Finite Group Databasebeta

← C3×#10595238 #13174801

Subgroups — C3×#10595238 #13174801

Order 1728.

1814 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C22×C3×#626C211yesmaximal, characteristic, complemented
3C3×#64146C211yesmaximal, characteristic, complemented
4C32×#937C211yesmaximal, characteristic, complemented
5C3×#63981C211yesmaximal, characteristic, complemented
6C3×#63979C212yesmaximal, complemented
7C3×#63978C212yesmaximal, complemented
8C3×#63976C211yesmaximal, characteristic, complemented
9C3×#63955C211yesmaximal, characteristic, complemented
10C3×#63907C212yesmaximal, complemented
11C3×#63906C212yesmaximal, complemented
12C3×#5830—31nomaximal
13C3×#5592—31nomaximal
14#10595238C311yesmaximal, characteristic, direct product factor
15C23×C3×C3⋊D3C2211yescharacteristic
16C23×C32×D3C2211yescharacteristic
17C2×C33×D4C2211yescharacteristic
18C2×C3×#638C2212yescomplemented
19C2×C32×#67C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic, complemented
21C2×C32×#67C2212yescomplemented
22C22×C32×Dic3C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic, complemented
24C32×#237—24no—
25C2×C32×C4×D3C2211yescharacteristic, complemented
26C2×C32×Dic6C2211yescharacteristic, complemented
27C2×C3×#626—24no—
28C2×C3×#626C2212yes—
29C2×C3×#626C2212yes—
30C2×C3×#626C2212yescomplemented
31C2×C3×#625C2212yescomplemented
32C3×#3757C2211yescharacteristic
33C3×#3752C2212yescomplemented
34C32×#217C2211yescharacteristic
35C32×(C2×D3)⋊C4C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×#3722C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×Dic32C2212yescomplemented
40C2×C32×#41—31no—
41C22×C3×#67—31no—
42C2×C3×#237—21no—
43C2×C3×#237D311yescharacteristic, complemented
44C2×C3×#237C2×C311yescharacteristic, complemented
45C22×C3×D12—31no—
46C22×#626C2×C311yescharacteristic, complemented
47C32×#120—31no—
48#64146C2×C311yescharacteristic, complemented
49C3×#953—31no—
50C3×#947—32no—
51C3×#940—32no—
52C3×#940—32no—
53C3×#939—32no—
54C3×#937—21no—
55C3×#937—31no—
56C3×#937—31no—
57C3×#937—31no—
58C3×#937—31no—
59C3×#937—61no—
60C3×#937D311yescharacteristic, complemented
61C3×#937C2×C311yescharacteristic, complemented
62C3×#930—32no—
63C3×#930—32no—
64C3×#926—31no—
65C3×#885—32no—
66C3×#884—32no—
67C3×#882—31no—
68C3×#877—31no—
69#63981C2×C311yescharacteristic, complemented
70#63979C2×C312yescomplemented
71#63978C2×C312yescomplemented
72#63976C2×C311yescharacteristic, complemented
73#63955C2×C311yescharacteristic, complemented
74#63907C2×C312yescomplemented
75#63906C2×C312yescomplemented
76C23×C33C2311yescharacteristic
77C23×C33C2311yescharacteristic
78C22×C3×C3⋊D3—22no—
79C22×C3×C3⋊D3—42no—
80C22×C3×C3⋊D3C2312yes—
81C22×C32×D3—22no—
82C22×C32×D3—42no—
83C22×C32×D3C2312yes—
84C22×C32×D3C2311yescharacteristic
85C33×D4—22no—
86C2×C33×C4C2311yescharacteristic
