Finite Group Databasebeta

← C3×#10595236 #13174721

Subgroups — C3×#10595236 #13174721

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×C32×#237C211yesmaximal, characteristic, complemented
2C2×C3×#3799C211yesmaximal, characteristic, complemented
3C3×#64149C211yesmaximal, characteristic, complemented
4C32×#938C211yesmaximal, characteristic, complemented
5C3×#63979C212yesmaximal, complemented
6C3×#63978C212yesmaximal, complemented
7C3×#63958C212yesmaximal, complemented
8C3×#63952C212yesmaximal, complemented
9C3×#63909C211yesmaximal, characteristic, complemented
10C3×C4×#625C211yesmaximal, characteristic, complemented
11C3×#63843C211yesmaximal, characteristic, complemented
12C3×#5834—31nomaximal
13C3×#5599—31nomaximal
14#10595236C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×#638C2212yes—
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C32×#67C2212yes—
20C2×C32×#67C2212yes—
21C22×C32×Dic3C2212yes—
22C32×#237—24no—
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×Dic6C2211yescharacteristic
26C2×C3×#626C2212yes—
27C2×C3×#626C2212yes—
28C2×C3×#625C2211yescharacteristic
29C2×C3×#624C2212yes—
30C3×#3799—24no—
31C3×C4×C3⋊Dic3C2211yescharacteristic
32C32×#217C2212yes—
33C32×C4⋊Dic3C2211yescharacteristic
34C3×#3724C2211yescharacteristic
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2211yescharacteristic
39C3×Dic32C2212yes—
40C2×C32×#41—31no—
41C2×C3×#239—31no—
42C2×C3×#237—21no—
43C2×C3×#237D311yescharacteristic, complemented
44C2×C3×#237C2×C311yescharacteristic, complemented
45C2×C3×#235—31no—
46C2×#3799C2×C311yescharacteristic, complemented
47C32×#121—31no—
48#64149C2×C311yescharacteristic, complemented
49C3×Q8×Dic3—31no—
50C3×#940—31no—
51C3×#940—31no—
52C3×#940—32no—
53C3×#940—32no—
54C3×#940—61no—
55C3×#939—32no—
56C3×#938—21no—
57C3×#938—32no—
58C3×#938D311yescharacteristic, complemented
59C3×#938C2×C311yescharacteristic, complemented
60C3×#930—32no—
61C3×#930—31no—
62C3×C4×#67—31no—
63C3×C4×#67—31no—
64C3×C4×#67—32no—
65C3×#895—31no—
66C3×#887—31no—
67C3×#884—32no—
68C3×#67⋊C4—32no—
69#63979C2×C312yescomplemented
70#63978C2×C312yescomplemented
71#63958C2×C312yescomplemented
72#63952C2×C312yescomplemented
73#63909C2×C311yescharacteristic, complemented
74C4×#625C2×C311yescharacteristic, complemented
75#63843C2×C311yescharacteristic, complemented
76C23×C33C2312yes—
77C22×C3×C3⋊D3C2312yes—
78C22×C32×D3C2311yescharacteristic
79C22×C32×D3C2311yescharacteristic
80C33×D4—22no—
81C2×C33×C4C2311yescharacteristic
82C3×#638—24no—
83C3×#638—42no—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C3×C4⋊(C3⋊D3)—22no—
87C32×#67—24no—
88C32×#67—42no—
89C2×C32×Dic3—24no—
90C2×C32×Dic3C2311yescharacteristic
91C2×C32×Dic3C2312yes—
