Finite Group Databasebeta

← C3×#10594419 #13173972

Subgroups — C3×#10594419 #13173972

Order 1728.

1112 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64105C211yesmaximal, characteristic, complemented
2C32×#894C211yesmaximal, characteristic, complemented
3C32×#887C211yesmaximal, characteristic, complemented
4C3×#63907C211yesmaximal, characteristic, complemented
5C3×C4×#626C211yesmaximal, characteristic, complemented
6C3×#63887C211yesmaximal, characteristic, complemented
7C3×#63886C211yesmaximal, characteristic
8C3×#63877C211yesmaximal, characteristic, complemented
9C3×#63868C211yesmaximal, characteristic, complemented
10C3×#63860C211yesmaximal, characteristic, complemented
11C3×#63859C211yesmaximal, characteristic, complemented
12C3×#63853C211yesmaximal, characteristic, complemented
13C3×#63852C211yesmaximal, characteristic, complemented
14C3×#63851C211yesmaximal, characteristic, complemented
15C3×#63840C211yesmaximal, characteristic, complemented
16C3×#5662—31nomaximal
17C3×#5582—31nomaximal
18#10594419C311yesmaximal, characteristic, direct product factor
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×C32×D12C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C2×C3×#627C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×C4×Dic3C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41C32×C4×Dic3C2211yescharacteristic
42C3×#3724C2211yescharacteristic
43C3×Dic3⋊Dic3C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×#3722C2211yescharacteristic
47C3×#3722C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×#123—31no—
55C32×C4×Q8—31no—
56#64105C2×C311yescharacteristic, complemented
57C3×#947—31no—
58C3×#946—31no—
59C3×#939—31no—
60C3×#936—31no—
61C3×C4×#67—31no—
62C3×#924—31no—
63C3×#898—31no—
64C3×#896—31no—
65C3×#896—31no—
66C3×#896—31no—
67C3×#896—61no—
68C3×#895—31no—
69C3×#894—21no—
70C3×#894—31no—
71C3×#894D311yescharacteristic, complemented
72C3×#894C2×C311yescharacteristic, complemented
73C3×#888—31no—
74C3×#888—31no—
75C3×#887—21no—
76C3×#887D311yescharacteristic, complemented
77C3×#887C2×C311yescharacteristic, complemented
78C3×#885—31no—
79C3×#885—31no—
80C3×#883—31no—
81C3×#879—31no—
82C3×#878—31no—
83C3×#877—31no—
84C3×#876—31no—
85C3×#876—31no—
86C3×#875—31no—
87C3×#875—31no—
88C3×C4×D12—31no—
89C3×#872—31no—
90#63907C2×C311yescharacteristic, complemented
91C4×#626C2×C311yescharacteristic, complemented
92#63887C2×C311yescharacteristic, complemented
93#63886C2×C311yescharacteristic
94#63877C2×C311yescharacteristic, complemented
95#63868C2×C311yescharacteristic, complemented
96#63860C2×C311yescharacteristic, complemented
97#63859C2×C311yescharacteristic, complemented
98#63853C2×C311yescharacteristic, complemented
