Finite Group Databasebeta

← C3×#10595078 #13174675

Subgroups — C3×#10595078 #13174675

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×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3C32×#930C211yesmaximal, characteristic, complemented
4C32×C4×#67C211yesmaximal, characteristic, complemented
5C3×#63983C212yesmaximal, complemented
6C3×#63958C212yesmaximal, complemented
7C3×#63921C212yesmaximal, complemented
8C3×#63894C211yesmaximal, characteristic, complemented
9C3×#63860C211yesmaximal, characteristic, complemented
10C3×#63857C211yesmaximal, characteristic, complemented
11C3×#63853C212yesmaximal, complemented
12C3×#5612—31nomaximal
13C3×#5550—31nomaximal
14#10595078C311yesmaximal, characteristic, direct product factor
15C22×C3×D32C2212yes—
16C22×C33×C4C2211yescharacteristic, complemented
17C2×C3×#638C2212yescomplemented
18C3×#3828—24no—
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2212yescomplemented
21C2×C3×#634C2211yescharacteristic, complemented
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2212yescomplemented
24C2×C32×D12C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C3×#626C2212yes—
27C2×C3×#624C2212yescomplemented
28C3×D3×D12—24no—
29C32×#217C2211yescharacteristic, complemented
30C32×(C2×D3)⋊C4C2211yescharacteristic
31C32×(C2×D3)⋊C4C2212yescomplemented
32C32×C4⋊Dic3C2211yescharacteristic, complemented
33C32×Dic3⋊C4C2211yescharacteristic, complemented
34C32×C4×Dic3C2211yescharacteristic, complemented
35C3×Dic3⋊Dic3C2212yescomplemented
36C3×#3722C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×#3828C2×C311yescharacteristic, complemented
41C2×C3×D3×D4—31no—
42C2×C3×#235—31no—
43C2×C3×#235—31no—
44C2×C3×#235—61no—
45C22×C3×D12—31no—
46C2×D3×D12C2×C311yescharacteristic, complemented
47C32×#121—31no—
48C32×C4×D4—31no—
49C3×#938—32no—
50C3×#937—32no—
51C3×#937—32no—
52C3×#936—31no—
53C3×#930—21no—
54C3×#930D311yescharacteristic, complemented
55C3×#930C2×C311yescharacteristic, complemented
56C3×C4×#67—21no—
57C3×C4×#67D311yescharacteristic, complemented
58C3×C4×#67C2×C311yescharacteristic, complemented
59C3×#924—31no—
60C3×#897—31no—
61C3×#894—32no—
62C3×#893—31no—
63C3×#884—32no—
64C3×#883—32no—
65C3×D3×C22⋊C4—32no—
66C3×D3×C22⋊C4—32no—
67C3×#875—31no—
68C3×C4×D12—31no—
69#63983C2×C312yescomplemented
70#63958C2×C312yescomplemented
71#63921C2×C312yescomplemented
72#63894C2×C311yescharacteristic, complemented
73#63860C2×C311yescharacteristic, complemented
74#63857C2×C311yescharacteristic, complemented
75#63853C2×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—24no—
87C2×C3×C3⋊Dic3C2312yes—
88C3×C4⋊(C3⋊D3)D414yescomplemented
89C3×C4×C3⋊D3—24no—
90C3×#634—22no—
91C32×#67—22no—
92C32×#67—42no—
93C2×C32×Dic3C2311yescharacteristic