92C2×C32×Dic3C2311yescharacteristic
93C2×C32×Dic3C2312yes—
94C32×C4×D3—22no—
95C32×C4×D3—22no—
96C32×Dic6D414yescomplemented
97C3×#626—24no—
98C3×#626—42no—
99C3×#625—22no—
100C3×#624—24no—
101C3×#550—91no—
102#5834—31no—
103#5599—31no—
104C32×#41—64no—
105C2×C32×Q8—31no—
106C2×C32×D4—21no—
107C2×C32×D4—21no—
108C2×C32×D4—21no—
109C2×C32×D4—32no—
110C2×C32×D4—32no—
111C2×C32×D4—41no—
112C2×C32×D4C2×D311yescharacteristic
113C2×C32×D4C2×D311yescharacteristic
114C2×C32×D4C22×C311yescharacteristic
115C22×C32×C4—32no—
116C22×C32×C4—31no—
117C22×C32×C4—31no—
118C2×#638C22×C312yes—
119C2×#638C22×C312yes—
120C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
121C2×C3×#67—22no—
122C2×C3×#67—22no—
123C2×C3×#67—32no—
124C2×C3×#67—32no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—32no—
128C2×C3×#67—32no—
129C2×C3×#67—32no—
130C2×C3×#67—32no—
131C2×C3×#67—62no—
132C2×C3×#67—62no—
133C2×C3×#67C2×D312yes—
134C2×C3×#67C2×D312yes—
135C2×C3×#67C22×C312yes—
136C2×C3×#67C22×C312yes—
137C22×C3×Dic3—22no—
138C22×C3×Dic3C2×D312yes—
139C22×C3×Dic3C22×C312yes—
140C3×#239—64no—
141C3×#237—28no—
142C3×#237—24no—
143C3×#237—24no—
144C3×#235—64no—
145C2×C3×D12—32no—
146C2×C3×D12—31no—
147C2×C3×D12—31no—
148C2×C3×D12—32no—
149C2×C3×D12—61no—
150C2×C3×C4×D3—21no—
151C2×C3×C4×D3—21no—
152C2×C3×C4×D3—32no—
153C2×C3×C4×D3—32no—
154C2×C3×C4×D3C2×D311yescharacteristic
155C2×C3×C4×D3C2×D311yescharacteristic
156C2×C3×C4×D3C22×C311yescharacteristic
157C2×C3×C4×D3C22×C311yescharacteristic
158C2×C3×Dic6—21no—
159C2×C3×Dic6C2×D311yescharacteristic
160C2×C3×Dic6C22×C311yescharacteristic
161C2×#626C22×C312yes—
162C2×#626C22×C312yes—
163C2×#625C22×C311yescharacteristic
164C2×#624C22×C312yes—
165#3799—24no—
166C32×C4⋊C4—31no—
167C32×C22⋊C4—32no—
168C4×C3⋊Dic3C22×C311yescharacteristic
169C3×#217—22no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217C2×D312yes—
173C3×#217C22×C312yes—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—32no—
177C3×(C2×D3)⋊C4—32no—
178C3×C4⋊Dic3—21no—
179C3×C4⋊Dic3—32no—
180C3×C4⋊Dic3C2×D311yescharacteristic
181C3×C4⋊Dic3C22×C311yescharacteristic
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—32no—
184C3×Dic3⋊C4—31no—
185C3×C4×Dic3—31no—
186C3×C4×Dic3—31no—
187C3×C4×Dic3—32no—
188C3×C4×Dic3—32no—
189C3×C4×Dic3—61no—
190#3724C22×C311yescharacteristic
191Dic3⋊Dic3C22×C312yes—
192#3722C22×C312yes—
193(C2×D3)⋊Dic3C22×C311yescharacteristic
194(C2×D3)⋊Dic3C22×C311yescharacteristic
195Dic32C22×C312yes—
196C22×C33—22no—
197C22×C33—22no—
198C22×C33—22no—
199C22×C33C2411yescharacteristic
200C2×C3×C3⋊D3—22no—
201C2×C3×C3⋊D3—22no—
202C2×C3×C3⋊D3—22no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C33×C4C2×D412yes—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3#4112yescomplemented