99#63852C2×C311yescharacteristic, complemented
100#63851C2×C311yescharacteristic, complemented
101#63840C2×C311yescharacteristic, complemented
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C3×C4×C3⋊D3—41no—
112C3×#634—41no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C32×D12—41no—
120C32×C4×D3—41no—
121C32×Dic6—22no—
122C3×#627—41no—
123C3×#626—22no—
124C3×#626—41no—
125C3×D3×Dic3—22no—
126C3×#542—91no—
127#5662—31no—
128#5582—31no—
129C2×C32×Q8—31no—
130C2×C32×D4—31no—
131C22×C32×C4—31no—
132C2×C4×C3⋊D3C22×C311yescharacteristic
133C2×#634C22×C311yescharacteristic
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C22×C3×Dic3—31no—
137C2×C3×D12—21no—
138C2×C3×D12—31no—
139C2×C3×D12—31no—
140C2×C3×D12C2×D311yescharacteristic
141C2×C3×D12C22×C311yescharacteristic
142C2×C3×C4×D3—21no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—61no—
147C2×C3×C4×D3C2×D311yescharacteristic
148C2×C3×C4×D3C22×C311yescharacteristic
149C2×C3×Dic6—21no—
150C2×C3×Dic6—31no—
151C2×C3×Dic6—31no—
152C2×C3×Dic6—31no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—61no—
155C2×C3×Dic6C2×D311yescharacteristic
156C2×C3×Dic6C22×C311yescharacteristic
157C2×#627C22×C311yescharacteristic
158C2×#626C22×C311yescharacteristic
159C2×#626C22×C311yescharacteristic
160C2×D3×Dic3C22×C311yescharacteristic
161C32×C4⋊C4—21no—
162C32×C4⋊C4—21no—
163C32×C4⋊C4—21no—
164C32×C4⋊C4—31no—
165C32×C4⋊C4—31no—
166C32×C4⋊C4—31no—
167C32×C4⋊C4—41no—
168C32×C4⋊C4C2×D311yescharacteristic
169C32×C4⋊C4C2×D311yescharacteristic
170C32×C4⋊C4C22×C311yescharacteristic
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173C32×C22⋊C4—31no—
174C32×C42—31no—
175C32×C42—31no—
176C32×C42—31no—
177#3752C22×C311yescharacteristic
178#3752C22×C311yescharacteristic
179#3750C22×C311yescharacteristic
180#3750C22×C311yescharacteristic
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×(C2×D3)⋊C4—21no—
187C3×(C2×D3)⋊C4—21no—
188C3×(C2×D3)⋊C4—21no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—61no—
203C3×(C2×D3)⋊C4—61no—
204C3×(C2×D3)⋊C4C2×D311yescharacteristic
205C3×(C2×D3)⋊C4C2×D311yescharacteristic
206C3×(C2×D3)⋊C4C2×D311yescharacteristic
207C3×(C2×D3)⋊C4C22×C311yescharacteristic
208C3×(C2×D3)⋊C4C22×C311yescharacteristic
209C3×(C2×D3)⋊C4C22×C311yescharacteristic
210C3×C4⋊Dic3—31no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3—31no—
213C3×Dic3⋊C4—21no—
214C3×Dic3⋊C4—21no—
215C3×Dic3⋊C4—21no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—61no—
226C3×Dic3⋊C4—61no—
227C3×Dic3⋊C4C2×D311yescharacteristic
228C3×Dic3⋊C4C2×D311yescharacteristic
229C3×Dic3⋊C4C2×D311yescharacteristic
230C3×Dic3⋊C4C22×C311yescharacteristic
231C3×Dic3⋊C4C22×C311yescharacteristic