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2312yes—
96C2×C32×Dic3C2311yescharacteristic
97C32×D12—22no—
98C32×C4×D3—22no—
99C3×#626—24no—
100C3×#624—42no—
101C3×#546—91no—
102#5612—31no—
103#5550—31no—
104C23×C3×D3—32no—
105C23×C3×D3—32no—
106C22×D32C22×C312yes—
107C2×C32×D4—31no—
108C2×C32×D4—32no—
109C2×C32×D4—31no—
110C22×C32×C4—21no—
111C22×C32×C4—21no—
112C22×C32×C4—21no—
113C22×C32×C4—31no—
114C22×C32×C4—41no—
115C22×C32×C4C2×D311yescharacteristic, complemented
116C22×C32×C4C2×D311yescharacteristic, complemented
117C22×C32×C4C22×C311yescharacteristic, complemented
118C2×#638C22×C312yescomplemented
119#3828—24no—
120C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
121C2×C4×C3⋊D3C22×C312yescomplemented
122C2×#634C22×C311yescharacteristic, complemented
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
133C3×D3×D4—64no—
134C3×#235—64no—
135C3×#235—64no—
136C3×#235—68no—
137C2×C3×D12—21no—
138C2×C3×D12—31no—
139C2×C3×D12—31no—
140C2×C3×D12—32no—
141C2×C3×D12—64no—
142C2×C3×D12—61no—
143C2×C3×D12C2×D311yescharacteristic
144C2×C3×D12C22×C311yescharacteristic
145C2×C3×C4×D3—21no—
146C2×C3×C4×D3—32no—
147C2×C3×C4×D3—32no—
148C2×C3×C4×D3—32no—
149C2×C3×C4×D3—32no—
150C2×C3×C4×D3—62no—
151C2×C3×C4×D3C2×D311yescharacteristic
152C2×C3×C4×D3C22×C311yescharacteristic
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×C3×Dic6—61no—
156C2×#626C22×C312yes—
157C2×#624C22×C312yescomplemented
158D3×D12—24no—
159C32×C4⋊C4—31no—
160C32×C4⋊C4—31no—
161C32×C22⋊C4—31no—
162C32×C22⋊C4—31no—
163C32×C22⋊C4—32no—
164C32×C42—31no—
165C3×#217—21no—
166C3×#217—32no—
167C3×#217—32no—
168C3×#217—32no—
169C3×#217C2×D311yescharacteristic, complemented
170C3×#217C22×C311yescharacteristic, complemented
171C3×(C2×D3)⋊C4—21no—
172C3×(C2×D3)⋊C4—22no—
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)⋊C4C2×D311yescharacteristic
179C3×(C2×D3)⋊C4C2×D312yescomplemented
180C3×(C2×D3)⋊C4C22×C311yescharacteristic
181C3×(C2×D3)⋊C4C22×C312yescomplemented
182C3×C4⋊Dic3—21no—
183C3×C4⋊Dic3—32no—
184C3×C4⋊Dic3C2×D311yescharacteristic, complemented
185C3×C4⋊Dic3C22×C311yescharacteristic, complemented
186C3×Dic3⋊C4—21no—
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
193Dic3⋊Dic3C22×C312yescomplemented
194#3722C22×C312yescomplemented
195(C2×D3)⋊Dic3C22×C312yes—
196(C2×D3)⋊Dic3C22×C312yescomplemented
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⋊D3C2×D414yes—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—22no—
208C2×C32×D3—22no—
209C2×C32×D3—22no—
210C2×C32×D3#4112yescomplemented
211C3×D32—48no—
212C33×C4—21no—
213C33×C4C2×D412yes—
214C3×C3⋊Dic3—22no—
215C32×Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—22no—
219C2×C3×#41—91no—
220C22×C3×D4—91no—
221C2×D3×D4—31no—
222C2×#235—31no—
223C2×#235—31no—
224C2×#235—61no—
