24no—
90C32×#67—22no—
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93C2×C32×Dic3C2312yes—
94C2×C32×Dic3C2311yescharacteristic
95C32×D12D414yescomplemented
96C32×C4×D3—24no—
97C32×C4×D3—22no—
98C32×Dic6—22no—
99C3×#626—24no—
100C3×D3×Dic3—42no—
101C3×#546—91no—
102#5829—31no—
103#5550—31no—
104C23×C3×D3—32no—
105C23×C3×D3—32no—
106C22×D32C22×C312yes—
107C32×#41—64no—
108C2×C32×Q8—31no—
109C2×C32×D4—31no—
110C2×C32×D4—32no—
111C2×C32×D4—31no—
112C22×C32×C4—21no—
113C22×C32×C4—21no—
114C22×C32×C4—21no—
115C22×C32×C4—31no—
116C22×C32×C4—32no—
117C22×C32×C4—41no—
118C22×C32×C4C2×D311yescharacteristic, complemented
119C22×C32×C4C2×D311yescharacteristic, complemented
120C22×C32×C4C22×C311yescharacteristic, complemented
121C2×#638C22×C312yescomplemented
122C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
123C2×C3×#67—21no—
124C2×C3×#67—22no—
125C2×C3×#67—32no—
126C2×C3×#67—32no—
127C2×C3×#67—32no—
128C2×C3×#67—62no—
129C2×C3×#67C2×D311yescharacteristic
130C2×C3×#67C2×D312yescomplemented
131C2×C3×#67C22×C311yescharacteristic
132C2×C3×#67C22×C312yescomplemented
133C22×C3×Dic3—32no—
134C3×D3×D4—64no—
135C3×#235—28no—
136C3×#235—24no—
137C3×#235—24no—
138C2×C3×D12—21no—
139C2×C3×D12—32no—
140C2×C3×D12—31no—
141C2×C3×D12—31no—
142C2×C3×D12—64no—
143C2×C3×D12—61no—
144C2×C3×D12C2×D311yescharacteristic
145C2×C3×D12C22×C311yescharacteristic
146C2×C3×C4×D3—22no—
147C2×C3×C4×D3—21no—
148C2×C3×C4×D3—32no—
149C2×C3×C4×D3C2×D311yescharacteristic
150C2×C3×C4×D3C2×D312yescomplemented
151C2×C3×C4×D3C22×C311yescharacteristic
152C2×C3×C4×D3C22×C312yescomplemented
153C2×C3×Dic6—21no—
154C2×C3×Dic6C2×D311yescharacteristic, complemented
155C2×C3×Dic6C22×C311yescharacteristic, complemented
156C2×#626C22×C312yes—
157C2×D3×Dic3C22×C312yescomplemented
158D3×D12—24no—
159C32×C4⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C22⋊C4—31no—
162C32×C42—31no—
163#3752C22×C312yescomplemented
164C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
165C3×#217—21no—
166C3×#217—32no—
167C3×#217—32no—
168C3×#217C2×D311yescharacteristic, complemented
169C3×#217C22×C311yescharacteristic, complemented
170C3×(C2×D3)⋊C4—21no—
171C3×(C2×D3)⋊C4—32no—
172C3×(C2×D3)⋊C4—32no—
173C3×(C2×D3)⋊C4—32no—
174C3×(C2×D3)⋊C4—32no—
175C3×(C2×D3)⋊C4—32no—
176C3×(C2×D3)⋊C4—32no—
177C3×(C2×D3)⋊C4—32no—
178C3×(C2×D3)⋊C4—32no—
179C3×(C2×D3)⋊C4—62no—
180C3×(C2×D3)⋊C4C2×D311yescharacteristic
181C3×(C2×D3)⋊C4C22×C311yescharacteristic
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—61no—
185C3×Dic3⋊C4—21no—
186C3×Dic3⋊C4—32no—
187C3×Dic3⋊C4—32no—
188C3×Dic3⋊C4C2×D311yescharacteristic, complemented
189C3×Dic3⋊C4C22×C311yescharacteristic, complemented
190C3×C4×Dic3—21no—
191C3×C4×Dic3C2×D311yescharacteristic, complemented
192C3×C4×Dic3C22×C311yescharacteristic, complemented
193#3724C22×C312yescomplemented
194#3722C22×C312yescomplemented