232C3×Dic3⋊C4C22×C311yescharacteristic
233C3×C4×Dic3—21no—
234C3×C4×Dic3—21no—
235C3×C4×Dic3—21no—
236C3×C4×Dic3—31no—
237C3×C4×Dic3—31no—
238C3×C4×Dic3C2×D311yescharacteristic
239C3×C4×Dic3C2×D311yescharacteristic
240C3×C4×Dic3C2×D311yescharacteristic
241C3×C4×Dic3C22×C311yescharacteristic
242C3×C4×Dic3C22×C311yescharacteristic
243C3×C4×Dic3C22×C311yescharacteristic
244#3724C22×C311yescharacteristic
245Dic3⋊Dic3C22×C311yescharacteristic
246Dic3⋊Dic3C22×C311yescharacteristic
247Dic3⋊Dic3C22×C311yescharacteristic
248#3722C22×C311yescharacteristic
249#3722C22×C311yescharacteristic
250(C2×D3)⋊Dic3C22×C311yescharacteristic
251(C2×D3)⋊Dic3C22×C311yescharacteristic
252(C2×D3)⋊Dic3C22×C311yescharacteristic
253(C2×D3)⋊Dic3C22×C311yescharacteristic
254(C2×D3)⋊Dic3C22×C311yescharacteristic
255Dic32C22×C311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C2×C32×D3—21no—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C33×C4—21no—
267C33×C4—21no—
268C33×C4—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3#4112yes—
278C3×C4⋊Q8—91no—
279C3×#126—91no—
280C3×#126—91no—
281C3×#124—91no—
282C3×#124—91no—
283C3×#124—91no—
284C3×#123—31no—
285C3×#123—31no—
286C3×#123—61no—
287C3×#123—91no—
288C3×C22⋊Q8—91no—
289C3×C22⋊Q8—91no—
290C3×C22⋊Q8—91no—
291C3×#121—91no—
292C3×C4×Q8—31no—
293C3×C4×Q8—31no—
294C3×C4×Q8—61no—
295C3×C4×D4—91no—
296C3×#117—91no—
297#947—31no—
298#946—31no—
299#939—31no—
300#936—31no—
301C4×#67—31no—
302#924—31no—
303#898—31no—
304#896—31no—
305#896—31no—
306#896—31no—
307#896—61no—
308#895—31no—
309#894—31no—
310#894C3×D311yescharacteristic, complemented
311#888—31no—
312#888—31no—
313#887C3×D311yescharacteristic, complemented
314#885—31no—
315#885—31no—
316#883—31no—
317#879—31no—
318#878—31no—
319#877—31no—
320#876—31no—
321#876—31no—
322#875—31no—
323#875—31no—
324C4×D12—31no—
325#872—31no—
326C23×C32—31no—
327C23×C32—31no—
328C22×C3⋊D3C23×C311yescharacteristic
329C22×C3×D3—21no—
330C22×C3×D3—21no—
331C22×C3×D3—31no—
332C22×C3×D3—31no—
333C22×C3×D3—61no—
334C22×C3×D3C22×D311yescharacteristic
335C22×C3×D3C22×D311yescharacteristic
336C22×C3×D3C23×C311yescharacteristic
337C22×C3×D3C23×C311yescharacteristic
338C32×Q8—62no—
339C32×D4—121no—
340C2×C32×C4—21no—
341C2×C32×C4—21no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
344C2×C32×C4—21no—
345C2×C32×C4—21no—
346C2×C32×C4—21no—
347C2×C32×C4—21no—
348C2×C32×C4—21no—
349C2×C32×C4—31no—
350C2×C32×C4—31no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—41no—
356C2×C32×C4—41no—
357C2×C32×C4—41no—
358C2×C32×C4—121no—
359C2×C32×C4C22×D311yescharacteristic
360C2×C32×C4C22×D311yescharacteristic
361C2×C32×C4C22×D311yescharacteristic
362C2×C32×C4C22×D311yescharacteristic
363C2×C32×C4C22×D311yescharacteristic