225C22×D12—31no—
226C3×#124—91no—
227C3×#123—92no—
228C3×C22⋊Q8—91no—
229C3×#121—31no—
230C3×#121—31no—
231C3×#121—61no—
232C3×#121—92no—
233C3×#120—92no—
234C3×C4×D4—31no—
235C3×C4×D4—31no—
236C3×C4×D4—61no—
237C3×C4×D4—91no—
238C2×C3×C22⋊C4—92no—
239#938—32no—
240#937—32no—
241#937—32no—
242#936—31no—
243#930C3×D311yescharacteristic, complemented
244C4×#67C3×D311yescharacteristic, complemented
245#924—31no—
246#897—31no—
247#894—32no—
248#893—31no—
249#884—32no—
250#883—32no—
251D3×C22⋊C4—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×D312yes—
277C22×C3×D3C22×D311yescharacteristic
278C22×C3×D3C23×C312yes—
279C22×C3×D3C23×C311yescharacteristic
280C2×D32—24no—
281C2×D32—24no—
282C2×D32—42no—
283C32×D4—62no—
284C32×D4—62no—
285C32×D4—122no—
286C2×C32×C4—22no—
287C2×C32×C4—24no—
288C2×C32×C4—22no—
289C2×C32×C4—22no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4—31no—
297C2×C32×C4—32no—
298C2×C32×C4—31no—
299C2×C32×C4—31no—
300C2×C32×C4—41no—
301C2×C32×C4—41no—
302C2×C32×C4—42no—
303C2×C32×C4—42no—
304C2×C32×C4—44no—
305C2×C32×C4—62no—
306C2×C32×C4C22×D311yescharacteristic
307C2×C32×C4C22×D311yescharacteristic
308C2×C32×C4C22×D311yescharacteristic
309C2×C32×C4C22×D311yescharacteristic
310C2×C32×C4C23×C311yescharacteristic
311C2×C32×C4C23×C311yescharacteristic
312#638—24no—
313C2×C3⋊Dic3C23×C312yes—
314C4⋊(C3⋊D3)C3×D414yescomplemented
315C4×C3⋊D3—24no—
316#634—22no—
317C3×#67—24no—
318C3×#67—22no—
319C3×#67—22no—
320C3×#67—42no—
321C3×#67—42no—
322C3×#67—44no—
323C3×#67—64no—
324C3×#67—64no—
325C3×#67—64no—
326C3×#67—68no—
327C2×C3×Dic3—21no—
328C2×C3×Dic3—21no—
329C2×C3×Dic3—21no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—32no—
332C2×C3×Dic3—32no—
333C2×C3×Dic3—62no—
334C2×C3×Dic3C22×D311yescharacteristic
335C2×C3×Dic3C22×D311yescharacteristic
336C2×C3×Dic3C22×D312yes—
337C2×C3×Dic3C22×D311yescharacteristic
338C2×C3×Dic3C23×C312yes—
339C2×C3×Dic3C23×C311yescharacteristic
340C2×C3×Dic3C23×C311yescharacteristic
341C2×C3×Dic3C23×C311yescharacteristic
342C3×D12—22no—
343C3×D12—22no—
344C3×D12—34no—
345C3×D12—34no—
346C3×D12—42no—
347C3×D12—64no—
348C3×D12—64no—
349C3×C4×D3—22no—
350C3×C4×D3—22no—
351C3×C4×D3—42no—
352C3×C4×D3—64no—
353C3×C4×D3—64no—
354C3×C4×D3—68no—
355C3×C4×D3—122no—
356C3×C4×D3—122no—
357C3×Dic6—64no—
358C3×Dic6—62no—
359C3×Dic6—62no—
360#626—24no—
361#624—42no—
362#546—91noSylow
363C2×C33—41no—
364C2×C33C22×D411yescharacteristic
365C2×C33C2×#4111yescharacteristic
366C2×C33H(5,𝔽2)11yescharacteristic
367C3×C3⋊D3—24no—
368C32×D3—22no—
369C32×D3—42no—
370C24×C3—92no—
371C23×D3—32no—
372C23×D3—32no—
373C3×#41—184no—
374C2×C3×Q8—91no—
375C2×C3×D4—31no—
376C2×C3×D4—31no—
377C2×C3×D4—32no—
378C2×C3×D4—32no—
379C2×C3×D4—31no—
380C2×C3×D4—31no—
381C2×C3×D4—61no—
382C2×C3×D4—61no—
