Finite Group Databasebeta

← #13168409

Subgroups — #13168409

Order 1728.

1088 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723668C211yesmaximal, characteristic, complemented
2#11723447C211yesmaximal, characteristic, complemented
3#11723425C211yesmaximal, characteristic, complemented
4#11723424C211yesmaximal, characteristic, complemented
5C3×C4×#625C211yesmaximal, characteristic
6C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63857C211yesmaximal, characteristic, complemented
8#11723026C212yesmaximal, complemented
9#11723016C212yesmaximal, complemented
10#11722985C212yesmaximal
11#11722914C212yesmaximal, complemented
12#10594942—31nomaximal
13#10594849—31nomaximal
14#10594551—31nomaximal
15C2×C3×#634C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×C3×#625C2211yescharacteristic
19C2×C3×D3×Dic3C2212yes—
20C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4×C3⋊Dic3C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24#88815C2212yes—
25#88813C2212yes—
26#88806C2212yes—
27#88806C2212yes—
28Dic3⋊(C3⋊Dic3)C2212yes—
29(C2×D3)⋊(C3⋊Dic3)C2212yes—
30(C2×D3)⋊(C3⋊Dic3)C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32C3×#3724C2211yescharacteristic
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38#64135—31no—
39#64133—31no—
40#64099—31no—
41C3×C4×#67—31no—
42C3×C4×#67—31no—
43C2×C3×C4⋊Dic3—31no—
44C3×#924—31no—
45C3×#897—31no—
46C3×D3×C4⋊C4—31no—
47#63969—32no—
48#63961—32no—
49#63956—32no—
50#63955—32no—
51#63905—32no—
52C4×#625D311yescharacteristic
53D3×C4⋊Dic3D311yescharacteristic, complemented
54#63878—32no—
55#63870—32no—
56#63869—31no—
57#63869—31no—
58#63869—61no—
59#63861—32no—
60#63858—32no—
61#63857D311yescharacteristic, complemented
62#63856—31no—
63#63856—31no—
64#63856—61no—
65#63847—32no—
66#63847—32no—
67#63844—31no—
68#63843—31no—
69Dic3×Dic6—31no—
70#63841—31no—
71#63841—31no—
72#63841—32no—
73#63841—61no—
74C22×C32×D3C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C3×#634—22no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C32×C4×D3—22no—
87C32×C4×D3—22no—
88C3×#625—22no—
89C3×D3×Dic3—24no—
90#5639—91no—
91#5541—91no—
92#5513—91no—
93C22×C32×C4—31no—
94C22×C32×C4—31no—
95C2×#634C2×D311yescharacteristic
96C2×C3×#67—31no—
97C2×C3×#67—31no—
98C22×C3×Dic3—32no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—32no—
102C2×C3×C4×D3C2×D311yescharacteristic
103C2×C3×C4×D3C2×D311yescharacteristic
104C2×C3×C4×D3C2×D311yescharacteristic
105C2×C3×C4×D3C2×D311yescharacteristic
106C2×C3×Dic6—31no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—61no—
109C2×#625C2×D311yescharacteristic
110C2×D3×Dic3C2×D312yes—
111C32×C4⋊C4—31no—
112#3757—32no—
113#3757—32no—
114C4⋊(C3⋊Dic3)—31no—
115C4⋊(C3⋊Dic3)—31no—
116C4⋊(C3⋊Dic3)—31no—
117C4⋊(C3⋊Dic3)—32no—
118C4⋊(C3⋊Dic3)—61no—
119C4⋊(C3⋊Dic3)—61no—
120C4⋊(C3⋊Dic3)—61no—
121C4⋊(C3⋊Dic3)—121no—
122C4⋊(C3⋊Dic3)C2×D311yescharacteristic
123#3750—32no—
124#3750—32no—
125C4×C3⋊Dic3—32no—
126C4×C3⋊Dic3C2×D311yescharacteristic
127C3×#217—32no—
128C3×#217—31no—
129C3×#217—31no—
130C3×(C2×D3)⋊C4—32no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—32no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—61no—
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×Dic3⋊C4—32no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—31no—
145C3×C4×Dic3—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—61no—
148#3724—32no—
149#3724—32no—
150#3724—32no—
151#3724—32no—
152#3724—32no—
153#3724—62no—
154#3724—62no—
155#3724C2×D311yescharacteristic
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—62no—
161Dic3⋊Dic3C2×D312yes—
162Dic3⋊Dic3C2×D312yes—
