Finite Group Databasebeta

← C3×#10594808 #13174640

Subgroups — C3×#10594808 #13174640

Order 1728.

1198 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64133C211yesmaximal, characteristic
2C32×#924C211yesmaximal, characteristic
3C2×C32×C4×Dic3C211yesmaximal, characteristic
4C3×#63964C212yesmaximal
5C3×#63955C212yesmaximal
6C3×#63918C211yesmaximal, characteristic, complemented
7C3×#63867C212yesmaximal, complemented
8C3×#63866C211yesmaximal, characteristic, complemented
9C3×#63844C211yesmaximal, characteristic, complemented
10C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
11C3×#63837C212yesmaximal, complemented
12C3×#5622—31nomaximal
13C3×#5470—31nomaximal
14#10594808C311yesmaximal, characteristic, direct product factor
15C22×C33×C4C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×C3×#627C2212yes—
21C3×#3757C2212yes—
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#3750C2212yes—
24C32×#217C2212yes—
25C32×C4⋊Dic3C2211yescharacteristic
26C32×Dic3⋊C4C2212yes—
27C32×C4×Dic3C2211yescharacteristic
28C32×C4×Dic3C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31C3×#3724C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic32C2212yes—
37C3×Dic32C2212yes—
38C32×C22⋊Q8—31no—
39C2×C32×C42—31no—
40#64133C2×C311yescharacteristic
41C3×Q8×Dic3—31no—
42C3×#944—31no—
43C3×#926—32no—
44C3×#924—21no—
45C3×#924—31no—
46C3×#924—31no—
47C3×#924—32no—
48C3×#924—61no—
49C3×#924D311yescharacteristic
50C3×#924C2×C311yescharacteristic
51C2×C3×C4×Dic3—21no—
52C2×C3×C4×Dic3D311yescharacteristic
53C2×C3×C4×Dic3C2×C311yescharacteristic
54C3×#889—32no—
55C3×#888—31no—
56C3×#887—32no—
57C3×#887—31no—
58C3×#878—32no—
59C3×#877—32no—
60C3×#870—32no—
61C3×#869—31no—
62C3×#869—31no—
63C3×C4×Dic6—31no—
64C3×C4×Dic6—31no—
65C3×C4×Dic6—32no—
66#63964C2×C312yes—
67#63955C2×C312yes—
68#63918C2×C311yescharacteristic, complemented
69#63867C2×C312yescomplemented
70#63866C2×C311yescharacteristic, complemented
71#63844C2×C311yescharacteristic, complemented
72Dic3×Dic6C2×C311yescharacteristic, complemented
73#63837C2×C312yescomplemented
74C23×C33C2311yescharacteristic
75C2×C33×C4—22no—
76C2×C33×C4C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2312yes—
80C3×#634—22no—
81C2×C32×Dic3—22no—
82C2×C32×Dic3Q814yescomplemented
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89C32×Dic6—22no—
90C3×#627—24no—
91C3×#533—91no—
92#5622—31no—
93#5470—31no—
94C2×C32×Q8—31no—
95C22×C32×C4—21no—
96C22×C32×C4—21no—
97C22×C32×C4—21no—
98C22×C32×C4—31no—
99C22×C32×C4—31no—
100C22×C32×C4—41no—
101C22×C32×C4C2×D311yescharacteristic
102C22×C32×C4C2×D311yescharacteristic
103C22×C32×C4C22×C311yescharacteristic
104C2×#634C22×C311yescharacteristic
105C22×C3×Dic3—21no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3C2×D311yescharacteristic
108C22×C3×Dic3C2×D311yescharacteristic
109C22×C3×Dic3C22×C311yescharacteristic
110C22×C3×Dic3C22×C311yescharacteristic
111C2×C3×Dic6—21no—
112C2×C3×Dic6—31no—
113C2×C3×Dic6—31no—
114C2×C3×Dic6—32no—
115C2×C3×Dic6—32no—
116C2×C3×Dic6—61no—
117C2×C3×Dic6C2×D311yescharacteristic
118C2×C3×Dic6C22×C311yescharacteristic
119C2×#627C22×C312yes—
120C32×C4⋊C4—31no—
121C32×C4⋊C4—32no—