383C2×C3×D4—62no—
384C2×C3×D4—92no—
385C2×C3×D4—92no—
386C2×C3×D4—91no—
387C2×C3×D4—184no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—21no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—41no—
394C22×C3×C4—61no—
395C22×C3×C4—92no—
396C22×C3×C4—92no—
397C22×C3×C4D3211yescharacteristic, complemented
398C22×C3×C4C2×C3×D311yescharacteristic, complemented
399C22×C3×C4C2×C3×D311yescharacteristic, complemented
400C2×#67—32no—
401C2×#67—32no—
402C2×#67—32no—
403C2×#67—62no—
404C2×#67C2×C3×D311yescharacteristic
405C2×#67C2×C3×D312yescomplemented
406D3×D4—64no—
407#235—64no—
408#235—64no—
409#235—68no—
410C2×D12—31no—
411C2×D12—31no—
412C2×D12—32no—
413C2×D12—61no—
414C2×D12—64no—
415C2×D12C2×C3×D311yescharacteristic
416C2×C4×D3—32no—
417C2×C4×D3—32no—
418C2×C4×D3—32no—
419C2×C4×D3—32no—
420C2×C4×D3—62no—
421C2×C4×D3C2×C3×D311yescharacteristic
422C2×Dic6—31no—
423C2×Dic6—31no—
424C2×Dic6—61no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4—31no—
427C3×C4⋊C4—31no—
428C3×C4⋊C4—31no—
429C3×C4⋊C4—61no—
430C3×C4⋊C4—61no—
431C3×C4⋊C4—92no—
432C3×C22⋊C4—31no—
433C3×C22⋊C4—31no—
434C3×C22⋊C4—31no—
435C3×C22⋊C4—32no—
436C3×C22⋊C4—31no—
437C3×C22⋊C4—32no—
438C3×C22⋊C4—61no—
439C3×C22⋊C4—62no—
440C3×C22⋊C4—61no—
441C3×C22⋊C4—92no—
442C3×C22⋊C4—92no—
443C3×C22⋊C4—92no—
444C3×C22⋊C4—92no—
445C3×C42—31no—
446C3×C42—31no—
447C3×C42—61no—
448#217—32no—
449#217—32no—
450#217—32no—
451#217C2×C3×D311yescharacteristic, complemented
452(C2×D3)⋊C4—32no—
453(C2×D3)⋊C4—32no—
454(C2×D3)⋊C4—32no—
455(C2×D3)⋊C4—32no—
456(C2×D3)⋊C4—32no—
457(C2×D3)⋊C4C2×C3×D311yescharacteristic
458(C2×D3)⋊C4C2×C3×D312yescomplemented
459C4⋊Dic3—32no—
460C4⋊Dic3C2×C3×D311yescharacteristic, complemented
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—32no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—42no—
488C22×C32—42no—
489C22×C32—42no—
490C22×C32—61no—
491C22×C32—61no—
492C22×C32—62no—
493C22×C32—62no—
494C22×C32—62no—
495C22×C32C23×D311yescharacteristic
496C22×C32C23×D311yescharacteristic
497C22×C32C24×C311yescharacteristic
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3C2×C3×D414yes—
501C2×C3×D3—21no—
502C2×C3×D3—21no—
503C2×C3×D3—21no—
504C2×C3×D3—21no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—34no—
513C2×C3×D3—34no—
514C2×C3×D3—41no—
515C2×C3×D3—41no—
516C2×C3×D3—42no—
517C2×C3×D3—42no—
518C2×C3×D3—42no—
519C2×C3×D3—64no—
520C2×C3×D3—62no—
521C2×C3×D3—62no—
522C2×C3×D3—62no—
523C2×C3×D3—62no—
524C2×C3×D3—122no—
525C2×C3×D3—122no—
526C2×C3×D3—128no—
527C2×C3×D3—128no—
528C2×C3×D3#23512yescomplemented
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—61no—
543C32×C4—61no—
544C32×C4—61no—
545C32×C4—62no—
546C32×C4D3×D412yes—
547C32×C4D3×D412yes—
548C32×C4C2×C3×D412yes—
549C3⋊Dic3—22no—
550C3×Dic3—22no—
