Finite Group Databasebeta

← C3×#10595164 #13174727

Subgroups — C3×#10595164 #13174727

Order 1728.

1668 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×C3×#3795C211yesmaximal, characteristic, complemented
3C32×#940C211yesmaximal, characteristic, complemented
4C32×#938C211yesmaximal, characteristic, complemented
5C3×#63980C212yesmaximal, complemented
6C3×#63979C212yesmaximal, complemented
7C3×#67⋊Dic3C212yesmaximal, complemented
8C3×#63971C212yesmaximal, complemented
9C3×#63916C211yesmaximal, characteristic, complemented
10C3×C4×#626C211yesmaximal, characteristic, complemented
11C3×#63844C211yesmaximal, characteristic, complemented
12C3×#5718—31nomaximal
13C3×#5599—31nomaximal
14#10595164C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C22×C3×C3⋊Dic3C2212yes—
18C3×#3830—24no—
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×C32×#67C2212yes—
22C2×C32×#67C2212yes—
23C2×C32×#67C2212yes—
24C2×C32×D12C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×#626C2212yes—
28C2×C3×#625C2212yes—
29C2×C3×D3×Dic3C2212yes—
30C3×#3795—24no—
31C32×#217C2212yes—
32C32×C4⋊Dic3C2211yescharacteristic
33C32×C4×Dic3C2211yescharacteristic
34C3×#3724C2212yes—
35C3×Dic3⋊Dic3C2211yescharacteristic
36C3×#3722C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×(C2×D3)⋊Dic3C2211yescharacteristic
39C3×Dic32C2212yes—
40C2×#3830C2×C311yescharacteristic, complemented
41C2×C3×#237—31no—
42C2×C3×#237—31no—
43C2×C3×#237—31no—
44C2×C3×#237—61no—
45C2×C3×#235—31no—
46C2×#3795C2×C311yescharacteristic, complemented
47C32×#127—31no—
48C32×#121—31no—
49C3×#940—21no—
50C3×#940—32no—
51C3×#940—32no—
52C3×#940D311yescharacteristic, complemented
53C3×#940C2×C311yescharacteristic, complemented
54C3×#939—32no—
55C3×#939—32no—
56C3×#939—32no—
57C3×#938—21no—
58C3×#938—31no—
59C3×#938D311yescharacteristic, complemented
60C3×#938C2×C311yescharacteristic, complemented
61C3×D4×Dic3—32no—
62C3×C4×#67—31no—
63C3×#895—31no—
64C3×#887—31no—
65C3×#884—32no—
66C3×#67⋊C4—32no—
67C3×C4×D12—31no—
68C3×C4×Dic6—31no—
69#63980C2×C312yescomplemented
70#63979C2×C312yescomplemented
71#67⋊Dic3C2×C312yescomplemented
72#63971C2×C312yescomplemented
73#63916C2×C311yescharacteristic, complemented
74C4×#626C2×C311yescharacteristic, complemented
75#63844C2×C311yescharacteristic, complemented
76C23×C33C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3C2312yes—
79C22×C32×D3C2311yescharacteristic
80C33×D4—22no—
81C2×C33×C4C2311yescharacteristic
82C3×#638—24no—
83C2×C3×C3⋊Dic3—24no—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C3×C4×C3⋊D3—22no—
87C3×#634D414yescomplemented
88C32×#67—24no—
89C32×#67—42no—
90C32×#67—42no—
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2312yes—
93C2×C32×Dic3C2311yescharacteristic
94C2×C32×Dic3C2311yescharacteristic
95C32×D12—22no—
96C32×C4×D3—22no—
97C3×#626—22no—