122C32×C22⋊C4—32no—
123C32×C42—31no—
124C32×C42—31no—
125C32×C42—31no—
126C32×C42—31no—
127#3757C22×C312yes—
128C4⋊(C3⋊Dic3)C22×C311yescharacteristic
129#3750C22×C312yes—
130C3×#217—22no—
131C3×#217—32no—
132C3×#217—32no—
133C3×#217—62no—
134C3×#217C2×D312yes—
135C3×#217C22×C312yes—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—32no—
140C3×C4⋊Dic3—32no—
141C3×C4⋊Dic3—32no—
142C3×C4⋊Dic3—32no—
143C3×C4⋊Dic3—61no—
144C3×C4⋊Dic3C2×D311yescharacteristic
145C3×C4⋊Dic3C22×C311yescharacteristic
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—32no—
155C3×Dic3⋊C4—62no—
156C3×Dic3⋊C4C2×D312yes—
157C3×Dic3⋊C4C22×C312yes—
158C3×C4×Dic3—21no—
159C3×C4×Dic3—21no—
160C3×C4×Dic3—21no—
161C3×C4×Dic3—21no—
162C3×C4×Dic3—32no—
163C3×C4×Dic3—32no—
164C3×C4×Dic3—32no—
165C3×C4×Dic3—32no—
166C3×C4×Dic3C2×D311yescharacteristic
167C3×C4×Dic3C2×D311yescharacteristic
168C3×C4×Dic3C2×D311yescharacteristic
169C3×C4×Dic3C2×D311yescharacteristic
170C3×C4×Dic3C22×C311yescharacteristic
171C3×C4×Dic3C22×C311yescharacteristic
172C3×C4×Dic3C22×C311yescharacteristic
173C3×C4×Dic3C22×C311yescharacteristic
174#3724C22×C312yes—
175Dic3⋊Dic3C22×C312yes—
176Dic3⋊Dic3C22×C312yes—
177Dic3⋊Dic3C22×C312yes—
178Dic3⋊Dic3C22×C312yes—
179Dic32C22×C312yes—
180Dic32C22×C312yes—
181C22×C33—21no—
182C22×C33—21no—
183C22×C33C2×Q812yes—
184C22×C33C2411yescharacteristic
185C33×C4—21no—
186C33×C4#4112yes—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—22no—
189C32×Dic3—21no—
190C32×Dic3—22no—
191C32×Dic3—22no—
192C32×Dic3C2×Q812yes—
193C32×Dic3C2×Q812yes—
194C32×Dic3#4112yes—
195C3×C4⋊Q8—91no—
196C3×C4⋊Q8—91no—
197C3×#125—92no—
198C3×C22⋊Q8—31no—
199C3×C22⋊Q8—31no—
200C3×C22⋊Q8—61no—
201C3×C22⋊Q8—92no—
202C3×C22⋊Q8—91no—
203C3×C4×Q8—92no—
204C3×C4×Q8—91no—
205C3×C4×Q8—91no—
206C3×#117—92no—
207C2×C3×C42—31no—
208C2×C3×C42—31no—
209C2×C3×C42—61no—
210Q8×Dic3—31no—
211#944—31no—
212#926—32no—
213#924—31no—
214#924—31no—
215#924—32no—
216#924—61no—
217#924C3×D311yescharacteristic
218C2×C4×Dic3C3×D311yescharacteristic
219#889—32no—
220#888—31no—
221#887—32no—
222#887—31no—
223#878—32no—
224#877—32no—
225#870—32no—
226#869—31no—
227#869—31no—
228C4×Dic6—31no—
229C4×Dic6—31no—
230C4×Dic6—32no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—41no—
235C23×C32C22×D311yescharacteristic
236C23×C32C22×D311yescharacteristic
237C23×C32C23×C311yescharacteristic
238C32×Q8—62no—
239C2×C32×C4—22no—
240C2×C32×C4—24no—
241C2×C32×C4—22no—
242C2×C32×C4—22no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—34no—
250C2×C32×C4—31no—
251C2×C32×C4—31no—
252C2×C32×C4—31no—
253C2×C32×C4—32no—
254C2×C32×C4—32no—
255C2×C32×C4—31no—
256C2×C32×C4—41no—
257C2×C32×C4—41no—
258C2×C32×C4—42no—
259C2×C32×C4—42no—
260C2×C32×C4—44no—
261C2×C32×C4—62no—
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C23×C311yescharacteristic
267C2×C32×C4C23×C311yescharacteristic
268C2×C3⋊Dic3C23×C312yes—
269C2×C3⋊Dic3C23×C312yes—
270#634—22no—
271C2×C3×Dic3—24no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—24no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3Dic614yescomplemented
288C2×C3×Dic3C3×Q814yescomplemented
289C2×C3×Dic3C22×D312yes—