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—22no—
215C32×Dic3C2×D414yes—
216C2×C3×#41—31no—
217C2×C3×#41—31no—
218C2×C3×#41—61no—
219C2×C3×#41—91no—
220C2×#239—31no—
221C2×#237C3×D311yescharacteristic, complemented
222C2×#235—31no—
223C3×#127—92no—
224C3×#127—91no—
225C3×#121—31no—
226C3×#121—31no—
227C3×#121—61no—
228C3×#121—92no—
229C3×#121—91no—
230C3×#121—92no—
231C3×C4×Q8—91no—
232C3×C4×D4—92no—
233C3×C4×D4—91no—
234Q8×Dic3—31no—
235#940—31no—
236#940—31no—
237#940—32no—
238#940—32no—
239#940—61no—
240#939—32no—
241#938—32no—
242#938C3×D311yescharacteristic, complemented
243#930—32no—
244#930—31no—
245C4×#67—31no—
246C4×#67—31no—
247C4×#67—32no—
248#895—31no—
249#887—31no—
250#884—32no—
251#67⋊C4—32no—
252C23×C32—22no—
253C23×C32—22no—
254C23×C32—22no—
255C23×C32—31no—
256C23×C32—31no—
257C23×C32—42no—
258C23×C32C22×D312yes—
259C23×C32C22×D312yes—
260C23×C32C23×C312yes—
261C22×C3⋊D3C23×C312yes—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—32no—
265C22×C3×D3—32no—
266C22×C3×D3—62no—
267C22×C3×D3C22×D311yescharacteristic
268C22×C3×D3C22×D311yescharacteristic
269C22×C3×D3C23×C311yescharacteristic
270C22×C3×D3C23×C311yescharacteristic
271C32×Q8—34no—
272C32×D4—22no—
273C32×D4—24no—
274C32×D4—22no—
275C32×D4—22no—
276C32×D4—42no—
277C32×D4—42no—
278C32×D4—44no—
279C32×D4—64no—
280C32×D4—122no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—32no—
285C2×C32×C4—32no—
286C2×C32×C4—31no—
287C2×C32×C4—31no—
288C2×C32×C4—41no—
289C2×C32×C4—64no—
290C2×C32×C4—62no—
291C2×C32×C4—62no—
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C23×C311yescharacteristic
295#638—24no—
296#638—42no—
297C2×C3⋊Dic3C23×C311yescharacteristic
298C2×C3⋊Dic3C23×C311yescharacteristic
299C4⋊(C3⋊D3)—22no—
300C3×#67—28no—
301C3×#67—24no—
302C3×#67—24no—
303C3×#67—42no—
304C3×#67—42no—
305C3×#67—44no—
306C3×#67—62no—
307C3×#67—62no—
308C3×#67—64no—
309C3×#67—64no—
310C3×#67—64no—
311C3×#67—124no—
312C3×#67—122no—
313C3×#67—122no—
314C3×#67—122no—
315C3×#67—124no—
316C2×C3×Dic3—28no—
317C2×C3×Dic3—24no—
318C2×C3×Dic3—24no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—21no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—21no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—31no—
325C2×C3×Dic3—31no—
326C2×C3×Dic3—31no—
327C2×C3×Dic3—61no—
328C2×C3×Dic3—61no—
329C2×C3×Dic3C22×D312yes—
330C2×C3×Dic3C22×D311yescharacteristic
331C2×C3×Dic3C22×D311yescharacteristic
332C2×C3×Dic3C22×D312yes—
333C2×C3×Dic3C23×C312yes—
334C2×C3×Dic3C23×C311yescharacteristic
335C2×C3×Dic3C23×C311yescharacteristic
336C2×C3×Dic3C23×C312yes—
337C3×D12—64no—
338C3×D12—62no—
339C3×D12—62no—
340C3×D12—122no—
341C3×D12—122no—