98C3×#626—42no—
99C3×#625—24no—
100C3×D3×Dic3—24no—
101C3×#550—91no—
102#5718—31no—
103#5599—31no—
104C2×C32×D4—21no—
105C2×C32×D4—21no—
106C2×C32×D4—21no—
107C2×C32×D4—32no—
108C2×C32×D4—32no—
109C2×C32×D4—32no—
110C2×C32×D4—31no—
111C2×C32×D4—41no—
112C2×C32×D4C2×D311yescharacteristic
113C2×C32×D4C2×D311yescharacteristic
114C2×C32×D4C22×C311yescharacteristic
115C22×C32×C4—31no—
116C2×#638C22×C312yes—
117C22×C3⋊Dic3C22×C312yes—
118#3830—24no—
119C2×C4×C3⋊D3C22×C311yescharacteristic
120C2×#634C22×C311yescharacteristic
121C2×C3×#67—22no—
122C2×C3×#67—22no—
123C2×C3×#67—22no—
124C2×C3×#67—32no—
125C2×C3×#67—32no—
126C2×C3×#67—32no—
127C2×C3×#67—32no—
128C2×C3×#67—31no—
129C2×C3×#67—32no—
130C2×C3×#67—62no—
131C2×C3×#67C2×D312yes—
132C2×C3×#67C2×D312yes—
133C2×C3×#67C2×D312yes—
134C2×C3×#67C22×C312yes—
135C2×C3×#67C22×C312yes—
136C2×C3×#67C22×C312yes—
137C22×C3×Dic3—32no—
138C22×C3×Dic3—32no—
139C22×C3×Dic3—32no—
140C22×C3×Dic3—62no—
141C3×#237—64no—
142C3×#237—64no—
143C3×#237—64no—
144C3×#237—68no—
145C3×#235—64no—
146C2×C3×D12—21no—
147C2×C3×D12—31no—
148C2×C3×D12—32no—
149C2×C3×D12C2×D311yescharacteristic
150C2×C3×D12C22×C311yescharacteristic
151C2×C3×C4×D3—21no—
152C2×C3×C4×D3—32no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—61no—
156C2×C3×C4×D3C2×D311yescharacteristic
157C2×C3×C4×D3C22×C311yescharacteristic
158C2×C3×Dic6—31no—
159C2×C3×Dic6—31no—
160C2×C3×Dic6—61no—
161C2×#626C22×C311yescharacteristic
162C2×#626C22×C312yes—
163C2×#625C22×C312yes—
164C2×D3×Dic3C22×C312yes—
165#3795—24no—
166C32×C4⋊C4—31no—
167C32×C22⋊C4—32no—
168C32×C42—31no—
169C3×#217—22no—
170C3×#217—31no—
171C3×#217—32no—
172C3×#217C2×D312yes—
173C3×#217C22×C312yes—
174C3×(C2×D3)⋊C4—32no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×C4⋊Dic3—21no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3C2×D311yescharacteristic
181C3×C4⋊Dic3C22×C311yescharacteristic
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—32no—
184C3×Dic3⋊C4—32no—
185C3×C4×Dic3—21no—
186C3×C4×Dic3—32no—
187C3×C4×Dic3—32no—
188C3×C4×Dic3C2×D311yescharacteristic
189C3×C4×Dic3C22×C311yescharacteristic
190#3724C22×C312yes—
191Dic3⋊Dic3C22×C311yescharacteristic
192#3722C22×C311yescharacteristic
193(C2×D3)⋊Dic3C22×C311yescharacteristic
194(C2×D3)⋊Dic3C22×C312yes—
195Dic32C22×C312yes—
196C22×C33—22no—
197C22×C33—22no—
198C22×C33—22no—
199C22×C33C2411yescharacteristic
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C32×D3—22no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—22no—
207C2×C32×D3—21no—
208C2×C32×D3—22no—
209C33×C4C2×D412yes—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3C2×D414yes—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—22no—
215C32×Dic3#4112yescomplemented
216C2×C3×#41—91no—
217C2×C3×#41—91no—
218C2×#237—31no—
219C2×#237—31no—
220C2×#237—31no—
221C2×#237—61no—