87C3×#638—42no—
88C2×C3×C3⋊Dic3C2312yes—
89C32×#67—22no—
90C32×#67—22no—
91C32×#67—42no—
92C2×C32×Dic3—22no—
93C2×C32×Dic3D414yescomplemented
94C2×C32×Dic3C2312yes—
95C2×C32×Dic3C2311yescharacteristic
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C32×C4×D3—22no—
99C32×Dic6—22no—
100C3×#626—24no—
101C3×#626—24no—
102C3×#626—42no—
103C3×#625—42no—
104C3×#535—91no—
105#5830—31no—
106#5592—31no—
107C24×C32—31no—
108C23×C3⋊D3C22×C311yescharacteristic
109C23×C3×D3—21no—
110C23×C3×D3—31no—
111C23×C3×D3—31no—
112C23×C3×D3—61no—
113C23×C3×D3C2×D311yescharacteristic
114C23×C3×D3C22×C311yescharacteristic
115C32×#41—64no—
116C2×C32×Q8—31no—
117C2×C32×D4—21no—
118C2×C32×D4—21no—
119C2×C32×D4—21no—
120C2×C32×D4—31no—
121C2×C32×D4—31no—
122C2×C32×D4—32no—
123C2×C32×D4—41no—
124C2×C32×D4C2×D311yescharacteristic
125C2×C32×D4C2×D311yescharacteristic
126C2×C32×D4C22×C311yescharacteristic
127C22×C32×C4—31no—
128C22×C32×C4—31no—
129C22×C32×C4—31no—
130C2×#638C22×C312yescomplemented
131C2×C3×#67—21no—
132C2×C3×#67—21no—
133C2×C3×#67—22no—
134C2×C3×#67—32no—
135C2×C3×#67—32no—
136C2×C3×#67—32no—
137C2×C3×#67—32no—
138C2×C3×#67—32no—
139C2×C3×#67—32no—
140C2×C3×#67—32no—
141C2×C3×#67—62no—
142C2×C3×#67—64no—
143C2×C3×#67C2×D311yescharacteristic
144C2×C3×#67C2×D311yescharacteristic, complemented
145C2×C3×#67C2×D312yescomplemented
146C2×C3×#67C22×C311yescharacteristic
147C2×C3×#67C22×C311yescharacteristic, complemented
148C2×C3×#67C22×C312yescomplemented
149C22×C3×Dic3—21no—
150C22×C3×Dic3—21no—
151C22×C3×Dic3C2×D311yescharacteristic
152C22×C3×Dic3C2×D311yescharacteristic, complemented
153C22×C3×Dic3C22×C311yescharacteristic
154C22×C3×Dic3C22×C311yescharacteristic, complemented
155C3×#237—28no—
156C3×#237—24no—
157C3×#237—24no—
158C2×C3×D12—32no—
159C2×C3×D12—32no—
160C2×C3×D12—32no—
161C2×C3×D12—64no—
162C2×C3×C4×D3—21no—
163C2×C3×C4×D3C2×D311yescharacteristic, complemented
164C2×C3×C4×D3C22×C311yescharacteristic, complemented
165C2×C3×Dic6—21no—
166C2×C3×Dic6C2×D311yescharacteristic, complemented
167C2×C3×Dic6C22×C311yescharacteristic, complemented
168C2×#626—24no—
169C2×#626C22×C312yes—
170C2×#626C22×C312yes—
171C2×#626C22×C312yescomplemented
172C2×#625C22×C312yescomplemented
173C32×C22⋊C4—31no—
174C32×C22⋊C4—32no—
175#3757C22×C311yescharacteristic
176#3752C22×C312yescomplemented
177C3×#217—21no—
178C3×#217—31no—
179C3×#217—31no—
180C3×#217—32no—
181C3×#217—61no—
182C3×#217C2×D311yescharacteristic
183C3×#217C22×C311yescharacteristic
184C3×(C2×D3)⋊C4—22no—
185C3×(C2×D3)⋊C4—32no—
186C3×(C2×D3)⋊C4—32no—
187C3×(C2×D3)⋊C4—32no—
188C3×(C2×D3)⋊C4—32no—
189C3×(C2×D3)⋊C4—32no—
190C3×(C2×D3)⋊C4—62no—
191C3×(C2×D3)⋊C4C2×D312yescomplemented
192C3×(C2×D3)⋊C4C22×C312yescomplemented
193C3×C4⋊Dic3—32no—
194C3×Dic3⋊C4—32no—
195C3×C4×Dic3—32no—
196C3×C4×Dic3—32no—
197Dic3⋊Dic3C22×C312yescomplemented