163(C2×D3)⋊Dic3—32no—
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—62no—
168(C2×D3)⋊Dic3—62no—
169(C2×D3)⋊Dic3C2×D311yescharacteristic
170(C2×D3)⋊Dic3C2×D312yes—
171(C2×D3)⋊Dic3C2×D311yescharacteristic
172Dic32—32no—
173Dic32—32no—
174Dic32—32no—
175Dic32—32no—
176Dic32—32no—
177Dic32—62no—
178C22×C33C2411yescharacteristic
179C2×C32×D3—21no—
180C2×C32×D3—21no—
181C2×C32×D3—21no—
182C2×C32×D3—21no—
183C2×C32×D3—21no—
184C2×C32×D3#4112yes—
185C33×C4#4112yes—
186C3⋊(C3⋊Dic3)—22no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C32×Dic3—21no—
192C32×Dic3—22no—
193C32×Dic3—21no—
194C3×C22⋊Q8—91no—
195C3×C4×D4—91no—
196C2×C3×C4⋊C4—91no—
197#946—91no—
198Q8×Dic3—91no—
199#935—92no—
200#929—92no—
201C4×#67—31no—
202C4×#67—31no—
203#926—92no—
204#926—91no—
205#926—91no—
206#926—181no—
207C2×C4⋊Dic3—31no—
208#924—31no—
209#924—91no—
210#924—91no—
211#924—181no—
212#898—92no—
213#897—31no—
214#892—92no—
215#892—91no—
216D3×C4⋊C4—31no—
217#890—91no—
218#890—91no—
219#890—181no—
220#889—92no—
221#889—92no—
222#889—92no—
223#887—91no—
224#883—92no—
225#879—92no—
226#879—92no—
227#877—92no—
228#870—91no—
229C4×Dic6—91no—
230C23×C32—31no—
231C23×C32—31no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3C22×D311yescharacteristic
235C22×C3×D3C22×D311yescharacteristic
236C22×C3×D3C22×D311yescharacteristic
237C22×C3×D3C22×D311yescharacteristic
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—31no—
242C2×C32×C4—31no—
243C2×C32×C4—32no—
244C2×C32×C4—41no—
245C2×C32×C4—62no—
246C2×C32×C4—62no—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C3⋊Dic3—32no—
251C2×C3⋊Dic3—32no—
252C2×C3⋊Dic3—32no—
253C2×C3⋊Dic3—62no—
254C2×C3⋊Dic3—62no—
255C2×C3⋊Dic3—62no—
256C2×C3⋊Dic3—122no—
257C2×C3⋊Dic3C22×D311yescharacteristic
258C2×C3⋊Dic3C22×D312yes—
259C2×C3⋊Dic3C22×D312yes—
260C2×C3⋊Dic3C22×D311yescharacteristic
261#634—22no—
262C3×#67—62no—
263C3×#67—62no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—62no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—64no—
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D311yescharacteristic
286C3×C4×D3—24no—
287C3×C4×D3—22no—
288C3×C4×D3—22no—
289C3×C4×D3—22no—
290C3×C4×D3—22no—
291C3×C4×D3—42no—
292C3×C4×D3—64no—
293C3×Dic6—62no—
294C3×Dic6—62no—
295C3×Dic6—122no—
296#625—22no—
297D3×Dic3—24no—
298#552—271noSylow
299C2×C33C2×#4111yescharacteristic
300C2×C33C2×#4111yescharacteristic
301C2×C332−1+411yescharacteristic
302C32×D3—22no—
303C32×D3—41no—
304C2×C3×Q8—91no—
305C2×C3×D4—91no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—92no—
313C2×#67—31no—
314C2×#67—31no—
315C22×Dic3—32no—
316C2×C4×D3—32no—
317C2×C4×D3D3211yescharacteristic
318C2×C4×D3D3211yescharacteristic
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—61no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—91no—
326C3×C4⋊C4—92no—
327C3×C4⋊C4—92no—
328C3×C4⋊C4—91no—
329C3×C22⋊C4—91no—
330C3×C22⋊C4—91no—
331C3×C22⋊C4—92no—
332C3×C42—91no—
333#217—31no—
334#217—32no—
335#217—31no—
336#217—92no—
337#217—92no—
338#217—92no—
339#217—92no—
340#217—182no—
341#217—182no—
342(C2×D3)⋊C4—31no—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4—31no—
345(C2×D3)⋊C4—92no—
346(C2×D3)⋊C4—92no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—32no—
350C4⋊Dic3—32no—
351C4⋊Dic3—61no—
352C4⋊Dic3—92no—
353C4⋊Dic3—92no—
354C4⋊Dic3—92no—
355C4⋊Dic3—91no—
356C4⋊Dic3—91no—
357C4⋊Dic3—91no—
358C4⋊Dic3—182no—
359C4⋊Dic3—181no—
360C4⋊Dic3—181no—
361C4⋊Dic3—181no—
362C4⋊Dic3—361no—
363C4⋊Dic3D3211yescharacteristic
364Dic3⋊C4—32no—
365Dic3⋊C4—32no—
366Dic3⋊C4—31no—
367Dic3⋊C4—31no—
368Dic3⋊C4—92no—
369Dic3⋊C4—92no—