195#3722C22×C312yescomplemented
196(C2×D3)⋊Dic3C22×C312yes—
197(C2×D3)⋊Dic3C22×C312yescomplemented
198C22×C33—21no—
199C22×C33—21no—
200C22×C33—21no—
201C22×C33C2411yescharacteristic
202C2×C3×C3⋊D3—22no—
203C2×C3×C3⋊D3—22no—
204C2×C3×C3⋊D3—22no—
205C2×C32×D3—21no—
206C2×C32×D3—22no—
207C2×C32×D3—22no—
208C2×C32×D3—21no—
209C2×C32×D3C2×D414yes—
210C2×C32×D3#4112yescomplemented
211C3×D32—48no—
212C33×C4—21no—
213C33×C4C2×D412yes—
214C3×C3⋊Dic3—22no—
215C32×Dic3—22no—
216C32×Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C2×C3×#41—31no—
220C2×C3×#41—31no—
221C2×C3×#41—61no—
222C22×C3×D4—91no—
223C2×D3×D4—31no—
224C2×#235C3×D311yescharacteristic, complemented
225C22×D12—31no—
226C3×#124—91no—
227C3×#123—92no—
228C3×C22⋊Q8—91no—
229C3×#121—92no—
230C3×#121—91no—
231C3×#120—92no—
232C3×C4×D4—31no—
233C3×C4×D4—31no—
234C3×C4×D4—61no—
235C3×C4×D4—91no—
236C2×C3×C22⋊C4—92no—
237#947—31no—
238#946—31no—
239#939—32no—
240#937—32no—
241#937—32no—
242D4×Dic3—31no—
243#930—31no—
244#930—31no—
245#930—61no—
246#929—32no—
247C4×#67C3×D311yescharacteristic, complemented
248C2×(C2×D3)⋊C4—32no—
249#924—31no—
250#894—32no—
251#884—32no—
252D3×C22⋊C4—32no—
253#875—31no—
254C4×D12—31no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—31no—
259C23×C32—32no—
260C23×C32—41no—
261C23×C32C22×D311yescharacteristic
262C23×C32C22×D311yescharacteristic
263C23×C32C23×C311yescharacteristic
264C22×C3⋊D3C23×C312yes—
265C22×C3×D3—21no—
266C22×C3×D3—22no—
267C22×C3×D3—32no—
268C22×C3×D3—32no—
269C22×C3×D3—62no—
270C22×C3×D3—64no—
271C22×C3×D3—64no—
272C22×C3×D3—64no—
273C22×C3×D3—64no—
274C22×C3×D3—122no—
275C22×C3×D3—122no—
276C22×C3×D3C22×D311yescharacteristic
277C22×C3×D3C22×D312yes—
278C22×C3×D3C23×C312yes—
279C22×C3×D3C23×C311yescharacteristic
280C2×D32—24no—
281C2×D32—24no—
282C2×D32—42no—
283C32×Q8—62no—
284C32×D4—34no—
285C32×D4—62no—
286C32×D4—64no—
287C2×C32×C4—22no—
288C2×C32×C4—24no—
289C2×C32×C4—22no—
290C2×C32×C4—22no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4—31no—
298C2×C32×C4—32no—
299C2×C32×C4—31no—
300C2×C32×C4—31no—
301C2×C32×C4—41no—
302C2×C32×C4—41no—
303C2×C32×C4—42no—
304C2×C32×C4—42no—
305C2×C32×C4—44no—
306C2×C32×C4—64no—
307C2×C32×C4—62no—
308C2×C32×C4C22×D311yescharacteristic
309C2×C32×C4C22×D311yescharacteristic
310C2×C32×C4C22×D311yescharacteristic
311C2×C32×C4C22×D311yescharacteristic
312C2×C32×C4C23×C311yescharacteristic
313C2×C32×C4C23×C311yescharacteristic
314#638—42no—
315C2×C3⋊Dic3C23×C312yes—
316C4⋊(C3⋊D3)—22no—
317C3×#67—28no—
318C3×#67—24no—
319C3×#67—22no—
320C3×#67—24no—
321C3×#67—24no—
322C3×#67—22no—
323C3×#67—64no—
324C3×#67—122no—
325C3×#67—122no—
326C3×#67—124no—
327C2×C3×Dic3—21no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—21no—
330C2×C3×Dic3—21no—
331C2×C3×Dic3—32no—
332C2×C3×Dic3—32no—
333C2×C3×Dic3—62no—
334C2×C3×Dic3—122no—