198#3722C22×C312yescomplemented
199(C2×D3)⋊Dic3C22×C312yescomplemented
200Dic32C22×C312yescomplemented
201C22×C33—22no—
202C22×C33—21no—
203C22×C33—22no—
204C22×C33C2×D412yes—
205C22×C33C2411yescharacteristic
206C2×C3×C3⋊D3—22no—
207C2×C3×C3⋊D3—22no—
208C2×C3×C3⋊D3—22no—
209C2×C3×C3⋊D3—44no—
210C2×C32×D3—21no—
211C2×C32×D3—22no—
212C2×C32×D3—22no—
213C2×C32×D3—22no—
214C2×C32×D3—22no—
215C2×C32×D3—44no—
216C33×C4—21no—
217C3×C3⋊Dic3—22no—
218C32×Dic3—21no—
219C32×Dic3—22no—
220C32×Dic3C2×D412yes—
221C32×Dic3C2×D412yes—
222C2×C3×#41—31no—
223C2×C3×#41—31no—
224C2×C3×#41—61no—
225C22×C3×D4—91no—
226C22×#67—31no—
227C2×#237C3×D311yescharacteristic, complemented
228C22×D12—31no—
229C3×#127—92no—
230C3×#124—92no—
231C3×#121—92no—
232C3×#121—92no—
233C3×#120—31no—
234C3×#120—31no—
235C3×#120—61no—
236C3×#120—91no—
237C3×#120—91no—
238C3×#120—91no—
239C3×#117—91no—
240#953—31no—
241#947—32no—
242#940—32no—
243#940—32no—
244#939—32no—
245#937—31no—
246#937—31no—
247#937—31no—
248#937—31no—
249#937—61no—
250#937C3×D311yescharacteristic, complemented
251#930—32no—
252#930—32no—
253#926—31no—
254#885—32no—
255#884—32no—
256#882—31no—
257#877—31no—
258C23×C32—21no—
259C23×C32—21no—
260C23×C32—21no—
261C23×C32—21no—
262C23×C32—21no—
263C23×C32—21no—
264C23×C32—32no—
265C23×C32—31no—
266C23×C32—41no—
267C23×C32—41no—
268C23×C32—62no—
269C23×C32—122no—
270C23×C32C22×D311yescharacteristic
271C23×C32C22×D311yescharacteristic
272C23×C32C22×D311yescharacteristic
273C23×C32C22×D311yescharacteristic
274C23×C32C23×C311yescharacteristic
275C23×C32C23×C311yescharacteristic
276C22×C3⋊D3—22no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3C23×C312yes—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—21no—
283C22×C3×D3—32no—
284C22×C3×D3—32no—
285C22×C3×D3—42no—
286C22×C3×D3—42no—
287C22×C3×D3—42no—
288C22×C3×D3—44no—
289C22×C3×D3—62no—
290C22×C3×D3—62no—
291C22×C3×D3—62no—
292C22×C3×D3—122no—
293C22×C3×D3—122no—
294C22×C3×D3—122no—
295C22×C3×D3—124no—
296C22×C3×D3C22×D312yes—
297C22×C3×D3C22×D311yescharacteristic
298C22×C3×D3C23×C312yes—
299C22×C3×D3C23×C311yescharacteristic
300C32×Q8—62no—
301C32×D4—22no—
302C32×D4—24no—
303C32×D4—22no—
304C32×D4—22no—
305C32×D4—42no—
306C32×D4—42no—
307C32×D4—44no—
308C32×D4—62no—
309C32×D4—62no—
310C32×D4—122no—
311C2×C32×C4—21no—
312C2×C32×C4—21no—
313C2×C32×C4—21no—
314C2×C32×C4—34no—
315C2×C32×C4—31no—
316C2×C32×C4—31no—
317C2×C32×C4—32no—
318C2×C32×C4—31no—
319C2×C32×C4—41no—
320C2×C32×C4—62no—
321C2×C32×C4—62no—
322C2×C32×C4C22×D311yescharacteristic
323C2×C32×C4C22×D311yescharacteristic
324C2×C32×C4C23×C311yescharacteristic
325#638—42no—
326C2×C3⋊Dic3C23×C312yes—
327C3×#67—24no—
328C3×#67—24no—
329C3×#67—22no—
330C3×#67—22no—
331C3×#67—22no—
332C3×#67—22no—
333C3×#67—42no—
334C3×#67—42no—
335C3×#67—44no—
336C3×#67—64no—