342C3×C4×D3—24no—
343C3×C4×D3—22no—
344C3×C4×D3—22no—
345C3×C4×D3—22no—
346C3×C4×D3—22no—
347C3×C4×D3—42no—
348C3×C4×D3—64no—
349C3×C4×D3—64no—
350C3×Dic6—24no—
351C3×Dic6#6714yescomplemented
352C3×Dic6C3×D414yescomplemented
353#626—24no—
354#626—42no—
355#625—22no—
356#624—24no—
357#550—91noSylow
358C2×C33—42no—
359C2×C33C22×D411yescharacteristic
360C2×C33C2×#4111yescharacteristic
361C2×C33H(5,𝔽2)11yescharacteristic
362C3×C3⋊D3—42no—
363C32×D3—41no—
364C32×D3—41no—
365C3×#41—64no—
366C3×#41—64no—
367C3×#41—68no—
368C3×#41—184no—
369C2×C3×Q8—31no—
370C2×C3×Q8—31no—
371C2×C3×Q8—61no—
372C2×C3×D4—21no—
373C2×C3×D4—21no—
374C2×C3×D4—21no—
375C2×C3×D4—32no—
376C2×C3×D4—32no—
377C2×C3×D4—32no—
378C2×C3×D4—32no—
379C2×C3×D4—41no—
380C2×C3×D4—62no—
381C2×C3×D4—62no—
382C2×C3×D4—92no—
383C2×C3×D4—92no—
384C2×C3×D4—91no—
385C2×C3×D4—92no—
386C2×C3×D4—92no—
387C2×C3×D4—91no—
388C2×C3×D4D3211yescharacteristic
389C2×C3×D4C2×C3×D311yescharacteristic
390C2×C3×D4C2×C3×D311yescharacteristic
391C22×C3×C4—32no—
392C22×C3×C4—32no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—61no—
398C22×C3×C4—61no—
399C22×C3×C4—62no—
400C22×C3×C4—92no—
401C2×#67—32no—
402C2×#67—32no—
403C2×#67—31no—
404C2×#67—31no—
405C2×#67—32no—
406C2×#67—32no—
407C2×#67—32no—
408C2×#67—32no—
409C2×#67—62no—
410C2×#67—62no—
411C2×#67C2×C3×D312yes—
412C2×#67C2×C3×D312yes—
413C22×Dic3C2×C3×D312yes—
414#239—64no—
415#237—24no—
416#235—64no—
417C2×D12—32no—
418C2×D12—31no—
419C2×D12—31no—
420C2×D12—32no—
421C2×D12—61no—
422C2×C4×D3—32no—
423C2×C4×D3—32no—
424C2×C4×D3C2×C3×D311yescharacteristic
425C2×C4×D3C2×C3×D311yescharacteristic
426C2×Dic6C2×C3×D311yescharacteristic
427C3×C4⋊C4—31no—
428C3×C4⋊C4—31no—
429C3×C4⋊C4—61no—
430C3×C4⋊C4—91no—
431C3×C4⋊C4—92no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—32no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—92no—
436C3×C22⋊C4—91no—
437C3×C22⋊C4—91no—
438C3×C42—92no—
439C3×C42—91no—
440#217—31no—
441#217—31no—
442#217C2×C3×D312yes—
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—31no—
445(C2×D3)⋊C4—32no—
446(C2×D3)⋊C4—32no—
447C4⋊Dic3—32no—
448C4⋊Dic3C2×C3×D311yescharacteristic
449Dic3⋊C4—31no—
450Dic3⋊C4—32no—
451Dic3⋊C4—31no—
452C4×Dic3—31no—
453C4×Dic3—31no—
454C4×Dic3—32no—
455C4×Dic3—32no—
456C4×Dic3—61no—
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—61no—
482C22×C32—61no—
483C22×C32—61no—
484C22×C32—61no—
485C22×C32—61no—
486C22×C32—82no—
487C22×C32—82no—
488C22×C32C23×D311yescharacteristic
489C22×C32C23×D311yescharacteristic
490C22×C32C24×C311yescharacteristic
491C2×C3⋊D3—22no—
492C2×C3⋊D3—22no—
493C2×C3⋊D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—21no—
497C2×C3×D3—21no—
498C2×C3×D3—21no—
499C2×C3×D3—21no—