290C2×C3×Dic3C22×D312yes—
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C23×C312yes—
296C2×C3×Dic3C23×C312yes—
297C2×C3×Dic3C23×C311yescharacteristic
298C2×C3×Dic3C23×C311yescharacteristic
299C2×C3×Dic3C23×C311yescharacteristic
300C2×C3×Dic3C23×C311yescharacteristic
301C3×Dic6—22no—
302C3×Dic6—22no—
303C3×Dic6—42no—
304C3×Dic6—64no—
305C3×Dic6—62no—
306C3×Dic6—62no—
307C3×Dic6—64no—
308C3×Dic6—122no—
309#627—24no—
310#533—91noSylow
311C2×C33—22no—
312C2×C33C22×Q811yescharacteristic
313C2×C33C2×#4111yescharacteristic
314C2×C33C2×#4111yescharacteristic
315C2×C3×Q8—31no—
316C2×C3×Q8—31no—
317C2×C3×Q8—61no—
318C2×C3×Q8—92no—
319C2×C3×Q8—91no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—41no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4D3211yescharacteristic
331C22×C3×C4C2×C3×D311yescharacteristic
332C22×C3×C4C2×C3×D311yescharacteristic
333C22×Dic3C2×C3×D311yescharacteristic
334C22×Dic3C2×C3×D311yescharacteristic
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—32no—
338C2×Dic6—32no—
339C2×Dic6—61no—
340C2×Dic6C2×C3×D311yescharacteristic
341C3×C4⋊C4—32no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—32no—
345C3×C4⋊C4—62no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—92no—
348C3×C4⋊C4—92no—
349C3×C4⋊C4—92no—
350C3×C4⋊C4—92no—
351C3×C4⋊C4—92no—
352C3×C4⋊C4—92no—
353C3×C4⋊C4—91no—
354C3×C22⋊C4—32no—
355C3×C22⋊C4—32no—
356C3×C22⋊C4—62no—
357C3×C22⋊C4—92no—
358C3×C42—31no—
359C3×C42—31no—
360C3×C42—31no—
361C3×C42—31no—
362C3×C42—31no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—61no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42—61no—
370C3×C42—92no—
371C3×C42—92no—
372#217—32no—
373#217—32no—
374#217—62no—
375#217C2×C3×D312yes—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—32no—
379C4⋊Dic3—32no—
380C4⋊Dic3—32no—
381C4⋊Dic3—32no—
382C4⋊Dic3—61no—
383C4⋊Dic3C2×C3×D311yescharacteristic
384Dic3⋊C4—32no—
385Dic3⋊C4—32no—
386Dic3⋊C4—32no—
387Dic3⋊C4—32no—
388Dic3⋊C4—32no—
389Dic3⋊C4—32no—
390Dic3⋊C4—32no—
391Dic3⋊C4—32no—
392Dic3⋊C4—62no—
393Dic3⋊C4C2×C3×D312yes—
394C4×Dic3—32no—
395C4×Dic3—32no—
396C4×Dic3—32no—
397C4×Dic3—32no—
398C4×Dic3C2×C3×D311yescharacteristic
399C4×Dic3C2×C3×D311yescharacteristic
400C4×Dic3C2×C3×D311yescharacteristic
401C4×Dic3C2×C3×D311yescharacteristic
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—22no—
405C22×C32—22no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—22no—
416C22×C32—42no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—42no—
423C22×C32—42no—
424C22×C32C2×Dic612yes—
425C22×C32D3×Q812yes—
426C22×C32C2×C3×Q812yes—
427C22×C32C23×D311yescharacteristic
428C22×C32C23×D311yescharacteristic
429C22×C32C24×C311yescharacteristic
430C32×C4—21no—
431C32×C4—22no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—22no—
435C32×C4—22no—
436C32×C4—22no—
437C32×C4—32no—
438C32×C4—32no—
439C32×C4—32no—
440C32×C4—42no—
441C32×C4—41no—
442C32×C4—41no—
443C32×C4—42no—
444C32×C4—61no—
445C32×C4—62no—
446C32×C4—62no—
447C32×C4#23512yes—
448C32×C4#23712yes—
449C32×C4C3×#4112yes—
450C3⋊Dic3—22no—
451C3⋊Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—21no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—21no—