337C3×#67—64no—
338C3×#67—122no—
339C3×#67—122no—
340C3×#67—122no—
341C3×#67—122no—
342C3×#67—122no—
343C3×#67—124no—
344C2×C3×Dic3—24no—
345C2×C3×Dic3—22no—
346C2×C3×Dic3—22no—
347C2×C3×Dic3—24no—
348C2×C3×Dic3—21no—
349C2×C3×Dic3—21no—
350C2×C3×Dic3—21no—
351C2×C3×Dic3—22no—
352C2×C3×Dic3—32no—
353C2×C3×Dic3—32no—
354C2×C3×Dic3—62no—
355C2×C3×Dic3#6714yescomplemented
356C2×C3×Dic3C3×D414yescomplemented
357C2×C3×Dic3C22×D312yes—
358C2×C3×Dic3C22×D311yescharacteristic
359C2×C3×Dic3C22×D311yescharacteristic
360C2×C3×Dic3C22×D311yescharacteristic
361C2×C3×Dic3C23×C312yes—
362C2×C3×Dic3C23×C311yescharacteristic
363C2×C3×Dic3C23×C311yescharacteristic
364C2×C3×Dic3C23×C311yescharacteristic
365C3×D12—64no—
366C3×D12—64no—
367C3×D12—122no—
368C3×C4×D3—24no—
369C3×C4×D3—22no—
370C3×C4×D3—22no—
371C3×Dic6—24no—
372C3×Dic6—22no—
373C3×Dic6—22no—
374#626—24no—
375#626—24no—
376#626—42no—
377#625—42no—
378#535—91noSylow
379C2×C33—22no—
380C2×C33—41no—
381C2×C33C22×D411yescharacteristic
382C2×C33H(5,𝔽2)12yes—
383C3×C3⋊D3—42no—
384C32×D3—41no—
385C32×D3—42no—
386C24×C3—31no—
387C24×C3—31no—
388C24×C3—61no—
389C24×C3—91no—
390C23×D3—31no—
391C23×D3—31no—
392C23×D3—61no—
393C23×D3C2×C3×D311yescharacteristic
394C3×#41—64no—
395C3×#41—64no—
396C3×#41—68no—
397C2×C3×Q8—31no—
398C2×C3×Q8—31no—
399C2×C3×Q8—61no—
400C2×C3×D4—21no—
401C2×C3×D4—21no—
402C2×C3×D4—21no—
403C2×C3×D4—31no—
404C2×C3×D4—31no—
405C2×C3×D4—31no—
406C2×C3×D4—31no—
407C2×C3×D4—32no—
408C2×C3×D4—32no—
409C2×C3×D4—41no—
410C2×C3×D4—61no—
411C2×C3×D4—61no—
412C2×C3×D4—62no—
413C2×C3×D4—92no—
414C2×C3×D4—92no—
415C2×C3×D4—92no—
416C2×C3×D4—92no—
417C2×C3×D4—92no—
418C2×C3×D4—184no—
419C2×C3×D4D3211yescharacteristic
420C2×C3×D4C2×C3×D311yescharacteristic
421C2×C3×D4C2×C3×D311yescharacteristic
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—31no—
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—61no—
429C22×C3×C4—61no—
430C22×C3×C4—61no—
431C2×#67—32no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—32no—
435C2×#67—32no—
436C2×#67—32no—
437C2×#67—32no—
438C2×#67—62no—
439C2×#67—64no—
440C2×#67C2×C3×D311yescharacteristic
441C2×#67C2×C3×D311yescharacteristic, complemented
442C2×#67C2×C3×D312yescomplemented
443C22×Dic3C2×C3×D311yescharacteristic
444C22×Dic3C2×C3×D311yescharacteristic, complemented
445#237—24no—
446C2×D12—32no—
447C2×D12—32no—
448C2×D12—32no—
449C2×D12—64no—
450C2×C4×D3C2×C3×D311yescharacteristic, complemented
451C2×Dic6C2×C3×D311yescharacteristic, complemented
452C3×C4⋊C4—92no—
453C3×C22⋊C4—31no—
454C3×C22⋊C4—31no—
455C3×C22⋊C4—32no—
456C3×C22⋊C4—32no—
457C3×C22⋊C4—62no—
458C3×C22⋊C4—61no—
459C3×C22⋊C4—92no—
460C3×C22⋊C4—92no—
461C3×C22⋊C4—91no—
462C3×C22⋊C4—92no—
463C3×C42—92no—
464#217—31no—
465#217—31no—
466#217—32no—
467#217—61no—
468#217C2×C3×D311yescharacteristic
469(C2×D3)⋊C4—32no—