551C3×Dic3—21no—
552C3×Dic3—21no—
553C3×Dic3—22no—
554C3×Dic3—21no—
555C3×Dic3—21no—
556C3×Dic3—21no—
557C3×Dic3—21no—
558C3×Dic3—22no—
559C3×Dic3—41no—
560C3×Dic3—41no—
561C3×Dic3—42no—
562C3×Dic3—64no—
563C3×Dic3—62no—
564C3×Dic3—62no—
565C2×#41—91no—
566C22×D4—91no—
567#124—91no—
568#123—92no—
569C22⋊Q8—91no—
570#121—31no—
571#121—92no—
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—31no—
582C23×C3—32no—
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×D312yes—
604C22×D3C22×C3×D311yescharacteristic
605C3×Q8—182no—
606C3×D4—62no—
607C3×D4—62no—
608C3×D4—64no—
609C3×D4—62no—
610C3×D4—62no—
611C3×D4—94no—
612C3×D4—122no—
613C3×D4—122no—
614C3×D4—122no—
615C3×D4—124no—
616C3×D4—184no—
617C3×D4—184no—
618C2×C3×C4—24no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—32no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—32no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—42no—
637C2×C3×C4—42no—
638C2×C3×C4—44no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—62no—
647C2×C3×C4—92no—
648C2×C3×C4—122no—
649C2×C3×C4—184no—
650C2×C3×C4—362no—
651C2×C3×C4C2×D3211yescharacteristic
652C2×C3×C4C2×D3211yescharacteristic
653C2×C3×C4C22×C3×D311yescharacteristic
654C2×C3×C4C22×C3×D311yescharacteristic
655C2×C3×C4C22×C3×D311yescharacteristic
656C2×C3×C4C22×C3×D311yescharacteristic
657#67—22no—
658#67—42no—
659#67—64no—
660#67—64no—
661#67—64no—
662#67—68no—
663C2×Dic3—32no—
664C2×Dic3—32no—
665C2×Dic3—62no—
666C2×Dic3C22×C3×D311yescharacteristic
667C2×Dic3C22×C3×D311yescharacteristic
668C2×Dic3C22×C3×D312yes—
669C2×Dic3C22×C3×D311yescharacteristic
670D12—22no—
671D12—34no—
672D12—34no—
673D12—64no—
674D12—64no—
675C4×D3—22no—
676C4×D3—64no—
677C4×D3—64no—
678C4×D3—68no—
679C4×D3—122no—
680C4×D3—122no—
681Dic6—64no—
682Dic6—62no—
683Dic6—62no—
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—62no—
704C2×C32—122no—
705C2×C32C2×#23511yescharacteristic
706C2×C32C2×D3×D411yescharacteristic
707C2×C32C2×D3×D411yescharacteristic
708C2×C32#100411yescharacteristic
709C2×C32D3×#4111yescharacteristic
710C2×C32#100911yescharacteristic
711C2×C32C22×C3×D411yescharacteristic
712C2×C32C2×C3×#4111yescharacteristic
713C2×C32C3×H(5,𝔽2)11yescharacteristic
714C3⋊D3—24no—
715C3×D3—22no—
716C3×D3—22no—
717C3×D3—42no—
718C3×D3—42no—
719C3×D3—42no—
720C3×D3—64no—
721C3×D3—64no—
722C3×D3—82no—
723C3×D3—124no—
724C24—92no—
725#41—184no—
726C2×Q8—91no—
727C2×D4—31no—
728C2×D4—32no—
729C2×D4—31no—
730C2×D4—92no—
731C2×D4—92no—
732C2×D4—91no—
733C2×D4—184no—
734C22×C4—31no—
735C22×C4—92no—
736C22×C4—92no—
737C22×C4C3×D3211yescharacteristic, complemented
738C4⋊C4—31no—
739C4⋊C4—31no—
740C4⋊C4—92no—
741C22⋊C4—31no—
742C22⋊C4—31no—
743C22⋊C4—32no—