459C3×Dic3—22no—
460C3×Dic3—22no—
461C3×Dic3—22no—
462C3×Dic3—42no—
463C3×Dic3—42no—
464C3×Dic3—62no—
465C3×Dic3—62no—
466C3×Dic3—62no—
467C3×Dic3—62no—
468C3×Dic3—122no—
469C3×Dic3—122no—
470C3×Dic3C2×Dic612yes—
471C3×Dic3C2×Dic612yes—
472C3×Dic3#23512yes—
473C3×Dic3C2×C3×Q812yes—
474C3×Dic3C2×C3×Q812yes—
475C3×Dic3C3×#4112yes—
476C4⋊Q8—91no—
477C4⋊Q8—91no—
478#125—92no—
479C22⋊Q8—31no—
480C22⋊Q8—92no—
481C22⋊Q8—91no—
482C4×Q8—92no—
483C4×Q8—91no—
484C4×Q8—91no—
485#117—92no—
486C2×C42—31no—
487C33#53311yescharacteristic, complemented, Sylow
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—41no—
492C23×C3C2×D3211yescharacteristic
493C23×C3C22×C3×D311yescharacteristic
494C23×C3C22×C3×D311yescharacteristic
495C3×Q8—62no—
496C3×Q8—62no—
497C3×Q8—122no—
498C3×Q8—184no—
499C3×Q8—182no—
500C2×C3×C4—24no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—34no—
517C2×C3×C4—34no—
518C2×C3×C4—31no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
523C2×C3×C4—31no—
524C2×C3×C4—42no—
525C2×C3×C4—42no—
526C2×C3×C4—44no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—64no—
534C2×C3×C4—62no—
535C2×C3×C4—62no—
536C2×C3×C4—62no—
537C2×C3×C4—62no—
538C2×C3×C4—64no—
539C2×C3×C4—92no—
540C2×C3×C4—92no—
541C2×C3×C4C2×D3211yescharacteristic
542C2×C3×C4C2×D3211yescharacteristic
543C2×C3×C4C22×C3×D311yescharacteristic
544C2×C3×C4C22×C3×D311yescharacteristic
545C2×C3×C4C22×C3×D311yescharacteristic
546C2×C3×C4C22×C3×D311yescharacteristic
547C2×Dic3—22no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—32no—
551C2×Dic3—32no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3C3×Dic614yescomplemented
555C2×Dic3C22×C3×D312yes—
556C2×Dic3C22×C3×D312yes—
557C2×Dic3C22×C3×D311yescharacteristic
558C2×Dic3C22×C3×D311yescharacteristic
559C2×Dic3C22×C3×D311yescharacteristic
560C2×Dic3C22×C3×D311yescharacteristic
561Dic6—22no—
562Dic6—64no—
563Dic6—62no—
564Dic6—62no—
565Dic6—64no—
566Dic6—122no—
567C2×C32—22no—
568C2×C32—24no—
569C2×C32—22no—
570C2×C32—22no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—41no—
581C2×C32—41no—
582C2×C32—41no—
583C2×C32—42no—
584C2×C32—42no—
585C2×C32—44no—
586C2×C32C22×Dic611yescharacteristic
587C2×C32C2×#23511yescharacteristic
588C2×C32C2×#23511yescharacteristic
589C2×C32C2×#23711yescharacteristic
590C2×C32C2×D3×Q811yescharacteristic
591C2×C32D3×#4111yescharacteristic
592C2×C32C22×C3×Q811yescharacteristic
593C2×C32C2×C3×#4111yescharacteristic
594C2×C32C2×C3×#4111yescharacteristic
595C2×Q8—31no—
596C2×Q8—92no—
597C2×Q8—91no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4C3×D3211yescharacteristic
601C4⋊C4—32no—
602C4⋊C4—31no—
603C4⋊C4—92no—
604C4⋊C4—92no—
605C4⋊C4—92no—
606C4⋊C4—92no—
607C4⋊C4—92no—
608C4⋊C4—92no—
609C4⋊C4—91no—
610C22⋊C4—32no—
611C22⋊C4—92no—
612C42—31no—
613C42—31no—
614C42—31no—
615C42—31no—
616C42—92no—
617C42—92no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—42no—
640C22×C3D3×Dic612yes—
641C22×C3C2×C3×Dic612yes—
642C22×C3C3×D3×Q812yes—
643C22×C3C22×D3211yescharacteristic
644C22×C3C23×C3×D311yescharacteristic
645C22×C3C23×C3×D311yescharacteristic
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—22no—