222C2×#235—31no—
223C3×#127—31no—
224C3×#127—31no—
225C3×#127—61no—
226C3×#127—92no—
227C3×#121—31no—
228C3×#121—31no—
229C3×#121—61no—
230C3×#121—92no—
231C3×#121—91no—
232C3×#121—92no—
233C3×C4×Q8—91no—
234C3×C4×D4—91no—
235C3×C4×D4—92no—
236#940—32no—
237#940—32no—
238#940C3×D311yescharacteristic, complemented
239#939—32no—
240#939—32no—
241#939—32no—
242#938—31no—
243#938C3×D311yescharacteristic, complemented
244D4×Dic3—32no—
245C4×#67—31no—
246#895—31no—
247#887—31no—
248#884—32no—
249#67⋊C4—32no—
250C4×D12—31no—
251C4×Dic6—31no—
252C23×C32—22no—
253C23×C32—22no—
254C23×C32—22no—
255C23×C32—32no—
256C23×C32—31no—
257C23×C32—42no—
258C23×C32C22×D312yes—
259C23×C32C22×D312yes—
260C23×C32C23×C312yes—
261C22×C3⋊D3C23×C311yescharacteristic
262C22×C3×D3—21no—
263C22×C3×D3—22no—
264C22×C3×D3—31no—
265C22×C3×D3—31no—
266C22×C3×D3—61no—
267C22×C3×D3C22×D312yes—
268C22×C3×D3C22×D311yescharacteristic
269C22×C3×D3C23×C312yes—
270C22×C3×D3C23×C311yescharacteristic
271C32×D4—22no—
272C32×D4—24no—
273C32×D4—22no—
274C32×D4—22no—
275C32×D4—42no—
276C32×D4—42no—
277C32×D4—44no—
278C32×D4—64no—
279C32×D4—62no—
280C32×D4—122no—
281C32×D4—122no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—31no—
286C2×C32×C4—32no—
287C2×C32×C4—31no—
288C2×C32×C4—31no—
289C2×C32×C4—41no—
290C2×C32×C4—62no—
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C23×C311yescharacteristic
294#638—24no—
295C2×C3⋊Dic3—24no—
296C2×C3⋊Dic3C23×C311yescharacteristic
297C2×C3⋊Dic3C23×C312yes—
298C4×C3⋊D3—22no—
299#634C3×D414yescomplemented
300C3×#67—24no—
301C3×#67—24no—
302C3×#67—44no—
303C3×#67—42no—
304C3×#67—42no—
305C3×#67—42no—
306C3×#67—42no—
307C3×#67—44no—
308C3×#67—44no—
309C3×#67—64no—
310C3×#67—64no—
311C3×#67—64no—
312C3×#67—64no—
313C3×#67—68no—
314C3×#67—62no—
315C3×#67—122no—
316C2×C3×Dic3—21no—
317C2×C3×Dic3—21no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—21no—
320C2×C3×Dic3—32no—
321C2×C3×Dic3—32no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—62no—
325C2×C3×Dic3—61no—
326C2×C3×Dic3—64no—
327C2×C3×Dic3—64no—
328C2×C3×Dic3—64no—
329C2×C3×Dic3—68no—
330C2×C3×Dic3C22×D312yes—
331C2×C3×Dic3C22×D311yescharacteristic
332C2×C3×Dic3C22×D311yescharacteristic
333C2×C3×Dic3C22×D311yescharacteristic
334C2×C3×Dic3C23×C312yes—
335C2×C3×Dic3C23×C311yescharacteristic
336C2×C3×Dic3C23×C311yescharacteristic
337C2×C3×Dic3C23×C311yescharacteristic
338C3×D12—22no—
339C3×D12—22no—
340C3×D12—42no—
341C3×D12—62no—
342C3×D12—122no—
343C3×C4×D3—22no—
344C3×C4×D3—22no—
345C3×C4×D3—42no—
346C3×C4×D3—64no—
347C3×C4×D3—64no—
348C3×C4×D3—62no—
349C3×C4×D3—62no—
350C3×Dic6—34no—
351C3×Dic6—34no—
352C3×Dic6—64no—
353#626—22no—
354#626—42no—
355#625—24no—
356D3×Dic3—24no—
357#550—91noSylow
358C2×C33—42no—
359C2×C33C22×D411yescharacteristic
360C2×C33C2×#4111yescharacteristic