364C2×C32×C4C22×D311yescharacteristic
365C2×C32×C4C23×C311yescharacteristic
366C2×C32×C4C23×C311yescharacteristic
367C2×C32×C4C23×C311yescharacteristic
368C2×C3⋊Dic3C23×C311yescharacteristic
369C2×C3⋊Dic3C23×C311yescharacteristic
370C2×C3⋊Dic3C23×C311yescharacteristic
371C4×C3⋊D3—41no—
372#634—41no—
373C3×#67—62no—
374C3×#67—121no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—21no—
378C2×C3×Dic3—21no—
379C2×C3×Dic3—21no—
380C2×C3×Dic3—21no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—62no—
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C23×C311yescharacteristic
398C2×C3×Dic3C23×C311yescharacteristic
399C2×C3×Dic3C23×C311yescharacteristic
400C2×C3×Dic3C23×C311yescharacteristic
401C2×C3×Dic3C23×C311yescharacteristic
402C2×C3×Dic3C23×C311yescharacteristic
403C3×D12—41no—
404C3×D12—41no—
405C3×D12—42no—
406C3×D12—62no—
407C3×D12—121no—
408C3×C4×D3—41no—
409C3×C4×D3—41no—
410C3×C4×D3—42no—
411C3×C4×D3—62no—
412C3×C4×D3—121no—
413C3×C4×D3—121no—
414C3×C4×D3—122no—
415C3×Dic6—24no—
416C3×Dic6—22no—
417C3×Dic6—22no—
418C3×Dic6—121no—
419C3×Dic6—121no—
420C3×Dic6—121no—
421C3×Dic6—121no—
422C3×Dic6—122no—
423#627—41no—
424#626—22no—
425#626—41no—
426D3×Dic3—22no—
427#542—91noSylow
428C2×C33C2×#4111yescharacteristic
429C2×C33H(5,𝔽2)11yescharacteristic
430C2×C332−1+411yescharacteristic
431C3×C3⋊D3—41no—
432C32×D3—41no—
433C32×D3—41no—
434C2×C3×Q8—31no—
435C2×C3×Q8—31no—
436C2×C3×Q8—61no—
437C2×C3×Q8—91no—
438C2×C3×Q8—91no—
439C2×C3×D4—31no—
440C2×C3×D4—31no—
441C2×C3×D4—61no—
442C2×C3×D4—91no—
443C2×C3×D4—91no—
444C22×C3×C4—31no—
445C22×C3×C4—31no—
446C22×C3×C4—61no—
447C22×C3×C4—91no—
448C22×C3×C4—91no—
449C2×#67—31no—
450C2×#67—31no—
451C22×Dic3—31no—
452C2×D12—31no—
453C2×D12—31no—
454C2×D12C2×C3×D311yescharacteristic
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—31no—
458C2×C4×D3—61no—
459C2×C4×D3C2×C3×D311yescharacteristic
460C2×Dic6—31no—
461C2×Dic6—31no—
462C2×Dic6—31no—
463C2×Dic6—31no—
464C2×Dic6—61no—
465C2×Dic6C2×C3×D311yescharacteristic
466C3×C4⋊C4—21no—
467C3×C4⋊C4—21no—
468C3×C4⋊C4—21no—
469C3×C4⋊C4—31no—
470C3×C4⋊C4—31no—
471C3×C4⋊C4—31no—
472C3×C4⋊C4—31no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—31no—
475C3×C4⋊C4—41no—
476C3×C4⋊C4—61no—
477C3×C4⋊C4—61no—
478C3×C4⋊C4—61no—
479C3×C4⋊C4—91no—
480C3×C4⋊C4—91no—
481C3×C4⋊C4—91no—
482C3×C4⋊C4—91no—
483C3×C4⋊C4—91no—
484C3×C4⋊C4—91no—
485C3×C4⋊C4D3211yescharacteristic
486C3×C4⋊C4C2×C3×D311yescharacteristic
487C3×C4⋊C4C2×C3×D311yescharacteristic
488C3×C22⋊C4—31no—
489C3×C22⋊C4—31no—
490C3×C22⋊C4—31no—
491C3×C22⋊C4—31no—
492C3×C22⋊C4—31no—
493C3×C22⋊C4—31no—
494C3×C22⋊C4—61no—
495C3×C22⋊C4—61no—
496C3×C22⋊C4—61no—