653C3×C4—32no—
654C3×C4—32no—
655C3×C4—32no—
656C3×C4—32no—
657C3×C4—32no—
658C3×C4—32no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—62no—
664C3×C4—62no—
665C3×C4—62no—
666C3×C4—62no—
667C3×C4—61no—
668C3×C4—62no—
669C3×C4—62no—
670C3×C4—62no—
671C3×C4—62no—
672C3×C4—61no—
673C3×C4—122no—
674C3×C4—122no—
675C3×C4—182no—
676C3×C4—182no—
677C3×C4#380412yes—
678C3×C4C3×#23512yes—
679C3×C4C3×#23712yes—
680Dic3—21no—
681Dic3—22no—
682Dic3—22no—
683Dic3—62no—
684Dic3—62no—
685Dic3—62no—
686Dic3—62no—
687Dic3—122no—
688Dic3—122no—
689Dic3C2×C3×Dic612yes—
690Dic3C2×C3×Dic612yes—
691Dic3C3×#23512yes—
692C32—21no—
693C32—21no—
694C32—21no—
695C32—41no—
696C32#547011yescharacteristic, complemented
697C32#562211yescharacteristic, complemented
698C32C3×#53311yescharacteristic, complemented
699C23C2×C3×D3211yescharacteristic
700Q8—62no—
701Q8—184no—
702Q8—182no—
703C2×C4—22no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—34no—
708C2×C4—31no—
709C2×C4—32no—
710C2×C4—32no—
711C2×C4—62no—
712C2×C4—92no—
713C2×C4—92no—
714C2×C4C2×C3×D3211yescharacteristic
715C2×C4C2×C3×D3211yescharacteristic
716C2×C3—24no—
717C2×C3—22no—
718C2×C3—22no—
719C2×C3—22no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—42no—
730C2×C3—42no—
731C2×C3—44no—
732C2×C3—41no—
733C2×C3—41no—
734C2×C3—41no—
735C2×C3C2×D3×Dic611yescharacteristic
736C2×C3D3×#23511yescharacteristic
737C2×C3C2×#380411yescharacteristic
738C2×C3C22×C3×Dic611yescharacteristic
739C2×C3C2×C3×#23511yescharacteristic
740C2×C3C2×C3×#23511yescharacteristic
741C2×C3C2×C3×#23711yescharacteristic
742C2×C3C2×C3×D3×Q811yescharacteristic
743C2×C3C3×D3×#4111yescharacteristic
744C22—21no—
745C22—21no—
746C22C3×D3×Dic612yes—
747C22C22×C3×D3211yescharacteristic
748C4—21no—
749C4—32no—
750C4—32no—
751C4—32no—
752C4—62no—
753C4—61no—
754C4—62no—
755C4—182no—
756C4—182no—
757C4C3×#380412yes—
758C3—21no—
759C3—21no—
760C3—21no—
761C3—41no—
762C3#1059480811yescharacteristic, direct product factor
763C3C3×#547011yescharacteristic, complemented
764C3C3×#562211yescharacteristic, complemented
765C2—22no—
766C2C2×C3×D3×Dic611yescharacteristic
767C2C3×D3×#23511yescharacteristic
768C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C3×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
6. C3×#63918C2semidirect
7. C3×#63867C2semidirect
8. C3×#63866C2semidirect
9. C3×#63844C2semidirect
10. C3×Dic3×Dic6C2semidirect
11. C3×#63837C2semidirect
14. #10594808C3direct (N × H)
68. #63918C2×C3semidirect
69. #63867C2×C3semidirect
70. #63866C2×C3semidirect
71. #63844C2×C3semidirect
72. Dic3×Dic6C2×C3semidirect
73. #63837C2×C3semidirect
82. C2×C32×Dic3Q8semidirect
287. C2×C3×Dic3Dic6semidirect
288. C2×C3×Dic3C3×Q8semidirect
487. C33#533semidirect
554. C2×Dic3C3×Dic6semidirect
696. C32#5470semidirect
697. C32#5622semidirect
698. C32C3×#533semidirect
762. C3#10594808direct (N × H)
763. C3C3×#5470semidirect
764. C3C3×#5622semidirect

Maximal subgroups

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

subgroupindex
C3×#641332
C32×#9242
C2×C32×C4×Dic32
C3×#639642
C3×#639552
C3×#639182
C3×#638672
C3×#638662
C3×#638442
C3×Dic3×Dic62
C3×#638372
C3×#56223
C3×#54703
#105948083