361C2×C33H(5,𝔽2)11yescharacteristic
362C3×C3⋊D3—41no—
363C32×D3—41no—
364C32×D3—42no—
365C3×#41—184no—
366C3×#41—184no—
367C2×C3×Q8—91no—
368C2×C3×D4—21no—
369C2×C3×D4—21no—
370C2×C3×D4—21no—
371C2×C3×D4—32no—
372C2×C3×D4—32no—
373C2×C3×D4—32no—
374C2×C3×D4—32no—
375C2×C3×D4—32no—
376C2×C3×D4—32no—
377C2×C3×D4—31no—
378C2×C3×D4—31no—
379C2×C3×D4—41no—
380C2×C3×D4—61no—
381C2×C3×D4—62no—
382C2×C3×D4—62no—
383C2×C3×D4—62no—
384C2×C3×D4—91no—
385C2×C3×D4—92no—
386C2×C3×D4—92no—
387C2×C3×D4—92no—
388C2×C3×D4D3211yescharacteristic
389C2×C3×D4C2×C3×D311yescharacteristic
390C2×C3×D4C2×C3×D311yescharacteristic
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—61no—
394C22×C3×C4—92no—
395C22×C3×C4—92no—
396C22×C3×C4—91no—
397C2×#67—32no—
398C2×#67—32no—
399C2×#67—32no—
400C2×#67—32no—
401C2×#67—31no—
402C2×#67—32no—
403C2×#67—62no—
404C2×#67C2×C3×D312yes—
405C2×#67C2×C3×D312yes—
406C2×#67C2×C3×D312yes—
407C22×Dic3—32no—
408C22×Dic3—32no—
409C22×Dic3—32no—
410C22×Dic3—62no—
411#237—64no—
412#237—64no—
413#237—64no—
414#237—68no—
415#235—64no—
416C2×D12—31no—
417C2×D12—32no—
418C2×D12C2×C3×D311yescharacteristic
419C2×C4×D3—32no—
420C2×C4×D3—31no—
421C2×C4×D3—31no—
422C2×C4×D3—61no—
423C2×C4×D3C2×C3×D311yescharacteristic
424C2×Dic6—31no—
425C2×Dic6—31no—
426C2×Dic6—61no—
427C3×C4⋊C4—31no—
428C3×C4⋊C4—31no—
429C3×C4⋊C4—61no—
430C3×C4⋊C4—92no—
431C3×C4⋊C4—91no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—32no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—91no—
436C3×C22⋊C4—91no—
437C3×C22⋊C4—92no—
438C3×C42—31no—
439C3×C42—31no—
440C3×C42—61no—
441C3×C42—92no—
442#217—31no—
443#217—32no—
444#217C2×C3×D312yes—
445(C2×D3)⋊C4—31no—
446(C2×D3)⋊C4—32no—
447(C2×D3)⋊C4—31no—
448(C2×D3)⋊C4—31no—
449C4⋊Dic3—31no—
450C4⋊Dic3C2×C3×D311yescharacteristic
451Dic3⋊C4—32no—
452Dic3⋊C4—31no—
453Dic3⋊C4—32no—
454C4×Dic3—32no—
455C4×Dic3—32no—
456C4×Dic3C2×C3×D311yescharacteristic
457C22×C32—22no—
458C22×C32—24no—
459C22×C32—22no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—41no—
471C22×C32—42no—
472C22×C32—42no—
473C22×C32—44no—
474C22×C32—42no—
475C22×C32—42no—
476C22×C32—42no—
477C22×C32—42no—
478C22×C32—42no—
479C22×C32—42no—
480C22×C32—61no—
481C22×C32—62no—
482C22×C32—61no—
483C22×C32—61no—
484C22×C32—62no—
485C22×C32—62no—
486C22×C32—82no—
487C22×C32—82no—
488C22×C32C23×D311yescharacteristic
489C22×C32C23×D311yescharacteristic
490C22×C32C24×C311yescharacteristic
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—21no—
494C2×C3×D3—22no—
495C2×C3×D3—21no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—21no—
500C2×C3×D3—21no—
501C2×C3×D3—22no—
502C2×C3×D3—21no—
503C2×C3×D3—21no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—21no—
507C2×C3×D3—41no—
508C2×C3×D3—41no—
509C2×C3×D3—42no—
510C2×C3×D3—42no—
511C2×C3×D3—42no—