470(C2×D3)⋊C4—32no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—32no—
473(C2×D3)⋊C4—32no—
474(C2×D3)⋊C4—62no—
475(C2×D3)⋊C4C2×C3×D312yescomplemented
476C4⋊Dic3—32no—
477Dic3⋊C4—32no—
478C4×Dic3—32no—
479C4×Dic3—32no—
480C22×C32—21no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—21no—
488C22×C32—21no—
489C22×C32—22no—
490C22×C32—21no—
491C22×C32—21no—
492C22×C32—21no—
493C22×C32—22no—
494C22×C32—22no—
495C22×C32—22no—
496C22×C32—41no—
497C22×C32—42no—
498C22×C32—41no—
499C22×C32—41no—
500C22×C32—42no—
501C22×C32—42no—
502C22×C32—42no—
503C22×C32—42no—
504C22×C32—42no—
505C22×C32—42no—
506C22×C32—42no—
507C22×C32—61no—
508C22×C32—62no—
509C22×C32—62no—
510C22×C32—62no—
511C22×C32—62no—
512C22×C32—82no—
513C22×C32—82no—
514C22×C32—124no—
515C22×C32D3×D412yes—
516C22×C32C2×#6712yes—
517C22×C32C2×C3×D412yes—
518C22×C32C23×D311yescharacteristic
519C22×C32C23×D311yescharacteristic
520C22×C32C24×C311yescharacteristic
521C2×C3⋊D3—22no—
522C2×C3⋊D3—22no—
523C2×C3⋊D3—22no—
524C2×C3⋊D3—44no—
525C2×C3×D3—22no—
526C2×C3×D3—24no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—21no—
532C2×C3×D3—22no—
533C2×C3×D3—21no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—42no—
538C2×C3×D3—42no—
539C2×C3×D3—42no—
540C2×C3×D3—44no—
541C2×C3×D3—44no—
542C2×C3×D3—48no—
543C2×C3×D3—64no—
544C2×C3×D3—62no—
545C2×C3×D3—62no—
546C2×C3×D3—62no—
547C2×C3×D3—62no—
548C2×C3×D3—62no—
549C2×C3×D3—62no—
550C2×C3×D3—122no—
551C2×C3×D3—122no—
552C2×C3×D3—124no—
553C2×C3×D3—124no—
554C2×C3×D3—128no—
555C32×C4—21no—
556C32×C4—22no—
557C32×C4—21no—
558C32×C4—21no—
559C32×C4—32no—
560C32×C4—32no—
561C32×C4—41no—
562C32×C4—41no—
563C32×C4—42no—
564C32×C4—61no—
565C32×C4—62no—
566C3⋊Dic3—22no—
567C3×Dic3—22no—
568C3×Dic3—22no—
569C3×Dic3—21no—
570C3×Dic3—21no—
571C3×Dic3—22no—
572C3×Dic3—22no—
573C3×Dic3—22no—
574C3×Dic3—42no—
575C3×Dic3—62no—
576C3×Dic3—62no—
577C3×Dic3—122no—
578C3×Dic3C2×#6712yes—
579C3×Dic3C2×#6712yes—
580C3×Dic3C2×C3×D412yes—
581C3×Dic3C2×C3×D412yes—
582C2×#41—31no—
583C22×D4—91no—
584#127—92no—
585#124—92no—
586#121—92no—
587#121—92no—
588#120—31no—
589#120—91no—
590#120—91no—
591#120—91no—
592#117—91no—
593C33#53511yescharacteristic, complemented, Sylow
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—32no—
601C23×C3—31no—
602C23×C3—32no—
603C23×C3—31no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—62no—
607C23×C3—61no—
608C23×C3—62no—
609C23×C3—62no—
610C23×C3—92no—
611C23×C3—122no—
612C23×C3—122no—
613C23×C3—122no—
614C23×C3—124no—
615C23×C3—182no—
616C23×C3—362no—
617C23×C3C2×D3211yescharacteristic
618C23×C3C2×D3211yescharacteristic
619C23×C3C22×C3×D311yescharacteristic
620C23×C3C22×C3×D311yescharacteristic
621C23×C3C22×C3×D311yescharacteristic
622C23×C3C22×C3×D311yescharacteristic
623C22×D3—22no—
624C22×D3—32no—
625C22×D3—32no—