497C3×C22⋊C4—91no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C42—31no—
507C3×C42—31no—
508C3×C42—31no—
509C3×C42—31no—
510C3×C42—31no—
511C3×C42—31no—
512C3×C42—61no—
513C3×C42—61no—
514C3×C42—61no—
515C3×C42—91no—
516#217—31no—
517#217—31no—
518#217—31no—
519#217—31no—
520#217—31no—
521(C2×D3)⋊C4—31no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—61no—
535(C2×D3)⋊C4—61no—
536(C2×D3)⋊C4C2×C3×D311yescharacteristic
537(C2×D3)⋊C4C2×C3×D311yescharacteristic
538(C2×D3)⋊C4C2×C3×D311yescharacteristic
539C4⋊Dic3—31no—
540C4⋊Dic3—31no—
541C4⋊Dic3—31no—
542Dic3⋊C4—31no—
543Dic3⋊C4—31no—
544Dic3⋊C4—31no—
545Dic3⋊C4—31no—
546Dic3⋊C4—31no—
547Dic3⋊C4—31no—
548Dic3⋊C4—31no—
549Dic3⋊C4—31no—
550Dic3⋊C4—31no—
551Dic3⋊C4—61no—
552Dic3⋊C4—61no—
553Dic3⋊C4C2×C3×D311yescharacteristic
554Dic3⋊C4C2×C3×D311yescharacteristic
555Dic3⋊C4C2×C3×D311yescharacteristic
556C4×Dic3—31no—
557C4×Dic3—31no—
558C4×Dic3C2×C3×D311yescharacteristic
559C4×Dic3C2×C3×D311yescharacteristic
560C4×Dic3C2×C3×D311yescharacteristic
561C22×C32—21no—
562C22×C32—21no—
563C22×C32—21no—
564C22×C32—41no—
565C22×C32—61no—
566C22×C32—61no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32—61no—
570C22×C32—61no—
571C22×C32C23×D311yescharacteristic
572C22×C32C23×D311yescharacteristic
573C22×C32C24×C311yescharacteristic
574C2×C3⋊D3—21no—
575C2×C3⋊D3—21no—
576C2×C3⋊D3—21no—
577C2×C3×D3—22no—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—21no—
584C2×C3×D3—21no—
585C2×C3×D3—21no—
586C2×C3×D3—21no—
587C2×C3×D3—21no—
588C2×C3×D3—21no—
589C2×C3×D3—21no—
590C2×C3×D3—41no—
591C2×C3×D3—41no—
592C2×C3×D3—41no—
593C2×C3×D3—41no—
594C2×C3×D3—41no—
595C2×C3×D3—62no—
596C2×C3×D3—61no—
597C2×C3×D3—61no—
598C2×C3×D3—61no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—121no—
603C2×C3×D3—121no—
604C32×C4—21no—
605C32×C4—22no—
606C32×C4—21no—
607C32×C4—21no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—21no—
611C32×C4—21no—
612C32×C4—21no—
613C32×C4—21no—
614C32×C4—32no—
615C32×C4—41no—
616C32×C4—41no—
617C32×C4—42no—
618C32×C4—41no—
619C32×C4—41no—
620C32×C4—41no—
621C32×C4—41no—
622C32×C4—41no—
623C32×C4—41no—
624C32×C4—61no—
625C32×C4—61no—
626C32×C4—61no—
627C32×C4—61no—
628C32×C4—61no—
629C32×C4—81no—
630C32×C4—81no—
631C3⋊Dic3—21no—
632C3⋊Dic3—21no—
633C3⋊Dic3—21no—
634C3×Dic3—22no—
635C3×Dic3—22no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—22no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—41no—
650C3×Dic3—62no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—121no—
658C3×Dic3—121no—
659C3×Dic3#23512yes—
660C3×Dic3C3×#4112yes—
661C4⋊Q8—91no—
662#126—91no—
663#126—91no—
664#124—91no—
665#124—91no—
666#124—91no—
667#123—31no—
668#123—91no—
669C22⋊Q8—91no—
670C22⋊Q8—91no—
671C22⋊Q8—91no—