335C2×C3×Dic3C22×D311yescharacteristic
336C2×C3×Dic3C22×D311yescharacteristic
337C2×C3×Dic3C22×D311yescharacteristic
338C2×C3×Dic3C22×D312yes—
339C2×C3×Dic3C23×C312yes—
340C2×C3×Dic3C23×C311yescharacteristic
341C2×C3×Dic3C23×C311yescharacteristic
342C2×C3×Dic3C23×C311yescharacteristic
343C3×D12—24no—
344C3×D12—64no—
345C3×D12—62no—
346C3×D12—62no—
347C3×D12—122no—
348C3×D12#6714yescomplemented
349C3×D12C3×D414yescomplemented
350C3×C4×D3—28no—
351C3×C4×D3—24no—
352C3×C4×D3—24no—
353C3×C4×D3—22no—
354C3×C4×D3—22no—
355C3×C4×D3—42no—
356C3×C4×D3—122no—
357C3×Dic6—24no—
358C3×Dic6—22no—
359C3×Dic6—22no—
360#626—24no—
361D3×Dic3—42no—
362#546—91noSylow
363C2×C33—41no—
364C2×C33C22×D411yescharacteristic
365C2×C33C2×#4111yescharacteristic
366C2×C33H(5,𝔽2)11yescharacteristic
367C3×C3⋊D3—42no—
368C32×D3—22no—
369C32×D3—24no—
370C24×C3—92no—
371C23×D3—32no—
372C23×D3—32no—
373C3×#41—64no—
374C3×#41—64no—
375C3×#41—68no—
376C2×C3×Q8—31no—
377C2×C3×Q8—31no—
378C2×C3×Q8—61no—
379C2×C3×D4—31no—
380C2×C3×D4—32no—
381C2×C3×D4—31no—
382C2×C3×D4—32no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—61no—
386C2×C3×D4—61no—
387C2×C3×D4—62no—
388C2×C3×D4—92no—
389C2×C3×D4—92no—
390C2×C3×D4—91no—
391C2×C3×D4—184no—
392C22×C3×C4—21no—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—32no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—32no—
399C22×C3×C4—41no—
400C22×C3×C4—62no—
401C22×C3×C4—61no—
402C22×C3×C4—92no—
403C22×C3×C4D3211yescharacteristic, complemented
404C22×C3×C4C2×C3×D311yescharacteristic, complemented
405C22×C3×C4C2×C3×D311yescharacteristic, complemented
406C2×#67—32no—
407C2×#67—32no—
408C2×#67—32no—
409C2×#67—62no—
410C2×#67C2×C3×D311yescharacteristic
411C2×#67C2×C3×D312yescomplemented
412C22×Dic3—32no—
413D3×D4—64no—
414#235—24no—
415C2×D12—32no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—61no—
419C2×D12—64no—
420C2×D12C2×C3×D311yescharacteristic
421C2×C4×D3—32no—
422C2×C4×D3C2×C3×D311yescharacteristic
423C2×C4×D3C2×C3×D312yescomplemented
424C2×Dic6C2×C3×D311yescharacteristic, complemented
425C3×C4⋊C4—31no—
426C3×C4⋊C4—31no—
427C3×C4⋊C4—61no—
428C3×C4⋊C4—92no—
429C3×C4⋊C4—91no—
430C3×C22⋊C4—31no—
431C3×C22⋊C4—31no—
432C3×C22⋊C4—31no—
433C3×C22⋊C4—31no—
434C3×C22⋊C4—61no—
435C3×C22⋊C4—61no—
436C3×C22⋊C4—92no—
437C3×C22⋊C4—92no—
438C3×C22⋊C4—92no—
439C3×C22⋊C4—92no—
440C3×C22⋊C4—92no—
441C3×C42—31no—
442C3×C42—31no—
443C3×C42—61no—
444#217—32no—
445#217—32no—
446#217C2×C3×D311yescharacteristic, complemented
447(C2×D3)⋊C4—32no—
448(C2×D3)⋊C4—32no—
449(C2×D3)⋊C4—32no—
450(C2×D3)⋊C4—32no—
451(C2×D3)⋊C4—32no—
452(C2×D3)⋊C4—32no—
453(C2×D3)⋊C4—32no—
454(C2×D3)⋊C4—32no—
455(C2×D3)⋊C4—62no—
456(C2×D3)⋊C4C2×C3×D311yescharacteristic
457C4⋊Dic3—31no—
458C4⋊Dic3—31no—
459C4⋊Dic3—61no—
460Dic3⋊C4—32no—
461Dic3⋊C4—32no—
462Dic3⋊C4C2×C3×D311yescharacteristic, complemented