512C2×C3×D3—62no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—61no—
516C2×C3×D3—61no—
517C2×C3×D3—61no—
518C2×C3×D3—61no—
519C2×C3×D3—121no—
520C2×C3×D3—121no—
521C32×C4—22no—
522C32×C4—22no—
523C32×C4—22no—
524C32×C4—32no—
525C32×C4—42no—
526C32×C4—61no—
527C32×C4—61no—
528C32×C4—62no—
529C32×C4D3×D412yes—
530C32×C4D3×D412yes—
531C32×C4C2×C3×D412yes—
532C3⋊Dic3—21no—
533C3⋊Dic3C2×C3×D414yes—
534C3×Dic3—22no—
535C3×Dic3—21no—
536C3×Dic3—21no—
537C3×Dic3—22no—
538C3×Dic3—21no—
539C3×Dic3—22no—
540C3×Dic3—21no—
541C3×Dic3—22no—
542C3×Dic3—34no—
543C3×Dic3—34no—
544C3×Dic3—41no—
545C3×Dic3—42no—
546C3×Dic3—64no—
547C3×Dic3—62no—
548C3×Dic3—61no—
549C3×Dic3—61no—
550C3×Dic3#23712yescomplemented
551C3×Dic3C3×#4112yescomplemented
552C2×#41—91no—
553C2×#41—91no—
554#127—31no—
555#127—92no—
556#121—31no—
557#121—92no—
558#121—91no—
559#121—92no—
560C4×Q8—91no—
561C4×D4—91no—
562C4×D4—92no—
563C33#55011yescharacteristic, complemented, Sylow
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—31no—
568C23×C3—32no—
569C23×C3—32no—
570C23×C3—31no—
571C23×C3—42no—
572C23×C3—61no—
573C23×C3—62no—
574C23×C3—91no—
575C23×C3C2×D3212yes—
576C23×C3C22×C3×D312yes—
577C23×C3C22×C3×D312yes—
578C22×D3—31no—
579C22×D3—31no—
580C22×D3—61no—
581C22×D3C22×C3×D312yes—
582C22×D3C22×C3×D311yescharacteristic
583C3×Q8—94no—
584C3×D4—24no—
585C3×D4—22no—
586C3×D4—22no—
587C3×D4—22no—
588C3×D4—42no—
589C3×D4—42no—
590C3×D4—44no—
591C3×D4—64no—
592C3×D4—64no—
593C3×D4—62no—
594C3×D4—62no—
595C3×D4—122no—
596C3×D4—124no—
597C3×D4—122no—
598C3×D4—122no—
599C3×D4—122no—
600C3×D4—122no—
601C3×D4—124no—
602C3×D4—124no—
603C3×D4—182no—
604C3×D4—184no—
605C3×D4—184no—
606C3×D4—362no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—31no—
611C2×C3×C4—31no—
612C2×C3×C4—31no—
613C2×C3×C4—32no—
614C2×C3×C4—31no—
615C2×C3×C4—32no—
616C2×C3×C4—31no—
617C2×C3×C4—31no—
618C2×C3×C4—41no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—92no—
626C2×C3×C4—91no—
627C2×C3×C4—122no—
628C2×C3×C4—184no—
629C2×C3×C4—184no—
630C2×C3×C4—182no—
631C2×C3×C4C2×D3211yescharacteristic
632C2×C3×C4C22×C3×D311yescharacteristic
633C2×C3×C4C22×C3×D311yescharacteristic
634#67—24no—
635#67—42no—
636#67—42no—
637#67—64no—
638#67—64no—
639#67—64no—
640#67—64no—
641#67—68no—
642#67—62no—
643#67—122no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—31no—
647C2×Dic3—31no—
648C2×Dic3—62no—
649C2×Dic3—61no—
650C2×Dic3—64no—
651C2×Dic3—64no—
652C2×Dic3—64no—
653C2×Dic3—68no—
654C2×Dic3C22×C3×D312yes—
655C2×Dic3C22×C3×D311yescharacteristic
656C2×Dic3C22×C3×D311yescharacteristic
657C2×Dic3C22×C3×D311yescharacteristic
658D12—22no—
659D12—62no—
660D12—122no—
661C4×D3—22no—
662C4×D3—64no—
663C4×D3—64no—
664C4×D3—62no—
665C4×D3—62no—
666Dic6—34no—
667Dic6—34no—
668Dic6—64no—
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—41no—
679C2×C32—41no—