672#121—91no—
673C4×Q8—31no—
674C4×D4—91no—
675#117—91no—
676C33#54211yescharacteristic, complemented, Sylow
677C23×C3—31no—
678C23×C3—31no—
679C23×C3—31no—
680C23×C3—31no—
681C23×C3—61no—
682C23×C3—61no—
683C23×C3—91no—
684C22×D3—31no—
685C22×D3—31no—
686C22×D3—61no—
687C22×D3C22×C3×D311yescharacteristic
688C22×D3C22×C3×D311yescharacteristic
689C3×Q8—62no—
690C3×Q8—62no—
691C3×Q8—64no—
692C3×Q8—361no—
693C3×Q8—361no—
694C3×D4—121no—
695C3×D4—121no—
696C3×D4—122no—
697C3×D4—182no—
698C3×D4—361no—
699C2×C3×C4—21no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—21no—
705C2×C3×C4—21no—
706C2×C3×C4—21no—
707C2×C3×C4—21no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—31no—
715C2×C3×C4—31no—
716C2×C3×C4—31no—
717C2×C3×C4—31no—
718C2×C3×C4—31no—
719C2×C3×C4—31no—
720C2×C3×C4—41no—
721C2×C3×C4—41no—
722C2×C3×C4—41no—
723C2×C3×C4—61no—
724C2×C3×C4—61no—
725C2×C3×C4—61no—
726C2×C3×C4—61no—
727C2×C3×C4—61no—
728C2×C3×C4—61no—
729C2×C3×C4—91no—
730C2×C3×C4—91no—
731C2×C3×C4—91no—
732C2×C3×C4—121no—
733C2×C3×C4—121no—
734C2×C3×C4—122no—
735C2×C3×C4—182no—
736C2×C3×C4—361no—
737C2×C3×C4C2×D3211yescharacteristic
738C2×C3×C4C2×D3211yescharacteristic
739C2×C3×C4C2×D3211yescharacteristic
740C2×C3×C4C22×C3×D311yescharacteristic
741C2×C3×C4C22×C3×D311yescharacteristic
742C2×C3×C4C22×C3×D311yescharacteristic
743C2×C3×C4C22×C3×D311yescharacteristic
744C2×C3×C4C22×C3×D311yescharacteristic
745C2×C3×C4C22×C3×D311yescharacteristic
746#67—62no—
747#67—121no—
748C2×Dic3—31no—
749C2×Dic3—31no—
750C2×Dic3—31no—
751C2×Dic3—31no—
752C2×Dic3—31no—
753C2×Dic3—31no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—62no—
758C2×Dic3C22×C3×D311yescharacteristic
759C2×Dic3C22×C3×D311yescharacteristic
760C2×Dic3C22×C3×D311yescharacteristic
761C2×Dic3C22×C3×D311yescharacteristic
762C2×Dic3C22×C3×D311yescharacteristic
763C2×Dic3C22×C3×D311yescharacteristic
764D12—41no—
765D12—62no—
766D12—121no—
767C4×D3—41no—
768C4×D3—62no—
769C4×D3—121no—
770C4×D3—121no—
771C4×D3—122no—
772Dic6—22no—
773Dic6—121no—
774Dic6—121no—
775Dic6—121no—
776Dic6—121no—
777Dic6—122no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—41no—
788C2×C32—41no—
789C2×C32—41no—
790C2×C32—121no—
791C2×C32—121no—
792C2×C32C2×#23511yescharacteristic
793C2×C32#100411yescharacteristic
794C2×C32#100711yescharacteristic
795C2×C32D3×#4111yescharacteristic
796C2×C32#100911yescharacteristic
797C2×C32#101011yescharacteristic
798C2×C32C2×C3×#4111yescharacteristic
799C2×C32C3×H(5,𝔽2)11yescharacteristic
800C2×C32C3×2−1+411yescharacteristic
801C3⋊D3—41no—
802C3×D3—42no—
803C3×D3—41no—
804C3×D3—41no—
805C3×D3—41no—
806C3×D3—41no—
807C3×D3—81no—
808C3×D3—122no—
809C3×D3—121no—
810C3×D3—121no—
811C2×Q8—31no—
