Finite Group Databasebeta

← #13178336

Subgroups — #13178336

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
1C3×#64106C211yesmaximal, characteristic, complemented
2C3×#64101C211yesmaximal, characteristic, complemented
3C3×#64099C211yesmaximal, characteristic, complemented
4C4×#6295C211yesmaximal, characteristic
5#11723690C212yesmaximal
6#11723689C211yesmaximal, characteristic, complemented
7#11723683C212yesmaximal, complemented
8#11723680C212yesmaximal, complemented
9#11723675C212yesmaximal, complemented
10#11723674C211yesmaximal, characteristic, complemented
11#11723668C211yesmaximal, characteristic, complemented
12#10594584—31nomaximal
13#10594457—31nomaximal
14#10594456—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×#6295C2211yescharacteristic
19C2×#6294C2212yes—
20C33×C4⋊C4C2211yescharacteristic
21C3×#3752C2212yes—
22C3×#3752C2212yes—
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4⋊(C3⋊Dic3)C2212yes—
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2212yes—
27C3×#3750C2212yes—
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2212yes—
30#88815C2212yes—
31#88815C2212yes—
32#88815C2212yes—
33#88815C2211yescharacteristic
34#88814C2212yes—
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic
37#88813C2212yes—
38#64106D311yescharacteristic, complemented
39#64101D311yescharacteristic, complemented
40#64099D311yescharacteristic, complemented
41C3×#897—31no—
42C3×#897—31no—
43C3×#897—61no—
44C3×#892—31no—
45C3×#892—31no—
46C3×#892—61no—
47C3×#890—31no—
48C3×#890—31no—
49C3×#890—61no—
50C4×#626—31no—
51C4×#626—31no—
52C4×#625—31no—
53#63900—31no—
54#63891—32no—
55#63890—32no—
56D3×C4⋊Dic3—31no—
57D3×C4⋊Dic3—31no—
58#63878—32no—
59#63877—32no—
60#63872—32no—
61#63871—31no—
62#63869—32no—
63#63869—32no—
64#63861—32no—
65#63858—32no—
66#63857—31no—
67#63856—31no—
68#63854—32no—
69#63848—32no—
70#63844—31no—
71#63843—31no—
72Dic3×Dic6—31no—
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C3×C3⋊D3C2311yescharacteristic
76C2×C33×C4C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2312yes—
85C3×C4×C3⋊D3—22no—
86C3×C4×C3⋊D3—22no—
87C3×#634—22no—
88#6295—22no—
89#6294—24no—
90#5694—91no—
91#5642—91no—
92#5529—91no—
93C2×C4×C3⋊D3C2×D311yescharacteristic
94C2×C4×C3⋊D3C2×D311yescharacteristic
95C2×#634C2×D311yescharacteristic
96C2×C3×C4×D3—31no—
97C2×C3×C4×D3—31no—
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—61no—
101C2×C3×C4×D3—61no—
102C2×C3×Dic6—31no—
103C2×C3×Dic6—31no—
104C2×C3×Dic6—61no—
105C2×#626—31no—
106C2×#626—31no—
107C2×#625—31no—
108C2×#624—32no—
109C2×D3×Dic3—32no—
110C2×D3×Dic3—32no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4—41no—
115C32×C4⋊C4C2×D311yescharacteristic
116C32×C4⋊C4C2×D311yescharacteristic
117C32×C4⋊C4C2×D311yescharacteristic
118#3752C2×D312yes—
119#3752C2×D312yes—
120C4⋊(C3⋊Dic3)C2×D311yescharacteristic
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic
122C4⋊(C3⋊Dic3)C2×D312yes—
123C4⋊(C3⋊Dic3)C2×D312yes—
124#3750C2×D312yes—
125C4×C3⋊Dic3C2×D311yescharacteristic
126C4×C3⋊Dic3C2×D312yes—
127C3×(C2×D3)⋊C4—32no—
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—32no—
131C3×(C2×D3)⋊C4—62no—
132C3×(C2×D3)⋊C4—62no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—32no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—32no—
140C3×C4⋊Dic3—32no—
141C3×C4⋊Dic3—62no—
142C3×C4⋊Dic3—61no—
143C3×C4⋊Dic3—61no—
144C3×C4⋊Dic3—62no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—62no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—32no—