463C4×Dic3C2×C3×D311yescharacteristic, complemented
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32—21no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32—34no—
480C22×C32—32no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32—42no—
489C22×C32—42no—
490C22×C32—42no—
491C22×C32—62no—
492C22×C32—62no—
493C22×C32—61no—
494C22×C32—61no—
495C22×C32C23×D311yescharacteristic
496C22×C32C23×D311yescharacteristic
497C22×C32C24×C311yescharacteristic
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3×D3—21no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—21no—
505C2×C3×D3—21no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—21no—
509C2×C3×D3—22no—
510C2×C3×D3—24no—
511C2×C3×D3—41no—
512C2×C3×D3—42no—
513C2×C3×D3—42no—
514C2×C3×D3—41no—
515C2×C3×D3—62no—
516C2×C3×D3—62no—
517C2×C3×D3—62no—
518C2×C3×D3—62no—
519C2×C3×D3—62no—
520C2×C3×D3—62no—
521C2×C3×D3—122no—
522C2×C3×D3—122no—
523C2×C3×D3—122no—
524C2×C3×D3—128no—
525C2×C3×D3—128no—
526C2×C3×D3#23512yescomplemented
527C2×C3×D3C2×#6714yes—
528C2×C3×D3C2×C3×D414yes—
529C2×C3×D3C3×#4112yescomplemented
530D32—48no—
531C32×C4—21no—
532C32×C4—22no—
533C32×C4—21no—
534C32×C4—21no—
535C32×C4—22no—
536C32×C4—22no—
537C32×C4—22no—
538C32×C4—42no—
539C32×C4—41no—
540C32×C4—41no—
541C32×C4—42no—
542C32×C4—62no—
543C32×C4—61no—
544C32×C4—61no—
545C32×C4—61no—
546C32×C4D3×D412yes—
547C32×C4C2×#6712yes—
548C32×C4C2×C3×D412yes—
549C3⋊Dic3—22no—
550C3×Dic3—24no—
551C3×Dic3—22no—
552C3×Dic3—21no—
553C3×Dic3—21no—
554C3×Dic3—21no—
555C3×Dic3—22no—
556C3×Dic3—21no—
557C3×Dic3—22no—
558C3×Dic3—21no—
559C3×Dic3—21no—
560C3×Dic3—41no—
561C3×Dic3—41no—
562C3×Dic3—62no—
563C3×Dic3—62no—
564C3×Dic3—122no—
565C2×#41—31no—
566C22×D4—91no—
567#124—91no—
568#123—92no—
569C22⋊Q8—91no—
570#121—92no—
571#121—91no—
572#120—92no—
573C4×D4—31no—
574C4×D4—91no—
575C2×C22⋊C4—92no—
576C33#54611yescharacteristic, complemented, Sylow
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—31no—
581C23×C3—32no—
582C23×C3—31no—
583C23×C3—32no—
584C23×C3—41no—
585C23×C3—61no—
586C23×C3—62no—
587C23×C3—92no—
588C23×C3—184no—
589C23×C3—184no—
590C23×C3—362no—
591C23×C3C2×D3211yescharacteristic
592C23×C3C22×C3×D311yescharacteristic
593C23×C3C22×C3×D311yescharacteristic
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—62no—
597C22×D3—64no—
598C22×D3—64no—
599C22×D3—64no—
600C22×D3—64no—
601C22×D3—122no—
602C22×D3—122no—
603C22×D3C22×C3×D311yescharacteristic
604C22×D3C22×C3×D312yes—
605C3×Q8—64no—
606C3×Q8—62no—
607C3×Q8—62no—
608C3×D4—34no—
609C3×D4—34no—
610C3×D4—64no—
611C3×D4—62no—
612C3×D4—62no—
613C3×D4—64no—
614C3×D4—64no—
615C3×D4—64no—
616C3×D4—68no—
617C3×D4—184no—
618C3×D4—182no—
619C3×D4—362no—
620C2×C3×C4—24no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—22no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—31no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—32no—