812C2×Q8—91no—
813C2×Q8—91no—
814C2×D4—31no—
815C2×D4—91no—
816C2×D4—91no—
817C22×C4—31no—
818C22×C4—91no—
819C22×C4—91no—
820C4⋊C4—31no—
821C4⋊C4—31no—
822C4⋊C4—31no—
823C4⋊C4—91no—
824C4⋊C4—91no—
825C4⋊C4—91no—
826C4⋊C4—91no—
827C4⋊C4—91no—
828C4⋊C4—91no—
829C4⋊C4C3×D3211yescharacteristic
830C22⋊C4—31no—
831C22⋊C4—31no—
832C22⋊C4—31no—
833C22⋊C4—91no—
834C22⋊C4—91no—
835C22⋊C4—91no—
836C22⋊C4—91no—
837C22⋊C4—91no—
838C22⋊C4—91no—
839C22⋊C4—91no—
840C22⋊C4—91no—
841C22⋊C4—91no—
842C42—31no—
843C42—31no—
844C42—31no—
845C42—91no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—41no—
850C22×C3—62no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—61no—
856C22×C3—61no—
857C22×C3—61no—
858C22×C3—61no—
859C22×C3—61no—
860C22×C3—61no—
861C22×C3—61no—
862C22×C3—61no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3—121no—
868C22×C3—181no—
869C22×C3—181no—
870C22×C3—181no—
871C22×C3C22×D3211yescharacteristic
872C22×C3C23×C3×D311yescharacteristic
873C22×C3C23×C3×D311yescharacteristic
874C2×D3—21no—
875C2×D3—21no—
876C2×D3—21no—
877C2×D3—21no—
878C2×D3—21no—
879C2×D3—21no—
880C2×D3—62no—
881C2×D3—61no—
882C2×D3—61no—
883C2×D3—61no—
884C2×D3—61no—
885C2×D3—61no—
886C2×D3—61no—
887C2×D3—121no—
888C2×D3—121no—
889C3×C4—22no—
890C3×C4—21no—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—21no—
898C3×C4—21no—
899C3×C4—32no—
900C3×C4—32no—
901C3×C4—41no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—41no—
905C3×C4—41no—
906C3×C4—41no—
907C3×C4—41no—
908C3×C4—41no—
909C3×C4—42no—
910C3×C4—62no—
911C3×C4—62no—
912C3×C4—62no—
913C3×C4—61no—
914C3×C4—61no—
915C3×C4—61no—
916C3×C4—61no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—61no—
923C3×C4—81no—
924C3×C4—81no—
925C3×C4—121no—
926C3×C4—121no—
927C3×C4—121no—
928C3×C4—181no—
929C3×C4—181no—
930C3×C4—181no—
931Dic3—21no—
932Dic3—21no—
933Dic3—21no—
934Dic3—21no—
935Dic3—21no—
936Dic3—62no—
937Dic3—61no—
938Dic3—61no—
939Dic3—61no—
940Dic3—61no—
941Dic3—61no—
942Dic3—61no—
943Dic3—121no—
944Dic3—121no—
945Dic3C3×#23512yes—
946C32—21no—
947C32—21no—
948C32—21no—
949C32—41no—
950C32#558211yescharacteristic, complemented
951C32#566211yescharacteristic, complemented
952C32C3×#54211yescharacteristic, complemented
953C23—31no—
954C23—31no—
955C23—91no—
956Q8—62no—
957Q8—361no—
958Q8—361no—
959D4—121no—
960D4—182no—
961D4—361no—
962C2×C4—31no—
963C2×C4—31no—
964C2×C4—31no—
965C2×C4—31no—
966C2×C4—31no—
967C2×C4—31no—
968C2×C4—91no—
969C2×C4—91no—
970C2×C4—91no—
971C2×C4—121no—
972C2×C4—182no—
973C2×C4—361no—
974C2×C4C2×C3×D3211yescharacteristic
975C2×C4C2×C3×D3211yescharacteristic
976C2×C4C2×C3×D3211yescharacteristic
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—41no—
987C2×C3—41no—