500C2×C3×D3—21no—
501C2×C3×D3—21no—
502C2×C3×D3—21no—
503C2×C3×D3—21no—
504C2×C3×D3—21no—
505C2×C3×D3—21no—
506C2×C3×D3—21no—
507C2×C3×D3—21no—
508C2×C3×D3—41no—
509C2×C3×D3—41no—
510C2×C3×D3—41no—
511C2×C3×D3—41no—
512C2×C3×D3—62no—
513C2×C3×D3—62no—
514C2×C3×D3—62no—
515C2×C3×D3—62no—
516C2×C3×D3—62no—
517C2×C3×D3—62no—
518C2×C3×D3—122no—
519C2×C3×D3—122no—
520C2×C3×D3—122no—
521C32×C4—22no—
522C32×C4—22no—
523C32×C4—22no—
524C32×C4—34no—
525C32×C4—42no—
526C32×C4—61no—
527C32×C4—62no—
528C32×C4—61no—
529C32×C4D3×D412yes—
530C32×C4C2×#6712yes—
531C32×C4C2×C3×D412yes—
532C3⋊Dic3—21no—
533C3⋊Dic3C3×#4112yescomplemented
534C3×Dic3—22no—
535C3×Dic3—21no—
536C3×Dic3—22no—
537C3×Dic3—21no—
538C3×Dic3—21no—
539C3×Dic3—21no—
540C3×Dic3—22no—
541C3×Dic3—24no—
542C3×Dic3—32no—
543C3×Dic3—32no—
544C3×Dic3—41no—
545C3×Dic3—42no—
546C3×Dic3—62no—
547C3×Dic3—62no—
548C3×Dic3—61no—
549C3×Dic3—61no—
550C3×Dic3C2×#6714yes—
551C3×Dic3C2×C3×D414yes—
552C2×#41—31no—
553C2×#41—91no—
554#127—92no—
555#127—91no—
556#121—31no—
557#121—92no—
558#121—91no—
559#121—92no—
560C4×Q8—91no—
561C4×D4—92no—
562C4×D4—91no—
563C33#55011yescharacteristic, complemented, Sylow
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—31no—
568C23×C3—31no—
569C23×C3—31no—
570C23×C3—31no—
571C23×C3—42no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—92no—
575C23×C3C2×D3212yes—
576C23×C3C22×C3×D312yes—
577C23×C3C22×C3×D312yes—
578C22×D3—32no—
579C22×D3—32no—
580C22×D3—62no—
581C22×D3C22×C3×D311yescharacteristic
582C22×D3C22×C3×D311yescharacteristic
583C3×Q8—34no—
584C3×Q8—34no—
585C3×Q8—64no—
586C3×D4—24no—
587C3×D4—22no—
588C3×D4—22no—
589C3×D4—22no—
590C3×D4—42no—
591C3×D4—42no—
592C3×D4—44no—
593C3×D4—64no—
594C3×D4—64no—
595C3×D4—68no—
596C3×D4—122no—
597C3×D4—122no—
598C3×D4—124no—
599C3×D4—184no—
600C3×D4—184no—
601C3×D4—182no—
602C3×D4—182no—
603C3×D4—362no—
604C3×D4—362no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—31no—
612C2×C3×C4—31no—
613C2×C3×C4—32no—
614C2×C3×C4—31no—
615C2×C3×C4—31no—
616C2×C3×C4—41no—
617C2×C3×C4—61no—
618C2×C3×C4—62no—
619C2×C3×C4—61no—
620C2×C3×C4—62no—
621C2×C3×C4—64no—
622C2×C3×C4—64no—
623C2×C3×C4—64no—
624C2×C3×C4—68no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—62no—
628C2×C3×C4—62no—
629C2×C3×C4—91no—
630C2×C3×C4—91no—
631C2×C3×C4—122no—
632C2×C3×C4—184no—
633C2×C3×C4C2×D3211yescharacteristic
634C2×C3×C4C22×C3×D311yescharacteristic
635C2×C3×C4C22×C3×D311yescharacteristic
636#67—24no—
637#67—42no—
638#67—62no—
639#67—62no—
640#67—64no—
641#67—64no—
642#67—64no—
643#67—124no—
644#67—122no—
645#67—122no—
646#67—122no—
647#67—124no—
648C2×Dic3—24no—
649C2×Dic3—31no—
650C2×Dic3—31no—
651C2×Dic3—31no—