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—32no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—42no—
775C22×C3—41no—
776C22×C3—62no—
777C22×C3—61no—
778C22×C3—61no—
779C22×C3—61no—
780C22×C3—61no—
781C22×C3—62no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—94no—
788C22×C3—121no—
789C22×C3—121no—
790C22×C3—122no—
791C22×C3—122no—
792C22×C3—122no—
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—21no—
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—34no—
805C2×D3—34no—
806C2×D3—64no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—62no—
811C2×D3—122no—
812C2×D3—122no—
813C2×D3—128no—
814C2×D3—128no—
815C2×D3C3×#23512yescomplemented
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—62no—
828C3×C4—61no—
829C3×C4—61no—
830C3×C4—62no—
831C3×C4—61no—
832C3×C4—61no—
833C3×C4—61no—
834C3×C4—61no—
835C3×C4—62no—
836C3×C4—121no—
837C3×C4—122no—
838C3×C4—121no—
839C3×C4—182no—
840C3×C4#381112yes—
841C3×C4C3×D3×D412yes—
842C3×C4C3×D3×D412yes—
843Dic3—21no—
844Dic3—21no—
845Dic3—22no—
846Dic3—21no—
847Dic3—64no—
848Dic3—62no—
849Dic3—62no—
850C32—21no—
851C32—21no—
852C32—21no—
853C32—41no—
854C32#555011yescharacteristic, complemented
855C32#561211yescharacteristic, complemented
856C32C3×#54611yescharacteristic, complemented
857C23—31no—
858C23—32no—
859C23—92no—
860C23—184no—
861C23—184no—
862C23—362no—
863C23C2×C3×D3211yescharacteristic
864Q8—182no—
865D4—62no—
866D4—62no—
867D4—94no—
868D4—122no—
869D4—184no—
870D4—184no—
871C2×C4—22no—
872C2×C4—31no—
873C2×C4—31no—
874C2×C4—32no—
875C2×C4—31no—
876C2×C4—62no—
877C2×C4—92no—
878C2×C4—184no—
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—62no—
902C2×C3—62no—
903C2×C3—122no—
904C2×C3—122no—
905C2×C3—122no—
906C2×C3—184no—
907C2×C3—242no—
908C2×C3D3×#23511yescharacteristic
909C2×C3#6430711yescharacteristic
910C2×C3C2×#381111yescharacteristic
911C2×C3C2×C3×#23511yescharacteristic
912C2×C3C2×C3×D3×D411yescharacteristic
913C2×C3C2×C3×D3×D411yescharacteristic
914C2×C3C3×#100411yescharacteristic
915C2×C3C3×D3×#4111yescharacteristic
916C2×C3C3×#100911yescharacteristic
917D3—22no—
918D3—42no—
919D3—64no—
920D3—64no—
921D3—124no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—32no—
926C22—61no—
927C22—61no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—94no—
932C22—182no—
933C22—182no—
934C22—368no—
935C22C22×C3×D3211yescharacteristic
936C4—21no—
937C4—61no—
938C4—61no—
939C4—61no—
940C4—62no—
941C4—182no—
942C4C3×#381112yes—
943C3—21no—
944C3—21no—
945C3—21no—
946C3—41no—
947C3#1059507811yescharacteristic, direct product factor
948C3C3×#555011yescharacteristic, complemented
949C3C3×#561211yescharacteristic, complemented
950C2—41no—
951C2—62no—
952C2—122no—
953C2—184no—
954C2C3×D3×#23511yescharacteristic
955C2C3×#6430711yescharacteristic
956C2C2×C3×#381111yescharacteristic