988C2×C3—41no—
989C2×C3—122no—
990C2×C3—121no—
991C2×C3—121no—
992C2×C3—121no—
993C2×C3—121no—
994C2×C3—241no—
995C2×C3—361no—
996C2×C3D3×#23511yescharacteristic
997C2×C3#6431411yescharacteristic
998C2×C3#6431511yescharacteristic
999C2×C3C2×C3×#23511yescharacteristic
1000C2×C3C3×#100411yescharacteristic
1001C2×C3C3×#100711yescharacteristic
1002C2×C3C3×D3×#4111yescharacteristic
1003C2×C3C3×#100911yescharacteristic
1004C2×C3C3×#101011yescharacteristic
1005D3—41no—
1006D3—41no—
1007D3—122no—
1008D3—121no—
1009D3—121no—
1010C22—61no—
1011C22—61no—
1012C22—61no—
1013C22—61no—
1014C22—61no—
1015C22—61no—
1016C22—181no—
1017C22—181no—
1018C22—181no—
1019C22C22×C3×D3211yescharacteristic
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—32no—
1024C4—61no—
1025C4—61no—
1026C4—61no—
1027C4—61no—
1028C4—61no—
1029C4—181no—
1030C4—181no—
1031C4—181no—
1032C3—21no—
1033C3—21no—
1034C3—21no—
1035C3—41no—
1036C3#1059441911yescharacteristic, direct product factor
1037C3C3×#558211yescharacteristic, complemented
1038C3C3×#566211yescharacteristic, complemented
1039C2—121no—
1040C2—121no—
1041C2—361no—
1042C2C3×D3×#23511yescharacteristic
1043C2C3×#6431411yescharacteristic
1044C2C3×#6431511yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC3×#63886C2
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#542
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. C3×#64105C2semidirect
2. C32×#894C2semidirect
3. C32×#887C2semidirect
4. C3×#63907C2semidirect
5. C3×C4×#626C2semidirect
6. C3×#63887C2semidirect
8. C3×#63877C2semidirect
9. C3×#63868C2semidirect
10. C3×#63860C2semidirect
11. C3×#63859C2semidirect
12. C3×#63853C2semidirect
13. C3×#63852C2semidirect
14. C3×#63851C2semidirect
15. C3×#63840C2semidirect
18. #10594419C3direct (N × H)
56. #64105C2×C3semidirect
71. C3×#894D3semidirect
72. C3×#894C2×C3semidirect
76. C3×#887D3semidirect
77. C3×#887C2×C3semidirect
90. #63907C2×C3semidirect
91. C4×#626C2×C3semidirect
92. #63887C2×C3semidirect
94. #63877C2×C3semidirect
95. #63868C2×C3semidirect
96. #63860C2×C3semidirect
97. #63859C2×C3semidirect
98. #63853C2×C3semidirect
99. #63852C2×C3semidirect
100. #63851C2×C3semidirect
101. #63840C2×C3semidirect
310. #894C3×D3semidirect
313. #887C3×D3semidirect
676. C33#542semidirect
950. C32#5582semidirect
951. C32#5662semidirect
952. C32C3×#542semidirect
1036. C3#10594419direct (N × H)
1037. C3C3×#5582semidirect
1038. C3C3×#5662semidirect

Maximal subgroups

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

subgroupindex
C3×#641052
C32×#8942
C32×#8872
C3×#639072
C3×C4×#6262
C3×#638872
C3×#638862
C3×#638772
C3×#638682
C3×#638602
C3×#638592
C3×#638532
C3×#638522
C3×#638512
C3×#638402
C3×#56623
C3×#55823
#105944193