652C2×Dic3—31no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3C22×C3×D312yes—
656C2×Dic3C22×C3×D311yescharacteristic
657C2×Dic3C22×C3×D311yescharacteristic
658C2×Dic3C22×C3×D312yes—
659D12—64no—
660D12—62no—
661D12—62no—
662D12—122no—
663D12—122no—
664C4×D3—22no—
665C4×D3—22no—
666C4×D3—64no—
667C4×D3—64no—
668Dic6C3×#6714yescomplemented
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—121no—
690C2×C32C2×D3×D411yescharacteristic
691C2×C32#100411yescharacteristic
692C2×C32D3×#4111yescharacteristic
693C2×C32D3×#4111yescharacteristic
694C2×C32#100911yescharacteristic
695C2×C32C22×#6711yescharacteristic
696C2×C32C22×C3×D411yescharacteristic
697C2×C32C2×C3×#4111yescharacteristic
698C2×C32C3×H(5,𝔽2)11yescharacteristic
699C3⋊D3—42no—
700C3×D3—42no—
701C3×D3—42no—
702C3×D3—41no—
703C3×D3—41no—
704C3×D3—41no—
705C3×D3—41no—
706C3×D3—122no—
707C3×D3—122no—
708C3×D3—242no—
709#41—64no—
710#41—184no—
711C2×Q8—31no—
712C2×D4—32no—
713C2×D4—32no—
714C2×D4—92no—
715C2×D4—92no—
716C2×D4—91no—
717C2×D4—92no—
718C2×D4—92no—
719C2×D4—91no—
720C2×D4C3×D3211yescharacteristic
721C22×C4—32no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—92no—
725C4⋊C4—31no—
726C4⋊C4—91no—
727C4⋊C4—92no—
728C22⋊C4—32no—
729C22⋊C4—92no—
730C22⋊C4—91no—
731C22⋊C4—91no—
732C42—92no—
733C42—91no—
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—61no—
762C22×C3—61no—
763C22×C3—61no—
764C22×C3—61no—
765C22×C3—61no—
766C22×C3—61no—
767C22×C3—61no—
768C22×C3—61no—
769C22×C3—61no—
770C22×C3—61no—
771C22×C3—82no—
772C22×C3—82no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—182no—
778C22×C3—182no—
779C22×C3—182no—
780C22×C3C22×D3211yescharacteristic
781C22×C3C23×C3×D311yescharacteristic
782C22×C3C23×C3×D311yescharacteristic
783C2×D3—21no—
784C2×D3—21no—
785C2×D3—21no—
786C2×D3—21no—
787C2×D3—21no—
788C2×D3—21no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—122no—
796C2×D3—122no—
797C2×D3—122no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—34no—
802C3×C4—34no—
803C3×C4—42no—
804C3×C4—64no—
805C3×C4—62no—
806C3×C4—62no—
807C3×C4—61no—
808C3×C4—61no—
809C3×C4—61no—
810C3×C4—62no—
811C3×C4—61no—
812C3×C4—92no—
813C3×C4—121no—
814C3×C4—122no—
815C3×C4—181no—
816C3×C4D3×#6712yes—
817C3×C4C3×D3×D412yes—
818C3×C4C2×C3×#6712yes—
819Dic3—21no—
820Dic3—22no—
821Dic3—21no—
822Dic3—32no—
823Dic3—32no—
824Dic3—62no—
825Dic3—62no—
826Dic3—61no—
827Dic3—61no—
828Dic3C2×C3×#6714yes—
829C32—21no—
830C32—21no—
831C32—21no—
832C32—41no—
833C32#559911yescharacteristic, complemented
834C32#583411yescharacteristic, complemented
835C32C3×#55011yescharacteristic, complemented
836C23—31no—
837C23—31no—
838C23—92no—
839C23C2×C3×D3212yes—
840Q8—34no—
841D4—22no—
842D4—64no—
843D4—122no—
844D4—184no—
845D4—184no—