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×C3×#3828C2semidirect
2. C2×C3×D3×D12C2semidirect
3. C32×#930C2semidirect
4. C32×C4×#67C2semidirect
5. C3×#63983C2semidirect
6. C3×#63958C2semidirect
7. C3×#63921C2semidirect
8. C3×#63894C2semidirect
9. C3×#63860C2semidirect
10. C3×#63857C2semidirect
11. C3×#63853C2semidirect
14. #10595078C3direct (N × H)
16. C22×C33×C4C22semidirect
17. C2×C3×#638C22semidirect
20. C2×C3×C4×C3⋊D3C22semidirect
21. C2×C3×#634C22semidirect
23. C2×C32×#67C22semidirect
27. C2×C3×#624C22semidirect
29. C32×#217C22semidirect
31. C32×(C2×D3)⋊C4C22semidirect
32. C32×C4⋊Dic3C22semidirect
33. C32×Dic3⋊C4C22semidirect
34. C32×C4×Dic3C22semidirect
35. C3×Dic3⋊Dic3C22semidirect
36. C3×#3722C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
40. C2×#3828C2×C3semidirect
46. C2×D3×D12C2×C3semidirect
54. C3×#930D3semidirect
55. C3×#930C2×C3semidirect
57. C3×C4×#67D3semidirect
58. C3×C4×#67C2×C3semidirect
69. #63983C2×C3semidirect
70. #63958C2×C3semidirect
71. #63921C2×C3semidirect
72. #63894C2×C3semidirect
73. #63860C2×C3semidirect
74. #63857C2×C3semidirect
75. #63853C2×C3semidirect
88. C3×C4⋊(C3⋊D3)D4semidirect
115. C22×C32×C4C2×D3semidirect
116. C22×C32×C4C2×D3semidirect
117. C22×C32×C4C22×C3semidirect
118. C2×#638C22×C3semidirect
121. C2×C4×C3⋊D3C22×C3semidirect
122. C2×#634C22×C3semidirect
130. C2×C3×#67C2×D3semidirect
132. C2×C3×#67C22×C3semidirect
157. C2×#624C22×C3semidirect
169. C3×#217C2×D3semidirect
170. C3×#217C22×C3semidirect
179. C3×(C2×D3)⋊C4C2×D3semidirect
181. C3×(C2×D3)⋊C4C22×C3semidirect
184. C3×C4⋊Dic3C2×D3semidirect
185. C3×C4⋊Dic3C22×C3semidirect
188. C3×Dic3⋊C4C2×D3semidirect
189. C3×Dic3⋊C4C22×C3semidirect
191. C3×C4×Dic3C2×D3semidirect
192. C3×C4×Dic3C22×C3semidirect
193. Dic3⋊Dic3C22×C3semidirect
194. #3722C22×C3semidirect
196. (C2×D3)⋊Dic3C22×C3semidirect
197. (C2×D3)⋊Dic3C22×C3semidirect
210. C2×C32×D3#41semidirect
243. #930C3×D3semidirect
244. C4×#67C3×D3semidirect
314. C4⋊(C3⋊D3)C3×D4semidirect
397. C22×C3×C4D32semidirect
398. C22×C3×C4C2×C3×D3semidirect
399. C22×C3×C4C2×C3×D3semidirect
405. C2×#67C2×C3×D3semidirect
451. #217C2×C3×D3semidirect
458. (C2×D3)⋊C4C2×C3×D3semidirect
460. C4⋊Dic3C2×C3×D3semidirect
462. Dic3⋊C4C2×C3×D3semidirect
463. C4×Dic3C2×C3×D3semidirect
528. C2×C3×D3#235semidirect
529. C2×C3×D3C3×#41semidirect
576. C33#546semidirect
737. C22×C4C3×D32semidirect
815. C2×D3C3×#235semidirect
854. C32#5550semidirect
855. C32#5612semidirect
856. C32C3×#546semidirect
947. C3#10595078direct (N × H)
948. C3C3×#5550semidirect
949. C3C3×#5612semidirect

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×D3×D122
C32×#9302
C32×C4×#672
C3×#639832
C3×#639582
C3×#639212
C3×#638942
C3×#638602
C3×#638572
C3×#638532
C3×#56123
C3×#55503
#105950783