370Dic3⋊C4—92no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—182no—
378Dic3⋊C4—182no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—61no—
382C4×Dic3—92no—
383C4×Dic3—92no—
384C4×Dic3—92no—
385C4×Dic3—92no—
386C4×Dic3—92no—
387C4×Dic3—92no—
388C4×Dic3—182no—
389C22×C32—21no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—32no—
393C22×C32—41no—
394C22×C32—61no—
395C22×C32—61no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32—61no—
399C22×C32C23×D311yescharacteristic
400C22×C32C23×D311yescharacteristic
401C22×C32C23×D311yescharacteristic
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—22no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—22no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3#23512yes—
419C2×C3×D3#23712yes—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4—22no—
423C32×C4—42no—
424C32×C4—61no—
425C32×C4—62no—
426C32×C4—61no—
427C32×C4#23512yes—
428C32×C4#23712yes—
429C32×C4#23712yes—
430C3⋊Dic3—21no—
431C3⋊Dic3—22no—
432C3⋊Dic3—22no—
433C3⋊Dic3—21no—
434C3⋊Dic3—62no—
435C3⋊Dic3—62no—
436C3⋊Dic3—62no—
437C3⋊Dic3—122no—
438C3⋊Dic3—122no—
439C3⋊Dic3—122no—
440C3⋊Dic3—242no—
441C3×Dic3—22no—
442C3×Dic3—21no—
443C3×Dic3—22no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—22no—
448C3×Dic3—41no—
449C3×Dic3—42no—
450C3×Dic3—62no—
451C3×Dic3—62no—
452C3×Dic3—62no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—62no—
457C3×Dic3—61no—
458C3×Dic3—122no—
459C3×Dic3—122no—
460C3×Dic3—121no—
461C3×Dic3—121no—
462#126—272no—
463#125—271no—
464#125—272no—
465#123—272no—
466C22⋊Q8—91no—
467C22⋊Q8—271no—
468C4×Q8—271no—
469C4×D4—91no—
470#117—272no—
471#117—271no—
472C2×C4⋊C4—91no—
473C33#55211yescharacteristic, complemented, Sylow
474C23×C3—31no—
475C23×C3—31no—
476C23×C3—31no—
477C23×C3—31no—
478C23×C3—61no—
479C23×C3—61no—
480C22×D3C2×D3211yescharacteristic
481C22×D3C2×D3211yescharacteristic
482C3×Q8—182no—
483C3×D4—182no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—32no—
491C2×C3×C4—31no—
492C2×C3×C4—32no—
493C2×C3×C4—41no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—62no—
497C2×C3×C4—64no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—91no—
503C2×C3×C4—92no—
504C2×C3×C4—92no—
505C2×C3×C4—91no—
506C2×C3×C4—122no—
507C2×C3×C4—184no—
508C2×C3×C4C2×D3211yescharacteristic
509C2×C3×C4C2×D3211yescharacteristic
510C2×C3×C4C2×D3211yescharacteristic
511#67—62no—
512#67—62no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—62no—
524C2×Dic3—62no—
525C2×Dic3—64no—
526C2×Dic3—92no—
527C2×Dic3—92no—
528C2×Dic3—92no—
529C2×Dic3—182no—
530C2×Dic3—182no—
531C2×Dic3—182no—
532C2×Dic3—362no—
533C2×Dic3C2×D3211yescharacteristic
534C2×Dic3C2×D3211yescharacteristic
535C2×Dic3C2×D3212yes—
536C4×D3—22no—
537C4×D3—22no—
538C4×D3—64no—
539Dic6—62no—
540Dic6—62no—
541Dic6—122no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—41no—
552C2×C32—41no—
553C2×C32—41no—
554C2×C32—62no—
555C2×C32—121no—
556C2×C32C2×#23511yescharacteristic
557C2×C32C2×#23511yescharacteristic
558C2×C32C2×#23711yescharacteristic
559C2×C32C2×#23711yescharacteristic
560C2×C32C2×#23711yescharacteristic
561C2×C32#100711yescharacteristic
562C2×C32#100711yescharacteristic
563C2×C32D3×#4111yescharacteristic
564C2×C32#101011yescharacteristic
565C3×D3—22no—
566C3×D3—22no—
567C3×D3—42no—
568C3×D3—42no—
569C3×D3—41no—
570C3×D3—41no—
571C2×Q8—91no—
572C2×D4—91no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—92no—
576C4⋊C4—31no—
577C4⋊C4—92no—
578C4⋊C4—92no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—272no—
582C4⋊C4—272no—
583C4⋊C4—272no—
584C4⋊C4—272no—
585C4⋊C4—271no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—92no—