634C2×C3×C4—31no—
635C2×C3×C4—32no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—42no—
639C2×C3×C4—42no—
640C2×C3×C4—44no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—61no—
644C2×C3×C4—62no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—64no—
648C2×C3×C4—64no—
649C2×C3×C4—68no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—92no—
653C2×C3×C4—122no—
654C2×C3×C4—362no—
655C2×C3×C4C2×D3211yescharacteristic
656C2×C3×C4C2×D3211yescharacteristic
657C2×C3×C4C22×C3×D311yescharacteristic
658C2×C3×C4C22×C3×D311yescharacteristic
659C2×C3×C4C22×C3×D311yescharacteristic
660C2×C3×C4C22×C3×D311yescharacteristic
661#67—22no—
662#67—24no—
663#67—64no—
664#67—122no—
665#67—122no—
666#67—124no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—62no—
670C2×Dic3—122no—
671C2×Dic3C22×C3×D311yescharacteristic
672C2×Dic3C22×C3×D311yescharacteristic
673C2×Dic3C22×C3×D311yescharacteristic
674C2×Dic3C22×C3×D312yes—
675D12—64no—
676D12—62no—
677D12—62no—
678D12—122no—
679D12C3×#6714yescomplemented
680C4×D3—24no—
681C4×D3—22no—
682C4×D3—122no—
683Dic6—22no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—21no—
691C2×C32—21no—
692C2×C32—21no—
693C2×C32—41no—
694C2×C32—41no—
695C2×C32—41no—
696C2×C32—42no—
697C2×C32—42no—
698C2×C32—42no—
699C2×C32—44no—
700C2×C32—41no—
701C2×C32—41no—
702C2×C32—41no—
703C2×C32—64no—
704C2×C32—62no—
705C2×C32C2×#23511yescharacteristic
706C2×C32C2×D3×D411yescharacteristic
707C2×C32D3×#4111yescharacteristic
708C2×C32#100911yescharacteristic
709C2×C32#100911yescharacteristic
710C2×C32C22×#6711yescharacteristic
711C2×C32C22×C3×D411yescharacteristic
712C2×C32C2×C3×#4111yescharacteristic
713C2×C32C3×H(5,𝔽2)11yescharacteristic
714C3⋊D3—42no—
715C3×D3—22no—
716C3×D3—24no—
717C3×D3—22no—
718C3×D3—24no—
719C3×D3—42no—
720C3×D3—44no—
721C3×D3—122no—
722C3×D3—122no—
723C3×D3—242no—
724C24—92no—
725#41—64no—
726C2×Q8—31no—
727C2×D4—31no—
728C2×D4—32no—
729C2×D4—31no—
730C2×D4—92no—
731C2×D4—92no—
732C2×D4—91no—
733C2×D4—184no—
734C22×C4—32no—
735C22×C4—31no—
736C22×C4—92no—
737C22×C4C3×D3211yescharacteristic, complemented
738C4⋊C4—31no—
739C4⋊C4—92no—
740C4⋊C4—91no—
741C22⋊C4—31no—
742C22⋊C4—31no—
743C22⋊C4—92no—
744C22⋊C4—92no—
745C22⋊C4—92no—
746C22⋊C4—92no—
747C22⋊C4—92no—
748C42—31no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—32no—
765C22×C3—34no—
766C22×C3—34no—
767C22×C3—32no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—42no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—41no—
778C22×C3—64no—
779C22×C3—62no—
780C22×C3—62no—
781C22×C3—62no—
782C22×C3—61no—
783C22×C3—61no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—61no—
787C22×C3—61no—
788C22×C3—121no—
789C22×C3—122no—
790C22×C3—122no—
791C22×C3—121no—
792C22×C3—182no—
793C22×C3—182no—
794C22×C3—182no—
795C22×C3—368no—
796C22×C3C22×D3211yescharacteristic