680C2×C32—41no—
681C2×C32—42no—
682C2×C32—44no—
683C2×C32—42no—
684C2×C32—42no—
685C2×C32—82no—
686C2×C32—82no—
687C2×C32—84no—
688C2×C32—121no—
689C2×C32—122no—
690C2×C32C2×D3×D411yescharacteristic
691C2×C32C2×D3×D411yescharacteristic
692C2×C32C2×#23711yescharacteristic
693C2×C32#100411yescharacteristic
694C2×C32#100411yescharacteristic
695C2×C32D3×#4111yescharacteristic
696C2×C32C22×C3×D411yescharacteristic
697C2×C32C2×C3×#4111yescharacteristic
698C2×C32C3×H(5,𝔽2)11yescharacteristic
699C3⋊D3—41no—
700C3×D3—42no—
701C3×D3—42no—
702C3×D3—41no—
703C3×D3—41no—
704C3×D3—42no—
705C3×D3—82no—
706C3×D3—122no—
707C3×D3—121no—
708C3×D3—121no—
709#41—184no—
710#41—184no—
711C2×Q8—91no—
712C2×D4—32no—
713C2×D4—32no—
714C2×D4—32no—
715C2×D4—31no—
716C2×D4—91no—
717C2×D4—92no—
718C2×D4—92no—
719C2×D4—92no—
720C2×D4C3×D3211yescharacteristic
721C22×C4—31no—
722C22×C4—92no—
723C22×C4—92no—
724C22×C4—91no—
725C4⋊C4—31no—
726C4⋊C4—91no—
727C4⋊C4—92no—
728C22⋊C4—32no—
729C22⋊C4—91no—
730C22⋊C4—91no—
731C22⋊C4—92no—
732C42—31no—
733C42—92no—
734C22×C3—24no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—44no—
756C22×C3—41no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—61no—
760C22×C3—61no—
761C22×C3—62no—
762C22×C3—61no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—61no—
766C22×C3—61no—
767C22×C3—62no—
768C22×C3—61no—
769C22×C3—62no—
770C22×C3—82no—
771C22×C3—82no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—122no—
775C22×C3—122no—
776C22×C3—122no—
777C22×C3—181no—
778C22×C3—181no—
779C22×C3—181no—
780C22×C3C22×D3211yescharacteristic
781C22×C3C23×C3×D311yescharacteristic
782C22×C3C23×C3×D311yescharacteristic
783C2×D3—21no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—21no—
788C2×D3—21no—
789C2×D3—62no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—61no—
794C2×D3—61no—
795C2×D3—61no—
796C2×D3—121no—
797C2×D3—121no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—32no—
802C3×C4—32no—
803C3×C4—42no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—61no—
807C3×C4—62no—
808C3×C4—61no—
809C3×C4—61no—
810C3×C4—62no—
811C3×C4—61no—
812C3×C4—94no—
813C3×C4—121no—
814C3×C4—122no—
815C3×C4—181no—
816C3×C4#381112yes—
817C3×C4C3×D3×D412yes—
818C3×C4C3×D3×D412yes—
819Dic3—21no—
820Dic3—21no—
821Dic3—22no—
822Dic3—34no—
823Dic3—34no—
824Dic3—64no—
825Dic3—62no—
826Dic3—61no—
827Dic3—61no—
828Dic3C3×#23712yescomplemented
829C32—21no—
830C32—21no—
831C32—21no—
832C32—41no—
833C32#559911yescharacteristic, complemented
834C32#571811yescharacteristic, complemented
835C32C3×#55011yescharacteristic, complemented
836C23—31no—
837C23—32no—
838C23—91no—
839C23C2×C3×D3212yes—
840Q8—94no—
841D4—22no—
842D4—64no—
843D4—62no—
844D4—122no—
845D4—122no—
846D4—182no—
847D4—184no—
848D4—184no—
849D4—362no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—32no—