589C22⋊C4—272no—
590C22⋊C4—272no—
591C42—91no—
592C42—272no—
593C42—272no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—32no—
598C22×C3—32no—
599C22×C3—41no—
600C22×C3—62no—
601C22×C3—62no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3—61no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3—61no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—61no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3—121no—
616C22×C3C22×D3211yescharacteristic
617C22×C3C22×D3211yescharacteristic
618C22×C3C22×D3211yescharacteristic
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3#379512yes—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—42no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—61no—
632C3×C4—61no—
633C3×C4—62no—
634C3×C4—61no—
635C3×C4—61no—
636C3×C4—121no—
637C3×C4—122no—
638C3×C4—182no—
639C3×C4—181no—
640C3×C4—181no—
641C3×C4—182no—
642C3×C4#379512yes—
643C3×C4#380412yes—
644C3×C4#380512yes—
645Dic3—22no—
646Dic3—21no—
647Dic3—21no—
648Dic3—62no—
649Dic3—62no—
650Dic3—61no—
651Dic3—61no—
652Dic3—61no—
653Dic3—61no—
654Dic3—62no—
655Dic3—62no—
656Dic3—122no—
657Dic3—122no—
658Dic3—121no—
659Dic3—121no—
660Dic3—182no—
661Dic3—182no—
662Dic3—182no—
663Dic3—362no—
664Dic3—362no—
665Dic3—362no—
666Dic3—722no—
667C32—21no—
668C32—21no—
669C32—21no—
670C32—41no—
671C32#551311yescharacteristic, complemented
672C32#554111yescharacteristic, complemented
673C32#563911yescharacteristic, complemented
674C23—31no—
675C23—31no—
676Q8—182no—
677D4—182no—
678C2×C4—31no—
679C2×C4—32no—
680C2×C4—31no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—92no—
686C2×C4—92no—
687C2×C4—184no—
688C2×C4—272no—
689C2×C4D3311yescharacteristic
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—41no—
700C2×C3—41no—
701C2×C3—41no—
702C2×C3—62no—
703C2×C3—62no—
704C2×C3—122no—
705C2×C3—122no—
706C2×C3—121no—
707C2×C3—121no—
708C2×C3C2×#379511yescharacteristic
709C2×C3C2×#379511yescharacteristic
710C2×C3#6429711yescharacteristic
711C2×C3#6429711yescharacteristic
712C2×C3D3×#23511yescharacteristic
713C2×C3D3×#23711yescharacteristic
714C2×C3#6431611yescharacteristic
715C2×C3C2×#380411yescharacteristic
716C2×C3C2×#380511yescharacteristic
717D3—22no—
718D3—41no—
719C22—32no—
720C22—61no—
721C22—61no—
722C22—61no—
723C22—61no—
724C22—61no—
725C22C2×D3311yescharacteristic
726C4—62no—
727C4—61no—
728C4—61no—
729C4—182no—
730C4—181no—
731C4—181no—
732C4—182no—
733C4—542no—
734C4#8896112yes—
735C3—21no—
736C3—21no—
737C3—21no—
738C3—41no—
739C3#1059455111yescharacteristic, complemented
740C3#1059484911yescharacteristic, complemented
741C3#1059494211yescharacteristic, complemented
742C2—62no—
743C2—121no—
744C2D3×#379511yescharacteristic
745C2#1172439511yescharacteristic
746C2C2×#8896111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#625C22
hypercenterC2×C4D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723668C2semidirect
2. #11723447C2semidirect
3. #11723425C2semidirect
4. #11723424C2semidirect
6. C3×D3×C4⋊Dic3C2semidirect
7. C3×#63857C2semidirect
8. #11723026C2semidirect
9. #11723016C2semidirect
11. #11722914C2semidirect
53. D3×C4⋊Dic3D3semidirect
61. #63857D3semidirect
473. C33#552semidirect
671. C32#5513semidirect
672. C32#5541semidirect
673. C32#5639semidirect
739. C3#10594551semidirect
740. C3#10594849semidirect
741. C3#10594942semidirect

Maximal subgroups

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

subgroupindex
#117236682
#117234472
#117234252
#117234242
C3×C4×#6252
C3×D3×C4⋊Dic32
C3×#638572
#117230262
#117230162
#117229852
#117229142
#105949423
#105948493
#105945513