626C22×D3—42no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—122no—
631C22×D3—122no—
632C22×D3—122no—
633C22×D3—124no—
634C22×D3C22×C3×D312yes—
635C22×D3C22×C3×D311yescharacteristic
636C3×Q8—62no—
637C3×Q8—62no—
638C3×Q8—64no—
639C3×D4—24no—
640C3×D4—22no—
641C3×D4—22no—
642C3×D4—22no—
643C3×D4—42no—
644C3×D4—42no—
645C3×D4—44no—
646C3×D4—62no—
647C3×D4—62no—
648C3×D4—64no—
649C3×D4—64no—
650C3×D4—62no—
651C3×D4—62no—
652C3×D4—122no—
653C3×D4—122no—
654C3×D4—124no—
655C3×D4—184no—
656C3×D4—184no—
657C3×D4—362no—
658C3×D4—362no—
659C3×D4—362no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—31no—
664C2×C3×C4—31no—
665C2×C3×C4—31no—
666C2×C3×C4—31no—
667C2×C3×C4—34no—
668C2×C3×C4—34no—
669C2×C3×C4—32no—
670C2×C3×C4—31no—
671C2×C3×C4—32no—
672C2×C3×C4—31no—
673C2×C3×C4—41no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—64no—
678C2×C3×C4—62no—
679C2×C3×C4—62no—
680C2×C3×C4—62no—
681C2×C3×C4—64no—
682C2×C3×C4—62no—
683C2×C3×C4—62no—
684C2×C3×C4—64no—
685C2×C3×C4—92no—
686C2×C3×C4C2×D3211yescharacteristic
687C2×C3×C4C22×C3×D311yescharacteristic
688C2×C3×C4C22×C3×D311yescharacteristic
689#67—22no—
690#67—22no—
691#67—42no—
692#67—64no—
693#67—64no—
694#67—122no—
695#67—122no—
696#67—122no—
697#67—122no—
698#67—122no—
699#67—124no—
700C2×Dic3—22no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—62no—
704C2×Dic3C3×#6714yescomplemented
705C2×Dic3C22×C3×D312yes—
706C2×Dic3C22×C3×D311yescharacteristic
707C2×Dic3C22×C3×D311yescharacteristic
708C2×Dic3C22×C3×D311yescharacteristic
709D12—64no—
710D12—64no—
711D12—122no—
712C4×D3—22no—
713Dic6—22no—
714C2×C32—22no—
715C2×C32—22no—
716C2×C32—22no—
717C2×C32—22no—
718C2×C32—21no—
719C2×C32—21no—
720C2×C32—22no—
721C2×C32—22no—
722C2×C32—21no—
723C2×C32—41no—
724C2×C32—42no—
725C2×C32—42no—
726C2×C32—42no—
727C2×C32—42no—
728C2×C32—41no—
729C2×C32—42no—
730C2×C32—41no—
731C2×C32—41no—
732C2×C32—82no—
733C2×C32—81no—
734C2×C32—81no—
735C2×C32—82no—
736C2×C32—122no—
737C2×C32—121no—
738C2×C32C2×D3×D411yescharacteristic
739C2×C32#100412yes—
740C2×C32#100912yes—
741C2×C32C22×#6711yescharacteristic
742C2×C32C22×C3×D411yescharacteristic
743C2×C32C3×H(5,𝔽2)12yes—
744C3⋊D3—42no—
745C3×D3—42no—
746C3×D3—44no—
747C3×D3—41no—
748C3×D3—42no—
749C3×D3—41no—
750C3×D3—42no—
751C3×D3—124no—
752C3×D3—122no—
753C3×D3—122no—
754C24—31no—
755C24—91no—
756#41—64no—
757C2×Q8—31no—
758C2×D4—31no—
759C2×D4—31no—
760C2×D4—32no—
761C2×D4—92no—
762C2×D4—92no—
763C2×D4—92no—
764C2×D4—92no—
765C2×D4—92no—
766C2×D4—184no—
767C2×D4C3×D3211yescharacteristic
768C22×C4—31no—
769C22×C4—31no—
770C22×C4—31no—
771C4⋊C4—92no—
772C22⋊C4—31no—
773C22⋊C4—32no—
774C22⋊C4—92no—
775C22⋊C4—92no—
776C22⋊C4—91no—
777C22⋊C4—92no—
778C42—92no—
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—41no—
801C22×C3—41no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—41no—