797C22×C3C23×C3×D311yescharacteristic
798C22×C3C23×C3×D311yescharacteristic
799C2×D3—21no—
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—21no—
803C2×D3—62no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—122no—
810C2×D3—122no—
811C2×D3—122no—
812C2×D3—128no—
813C2×D3—128no—
814C2×D3C3×#23512yescomplemented
815C2×D3C2×C3×#6714yes—
816C3×C4—22no—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—22no—
823C3×C4—41no—
824C3×C4—41no—
825C3×C4—42no—
826C3×C4—42no—
827C3×C4—64no—
828C3×C4—62no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—62no—
832C3×C4—61no—
833C3×C4—62no—
834C3×C4—61no—
835C3×C4—61no—
836C3×C4—61no—
837C3×C4—121no—
838C3×C4—121no—
839C3×C4—182no—
840C3×C4D3×#6712yes—
841C3×C4C3×D3×D412yes—
842C3×C4C2×C3×#6712yes—
843Dic3—21no—
844Dic3—21no—
845Dic3—21no—
846Dic3—22no—
847Dic3—62no—
848Dic3—62no—
849Dic3—122no—
850C32—21no—
851C32—21no—
852C32—21no—
853C32—41no—
854C32#555011yescharacteristic, complemented
855C32#582911yescharacteristic, complemented
856C32C3×#54611yescharacteristic, complemented
857C23—31no—
858C23—32no—
859C23—92no—
860C23—184no—
861C23—184no—
862C23—362no—
863C23C2×C3×D3211yescharacteristic
864Q8—62no—
865D4—34no—
866D4—64no—
867D4—62no—
868D4—184no—
869D4—182no—
870D4—362no—
871C2×C4—22no—
872C2×C4—31no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—32no—
876C2×C4—64no—
877C2×C4—62no—
878C2×C4—92no—
879C2×C4—362no—
880C2×C4C2×C3×D3211yescharacteristic
881C2×C4C2×C3×D3211yescharacteristic
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—42no—
892C2×C3—42no—
893C2×C3—42no—
894C2×C3—44no—
895C2×C3—41no—
896C2×C3—41no—
897C2×C3—41no—
898C2×C3—41no—
899C2×C3—41no—
900C2×C3—41no—
901C2×C3—64no—
902C2×C3—62no—
903C2×C3—62no—
904C2×C3—64no—
905C2×C3—122no—
906C2×C3—124no—
907C2×C3—362no—
908C2×C3D3×#23511yescharacteristic
909C2×C3#6430811yescharacteristic
910C2×C3C2×D3×#6711yescharacteristic
911C2×C3C2×C3×#23511yescharacteristic
912C2×C3C2×C3×D3×D411yescharacteristic
913C2×C3C3×D3×#4111yescharacteristic
914C2×C3C3×#100911yescharacteristic
915C2×C3C3×#100911yescharacteristic
916C2×C3C22×C3×#6711yescharacteristic
917D3—22no—
918D3—24no—
919D3—122no—
920D3—122no—
921D3—242no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—34no—
926C22—32no—
927C22—61no—
928C22—62no—
929C22—62no—
930C22—61no—
931C22—182no—
932C22—182no—
933C22—182no—
934C22—368no—
935C22C22×C3×D3211yescharacteristic
936C4—21no—
937C4—62no—
938C4—61no—
939C4—61no—
940C4—61no—
941C4—182no—
942C4C3×D3×#6712yes—
943C3—21no—
944C3—21no—
945C3—21no—
946C3—41no—
947C3#1059506711yescharacteristic, direct product factor
948C3C3×#555011yescharacteristic, complemented
949C3C3×#582911yescharacteristic, complemented
950C2—41no—
951C2—62no—
952C2—64no—
953C2—362no—
954C2C3×D3×#23511yescharacteristic
955C2C3×#6430811yescharacteristic
956C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#546