152C3×C4×Dic3—61no—
153C3×C4×Dic3—62no—
154#3724—32no—
155#3724—32no—
156#3724—32no—
157#3724—31no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—31no—
166#3722—31no—
167#3722—31no—
168#3722—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—31no—
172(C2×D3)⋊Dic3—31no—
173(C2×D3)⋊Dic3—31no—
174(C2×D3)⋊Dic3—31no—
175Dic32—32no—
176Dic32—32no—
177Dic32—32no—
178C22×C33C2411yescharacteristic
179C2×C3×C3⋊D3—21no—
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3#4112yes—
185C33×C4—22no—
186C33×C4#4112yes—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—21no—
194C3×#125—91no—
195C3×C22⋊Q8—91no—
196C3×#117—91no—
197#946—91no—
198Q8×Dic3—91no—
199C4×#67—91no—
200C4×#67—91no—
201C2×C4⋊Dic3—91no—
202#924—91no—
203#898—92no—
204#898—92no—
205#897—31no—
206#897—31no—
207#897—61no—
208#897—91no—
209#894—92no—
210#892—31no—
211#892—31no—
212#892—61no—
213#892—92no—
214D3×C4⋊C4—91no—
215D3×C4⋊C4—91no—
216#890—31no—
217#890—31no—
218#890—61no—
219#890—92no—
220#890—92no—
221#887—91no—
222#886—92no—
223#883—92no—
224#879—92no—
225#877—92no—
226C4×D12—91no—
227#872—92no—
228#870—92no—
229C4×Dic6—91no—
230C22×C3⋊D3C22×D311yescharacteristic
231C22×C3⋊D3C22×D311yescharacteristic
232C22×C3×D3—31no—
233C22×C3×D3—31no—
234C22×C3×D3—31no—
235C22×C3×D3—31no—
236C22×C3×D3—61no—
237C22×C3×D3—61no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—22no—
242C2×C32×C4—22no—
243C2×C32×C4—22no—
244C2×C32×C4—41no—
245C2×C32×C4—42no—
246C2×C32×C4C22×D312yes—
247C2×C32×C4C22×D312yes—
248C2×C32×C4C22×D312yes—
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C3⋊Dic3C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D312yes—
254C2×C3⋊Dic3C22×D312yes—
255C2×C3⋊Dic3C22×D311yescharacteristic
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D312yes—
258C2×C3⋊Dic3C22×D311yescharacteristic
259C4×C3⋊D3—22no—
260C4×C3⋊D3—22no—
261#634—22no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—62no—
283C3×C4×D3—64no—
284C3×C4×D3—62no—
285C3×C4×D3—62no—
286C3×C4×D3—62no—
287C3×C4×D3—62no—
288C3×C4×D3—122no—
289C3×Dic6—62no—
290C3×Dic6—62no—
291C3×Dic6—122no—
292#626—62no—
293#626—62no—
294#625—62no—
295#624—64no—
296D3×Dic3—64no—
297D3×Dic3—64no—
298#552—271noSylow
299C2×C33C2×#4111yescharacteristic
300C2×C33C2×#4111yescharacteristic
301C2×C332−1+411yescharacteristic
302C3×C3⋊D3—22no—
303C3×C3⋊D3—41no—
304C2×C3×Q8—91no—
305C22×C3×C4—91no—
306C22×C3×C4—91no—
307C2×#67—91no—
308C2×#67—91no—
309C22×Dic3—92no—
310C2×D12—91no—
311C2×C4×D3—31no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—92no—
318C2×C4×D3—92no—
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—61no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—41no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—92no—
328C3×C4⋊C4—92no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—92no—
331C3×C4⋊C4D3211yescharacteristic
332C3×C4⋊C4D3211yescharacteristic
333C3×C4⋊C4D3211yescharacteristic
334C3×C22⋊C4—92no—
335C3×C22⋊C4—92no—
336C3×C42—91no—
337C3×C42—92no—
338#217—91no—
339#217—91no—
340#217—92no—
341(C2×D3)⋊C4—32no—
342(C2×D3)⋊C4—32no—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4—32no—
345(C2×D3)⋊C4—62no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—91no—
348(C2×D3)⋊C4—91no—
349(C2×D3)⋊C4—91no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—92no—
352(C2×D3)⋊C4—91no—
353C4⋊Dic3—31no—
354C4⋊Dic3—32no—
355C4⋊Dic3—32no—