805C22×C3—42no—
806C22×C3—62no—
807C22×C3—64no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—61no—
812C22×C3—62no—
813C22×C3—61no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—82no—
819C22×C3—82no—
820C22×C3—122no—
821C22×C3—122no—
822C22×C3—122no—
823C22×C3—124no—
824C22×C3—124no—
825C22×C3—128no—
826C22×C3—182no—
827C22×C3—182no—
828C22×C3—182no—
829C22×C3—364no—
830C22×C3D3×#6712yes—
831C22×C3C3×D3×D412yes—
832C22×C3C2×C3×#6712yes—
833C22×C3C22×D3211yescharacteristic
834C22×C3C23×C3×D311yescharacteristic
835C22×C3C23×C3×D311yescharacteristic
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—21no—
841C2×D3—44no—
842C2×D3—64no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—124no—
852C2×D3—124no—
853C2×D3—128no—
854C3×C4—22no—
855C3×C4—21no—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—32no—
859C3×C4—32no—
860C3×C4—32no—
861C3×C4—32no—
862C3×C4—41no—
863C3×C4—41no—
864C3×C4—42no—
865C3×C4—62no—
866C3×C4—62no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—61no—
870C3×C4—61no—
871C3×C4—62no—
872C3×C4—122no—
873C3×C4—182no—
874Dic3—22no—
875Dic3—21no—
876Dic3—62no—
877Dic3—62no—
878Dic3—122no—
879Dic3C2×C3×#6712yes—
880Dic3C2×C3×#6712yes—
881C32—21no—
882C32—21no—
883C32—21no—
884C32—41no—
885C32#559211yescharacteristic, complemented
886C32#583011yescharacteristic, complemented
887C32C3×#53511yescharacteristic, complemented
888C23—32no—
889C23—31no—
890C23—62no—
891C23—92no—
892C23—122no—
893C23—182no—
894C23—362no—
895C23C2×C3×D3211yescharacteristic
896C23C2×C3×D3211yescharacteristic
897Q8—62no—
898D4—22no—
899D4—62no—
900D4—62no—
901D4—122no—
902D4—184no—
903D4—184no—
904D4—362no—
905D4—362no—
906D4—362no—
907C2×C4—31no—
908C2×C4—31no—
909C2×C4—34no—
910C2×C4—32no—
911C2×C4—31no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—92no—
915C2×C4C2×C3×D3211yescharacteristic
916C2×C3—22no—
917C2×C3—22no—
918C2×C3—22no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—22no—
923C2×C3—22no—
924C2×C3—22no—
925C2×C3—42no—
926C2×C3—42no—
927C2×C3—42no—
928C2×C3—42no—
929C2×C3—41no—
930C2×C3—41no—
931C2×C3—41no—
932C2×C3—41no—
933C2×C3—42no—
934C2×C3—82no—
935C2×C3—81no—
936C2×C3—81no—
937C2×C3—82no—
938C2×C3—124no—
939C2×C3—122no—
940C2×C3—122no—
941C2×C3—121no—
942C2×C3—122no—
943C2×C3—121no—
944C2×C3—362no—
945C2×C3#6431412yes—
946C2×C3C2×D3×#6711yescharacteristic
947C2×C3C2×C3×D3×D411yescharacteristic
948C2×C3C3×#100412yes—
949C2×C3C3×#100912yes—
950C2×C3C22×C3×#6711yescharacteristic
951D3—41no—
952D3—42no—
953D3—124no—
954D3—122no—
955D3—122no—
956C22—22no—
957C22—21no—
958C22—22no—
959C22—61no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—124no—
965C22—182no—
966C22—182no—
967C22—182no—
968C22—364no—
969C22C3×D3×#6712yes—
970C22C22×C3×D3211yescharacteristic
971C4—21no—
972C4—32no—
973C4—32no—