846D4—182no—
847D4—182no—
848D4—362no—
849D4—362no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—31no—
853C2×C4—31no—
854C2×C4—64no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—91no—
858C2×C4—91no—
859C2×C4—184no—
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—122no—
882C2×C3—121no—
883C2×C3—121no—
884C2×C3—121no—
885C2×C3—121no—
886C2×C3—362no—
887C2×C3#6431211yescharacteristic
888C2×C3#6431411yescharacteristic
889C2×C3C2×D3×#6711yescharacteristic
890C2×C3C2×C3×D3×D411yescharacteristic
891C2×C3C3×#100411yescharacteristic
892C2×C3C3×D3×#4111yescharacteristic
893C2×C3C3×D3×#4111yescharacteristic
894C2×C3C3×#100911yescharacteristic
895C2×C3C22×C3×#6711yescharacteristic
896D3—41no—
897D3—41no—
898D3—122no—
899D3—122no—
900D3—242no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—61no—
905C22—61no—
906C22—61no—
907C22—61no—
908C22—61no—
909C22—61no—
910C22—182no—
911C22—182no—
912C22—182no—
913C22C22×C3×D3211yescharacteristic
914C4—34no—
915C4—61no—
916C4—61no—
917C4—62no—
918C4—92no—
919C4—181no—
920C4C3×D3×#6712yes—
921C3—21no—
922C3—21no—
923C3—21no—
924C3—41no—
925C3#1059523611yescharacteristic, direct product factor
926C3C3×#559911yescharacteristic, complemented
927C3C3×#583411yescharacteristic, complemented
928C2—42no—
929C2—121no—
930C2—121no—
931C2—362no—
932C2C3×#6431211yescharacteristic
933C2C3×#6431411yescharacteristic
934C2C2×C3×D3×#6711yescharacteristic
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×C32×#237C2semidirect
2. C2×C3×#3799C2semidirect
3. C3×#64149C2semidirect
4. C32×#938C2semidirect
5. C3×#63979C2semidirect
6. C3×#63978C2semidirect
7. C3×#63958C2semidirect
8. C3×#63952C2semidirect
9. C3×#63909C2semidirect
10. C3×C4×#625C2semidirect
11. C3×#63843C2semidirect
14. #10595236C3direct (N × H)
43. C2×C3×#237D3semidirect
44. C2×C3×#237C2×C3semidirect
46. C2×#3799C2×C3semidirect
48. #64149C2×C3semidirect
58. C3×#938D3semidirect
59. C3×#938C2×C3semidirect
69. #63979C2×C3semidirect
70. #63978C2×C3semidirect
71. #63958C2×C3semidirect
72. #63952C2×C3semidirect
73. #63909C2×C3semidirect
74. C4×#625C2×C3semidirect
75. #63843C2×C3semidirect
96. C32×Dic6D4semidirect
211. C3×C3⋊Dic3#41semidirect
221. C2×#237C3×D3semidirect
242. #938C3×D3semidirect
351. C3×Dic6#67semidirect
352. C3×Dic6C3×D4semidirect
533. C3⋊Dic3C3×#41semidirect
563. C33#550semidirect
668. Dic6C3×#67semidirect
833. C32#5599semidirect
834. C32#5834semidirect
835. C32C3×#550semidirect
925. C3#10595236direct (N × H)
926. C3C3×#5599semidirect
927. C3C3×#5834semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×C3×#37992
C3×#641492
C32×#9382
C3×#639792
C3×#639782
C3×#639582
C3×#639522
C3×#639092
C3×C4×#6252
C3×#638432
C3×#58343
C3×#55993
#105952363