853C2×C4—31no—
854C2×C4—62no—
855C2×C4—92no—
856C2×C4—91no—
857C2×C4—184no—
858C2×C4—184no—
859C2×C4—182no—
860C2×C4C2×C3×D3211yescharacteristic
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—44no—
871C2×C3—42no—
872C2×C3—42no—
873C2×C3—42no—
874C2×C3—41no—
875C2×C3—41no—
876C2×C3—41no—
877C2×C3—82no—
878C2×C3—82no—
879C2×C3—84no—
880C2×C3—122no—
881C2×C3—121no—
882C2×C3—122no—
883C2×C3—122no—
884C2×C3—121no—
885C2×C3—242no—
886C2×C3—361no—
887C2×C3D3×#23711yescharacteristic
888C2×C3#6431311yescharacteristic
889C2×C3C2×#381111yescharacteristic
890C2×C3C2×C3×D3×D411yescharacteristic
891C2×C3C2×C3×D3×D411yescharacteristic
892C2×C3C2×C3×#23711yescharacteristic
893C2×C3C3×#100411yescharacteristic
894C2×C3C3×#100411yescharacteristic
895C2×C3C3×D3×#4111yescharacteristic
896D3—41no—
897D3—42no—
898D3—122no—
899D3—121no—
900D3—121no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—61no—
905C22—62no—
906C22—62no—
907C22—61no—
908C22—61no—
909C22—62no—
910C22—181no—
911C22—181no—
912C22—181no—
913C22C22×C3×D3211yescharacteristic
914C4—32no—
915C4—61no—
916C4—61no—
917C4—62no—
918C4—94no—
919C4—181no—
920C4C3×#381112yes—
921C3—21no—
922C3—21no—
923C3—21no—
924C3—41no—
925C3#1059516411yescharacteristic, direct product factor
926C3C3×#559911yescharacteristic, complemented
927C3C3×#571811yescharacteristic, complemented
928C2—42no—
929C2—121no—
930C2—122no—
931C2—361no—
932C2C3×D3×#23711yescharacteristic
933C2C3×#6431311yescharacteristic
934C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#550
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×C3×#3830C2semidirect
2. C2×C3×#3795C2semidirect
3. C32×#940C2semidirect
4. C32×#938C2semidirect
5. C3×#63980C2semidirect
6. C3×#63979C2semidirect
7. C3×#67⋊Dic3C2semidirect
8. C3×#63971C2semidirect
9. C3×#63916C2semidirect
10. C3×C4×#626C2semidirect
11. C3×#63844C2semidirect
14. #10595164C3direct (N × H)
40. C2×#3830C2×C3semidirect
46. C2×#3795C2×C3semidirect
52. C3×#940D3semidirect
53. C3×#940C2×C3semidirect
59. C3×#938D3semidirect
60. C3×#938C2×C3semidirect
69. #63980C2×C3semidirect
70. #63979C2×C3semidirect
71. #67⋊Dic3C2×C3semidirect
72. #63971C2×C3semidirect
73. #63916C2×C3semidirect
74. C4×#626C2×C3semidirect
75. #63844C2×C3semidirect
87. C3×#634D4semidirect
215. C32×Dic3#41semidirect
238. #940C3×D3semidirect
243. #938C3×D3semidirect
299. #634C3×D4semidirect
550. C3×Dic3#237semidirect
551. C3×Dic3C3×#41semidirect
563. C33#550semidirect
828. Dic3C3×#237semidirect
833. C32#5599semidirect
834. C32#5718semidirect
835. C32C3×#550semidirect
925. C3#10595164direct (N × H)
926. C3C3×#5599semidirect
927. C3C3×#5718semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C2×C3×#37952
C32×#9402
C32×#9382
C3×#639802
C3×#639792
C3×#67⋊Dic32
C3×#639712
C3×#639162
C3×C4×#6262
C3×#638442
C3×#57183
C3×#55993
#105951643