974C4—61no—
975C4—62no—
976C4—182no—
977C3—21no—
978C3—21no—
979C3—21no—
980C3—41no—
981C3#1059523811yescharacteristic, direct product factor
982C3C3×#559211yescharacteristic, complemented
983C3C3×#583011yescharacteristic, complemented
984C2—22no—
985C2—41no—
986C2—122no—
987C2—121no—
988C2—362no—
989C2C3×#6431412yes—
990C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#535
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C22×C3×#626C2semidirect
3. C3×#64146C2semidirect
4. C32×#937C2semidirect
5. C3×#63981C2semidirect
6. C3×#63979C2semidirect
7. C3×#63978C2semidirect
8. C3×#63976C2semidirect
9. C3×#63955C2semidirect
10. C3×#63907C2semidirect
11. C3×#63906C2semidirect
14. #10595238C3direct (N × H)
18. C2×C3×#638C22semidirect
20. C2×C32×#67C22semidirect
21. C2×C32×#67C22semidirect
23. C22×C32×Dic3C22semidirect
25. C2×C32×C4×D3C22semidirect
26. C2×C32×Dic6C22semidirect
30. C2×C3×#626C22semidirect
31. C2×C3×#625C22semidirect
33. C3×#3752C22semidirect
35. C32×(C2×D3)⋊C4C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×#3722C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×Dic32C22semidirect
43. C2×C3×#237D3semidirect
44. C2×C3×#237C2×C3semidirect
46. C22×#626C2×C3semidirect
48. #64146C2×C3semidirect
60. C3×#937D3semidirect
61. C3×#937C2×C3semidirect
69. #63981C2×C3semidirect
70. #63979C2×C3semidirect
71. #63978C2×C3semidirect
72. #63976C2×C3semidirect
73. #63955C2×C3semidirect
74. #63907C2×C3semidirect
75. #63906C2×C3semidirect
93. C2×C32×Dic3D4semidirect
130. C2×#638C22×C3semidirect
144. C2×C3×#67C2×D3semidirect
145. C2×C3×#67C2×D3semidirect
147. C2×C3×#67C22×C3semidirect
148. C2×C3×#67C22×C3semidirect
152. C22×C3×Dic3C2×D3semidirect
154. C22×C3×Dic3C22×C3semidirect
163. C2×C3×C4×D3C2×D3semidirect
164. C2×C3×C4×D3C22×C3semidirect
166. C2×C3×Dic6C2×D3semidirect
167. C2×C3×Dic6C22×C3semidirect
171. C2×#626C22×C3semidirect
172. C2×#625C22×C3semidirect
176. #3752C22×C3semidirect
191. C3×(C2×D3)⋊C4C2×D3semidirect
192. C3×(C2×D3)⋊C4C22×C3semidirect
197. Dic3⋊Dic3C22×C3semidirect
198. #3722C22×C3semidirect
199. (C2×D3)⋊Dic3C22×C3semidirect
200. Dic32C22×C3semidirect
227. C2×#237C3×D3semidirect
250. #937C3×D3semidirect
355. C2×C3×Dic3#67semidirect
356. C2×C3×Dic3C3×D4semidirect
441. C2×#67C2×C3×D3semidirect
442. C2×#67C2×C3×D3semidirect
444. C22×Dic3C2×C3×D3semidirect
450. C2×C4×D3C2×C3×D3semidirect
451. C2×Dic6C2×C3×D3semidirect
475. (C2×D3)⋊C4C2×C3×D3semidirect
593. C33#535semidirect
704. C2×Dic3C3×#67semidirect
885. C32#5592semidirect
886. C32#5830semidirect
887. C32C3×#535semidirect
981. C3#10595238direct (N × H)
982. C3C3×#5592semidirect
983. C3C3×#5830semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C22×C3×#6262
C3×#641462
C32×#9372
C3×#639812
C3×#639792
C3×#639782
C3×#639762
C3×#639552
C3×#639072
C3×#639062
C3×#58303
C3×#55923
#105952383