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×C32×#235C2semidirect
2. C2×C3×D3×D12C2semidirect
3. C3×#64139C2semidirect
4. C32×C4×#67C2semidirect
5. C3×#63983C2semidirect
6. C3×#63971C2semidirect
7. C3×D3×(C2×D3)⋊C4C2semidirect
8. C3×Dic3×D12C2semidirect
9. C3×#63864C2semidirect
10. C3×#63856C2semidirect
11. C3×#63850C2semidirect
14. #10595067C3direct (N × H)
16. C22×C33×C4C22semidirect
17. C2×C3×#638C22semidirect
20. C2×C32×#67C22semidirect
24. C2×C32×C4×D3C22semidirect
25. C2×C32×Dic6C22semidirect
27. C2×C3×D3×Dic3C22semidirect
29. C3×#3752C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. C32×#217C22semidirect
33. C32×Dic3⋊C4C22semidirect
34. C32×C4×Dic3C22semidirect
35. C3×#3724C22semidirect
36. C3×#3722C22semidirect
37. C3×#3722C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
43. C2×C3×#235D3semidirect
44. C2×C3×#235C2×C3semidirect
46. C2×D3×D12C2×C3semidirect
48. #64139C2×C3semidirect
60. C3×C4×#67D3semidirect
61. C3×C4×#67C2×C3semidirect
69. #63983C2×C3semidirect
70. #63971C2×C3semidirect
71. D3×(C2×D3)⋊C4C2×C3semidirect
72. Dic3×D12C2×C3semidirect
73. #63864C2×C3semidirect
74. #63856C2×C3semidirect
75. #63850C2×C3semidirect
95. C32×D12D4semidirect
118. C22×C32×C4C2×D3semidirect
119. C22×C32×C4C2×D3semidirect
120. C22×C32×C4C22×C3semidirect
121. C2×#638C22×C3semidirect
130. C2×C3×#67C2×D3semidirect
132. C2×C3×#67C22×C3semidirect
150. C2×C3×C4×D3C2×D3semidirect
152. C2×C3×C4×D3C22×C3semidirect
154. C2×C3×Dic6C2×D3semidirect
155. C2×C3×Dic6C22×C3semidirect
157. C2×D3×Dic3C22×C3semidirect
163. #3752C22×C3semidirect
164. C4⋊(C3⋊Dic3)C22×C3semidirect
168. C3×#217C2×D3semidirect
169. C3×#217C22×C3semidirect
188. C3×Dic3⋊C4C2×D3semidirect
189. C3×Dic3⋊C4C22×C3semidirect
191. C3×C4×Dic3C2×D3semidirect
192. C3×C4×Dic3C22×C3semidirect
193. #3724C22×C3semidirect
194. #3722C22×C3semidirect
195. #3722C22×C3semidirect
197. (C2×D3)⋊Dic3C22×C3semidirect
210. C2×C32×D3#41semidirect
224. C2×#235C3×D3semidirect
247. C4×#67C3×D3semidirect
348. C3×D12#67semidirect
349. C3×D12C3×D4semidirect
403. C22×C3×C4D32semidirect
404. C22×C3×C4C2×C3×D3semidirect
405. C22×C3×C4C2×C3×D3semidirect
411. C2×#67C2×C3×D3semidirect
423. C2×C4×D3C2×C3×D3semidirect
424. C2×Dic6C2×C3×D3semidirect
446. #217C2×C3×D3semidirect
462. Dic3⋊C4C2×C3×D3semidirect
463. C4×Dic3C2×C3×D3semidirect
526. C2×C3×D3#235semidirect
529. C2×C3×D3C3×#41semidirect
576. C33#546semidirect
679. D12C3×#67semidirect
737. C22×C4C3×D32semidirect
814. C2×D3C3×#235semidirect
854. C32#5550semidirect
855. C32#5829semidirect
856. C32C3×#546semidirect
947. C3#10595067direct (N × H)
948. C3C3×#5550semidirect
949. C3C3×#5829semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C2×C3×D3×D122
C3×#641392
C32×C4×#672
C3×#639832
C3×#639712
C3×D3×(C2×D3)⋊C42
C3×Dic3×D122
C3×#638642
C3×#638562
C3×#638502
C3×#58293
C3×#55503
#105950673