356C4⋊Dic3—32no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—32no—
360C4⋊Dic3—31no—
361C4⋊Dic3—61no—
362C4⋊Dic3—62no—
363C4⋊Dic3—61no—
364C4⋊Dic3—62no—
365C4⋊Dic3—91no—
366C4⋊Dic3—92no—
367C4⋊Dic3—92no—
368C4⋊Dic3—92no—
369Dic3⋊C4—32no—
370Dic3⋊C4—32no—
371Dic3⋊C4—62no—
372Dic3⋊C4—92no—
373Dic3⋊C4—91no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—91no—
379Dic3⋊C4—92no—
380C4×Dic3—32no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—32no—
384C4×Dic3—61no—
385C4×Dic3—62no—
386C4×Dic3—92no—
387C4×Dic3—92no—
388C4×Dic3—92no—
389C22×C32—21no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—41no—
393C22×C32C23×D311yescharacteristic
394C22×C32C23×D311yescharacteristic
395C22×C32C23×D311yescharacteristic
396C2×C3⋊D3—21no—
397C2×C3⋊D3—21no—
398C2×C3⋊D3—21no—
399C2×C3⋊D3—21no—
400C2×C3⋊D3—21no—
401C2×C3⋊D3#23912yes—
402C2×C3×D3—32no—
403C2×C3×D3—32no—
404C2×C3×D3—62no—
405C2×C3×D3—61no—
406C2×C3×D3—61no—
407C2×C3×D3—61no—
408C2×C3×D3—61no—
409C2×C3×D3—62no—
410C2×C3×D3—61no—
411C2×C3×D3—61no—
412C2×C3×D3—61no—
413C2×C3×D3—61no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—121no—
417C2×C3×D3—121no—
418C2×C3×D3—121no—
419C2×C3×D3—121no—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4—22no—
423C32×C4—22no—
424C32×C4—22no—
425C32×C4—22no—
426C32×C4—42no—
427C32×C4—42no—
428C32×C4—42no—
429C32×C4—42no—
430C32×C4—82no—
431C32×C4#23512yes—
432C32×C4#23712yes—
433C32×C4#23912yes—
434C3⋊Dic3—21no—
435C3⋊Dic3—22no—
436C3⋊Dic3—21no—
437C3⋊Dic3—22no—
438C3⋊Dic3—22no—
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3×Dic3—62no—
442C3×Dic3—62no—
443C3×Dic3—61no—
444C3×Dic3—61no—
445C3×Dic3—62no—
446C3×Dic3—62no—
447C3×Dic3—61no—
448C3×Dic3—62no—
449C3×Dic3—61no—
450C3×Dic3—61no—
451C3×Dic3—62no—
452C3×Dic3—62no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—122no—
457C3×Dic3—121no—
458C3×Dic3—121no—
459C3×Dic3—122no—
460C3×Dic3—122no—
461C3×Dic3—121no—
462#126—272no—
463#125—91no—
464#125—272no—
465#123—272no—
466C22⋊Q8—91no—
467C22⋊Q8—271no—
468C4×Q8—271no—
469C4×D4—271no—
470#117—91no—
471#117—272no—
472C2×C4⋊C4—271no—
473C33#55211yescharacteristic, complemented, Sylow
474C23×C3—91no—
475C23×C3—91no—
476C22×D3—31no—
477C22×D3—31no—
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—61no—
481C22×D3—61no—
482C3×Q8—182no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—41no—
490C2×C3×C4—42no—
491C2×C3×C4—91no—
492C2×C3×C4—92no—
493C2×C3×C4—92no—
494C2×C3×C4—91no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—92no—
498C2×C3×C4—182no—
499C2×C3×C4—182no—
500C2×C3×C4C2×D3212yes—
501C2×C3×C4C2×D3212yes—
502C2×C3×C4C2×D3212yes—
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505C2×C3×C4C2×D3211yescharacteristic
506#67—182no—
507#67—182no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—32no—
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—32no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3—61no—
528C2×Dic3—62no—
529C2×Dic3—184no—
530D12—182no—
531C4×D3—64no—
532C4×D3—62no—
533C4×D3—62no—
534C4×D3—62no—
535C4×D3—62no—
536C4×D3—122no—
537C4×D3—184no—
538C4×D3—184no—
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×C32C2×#23511yescharacteristic
555C2×C32C2×#23711yescharacteristic
556C2×C32C2×#23911yescharacteristic
557C2×C32C2×#23911yescharacteristic
558C2×C32D3×#4111yescharacteristic
559C2×C32D3×#4111yescharacteristic
560C2×C32#101011yescharacteristic
561C2×C32#101011yescharacteristic
562C2×C32#101011yescharacteristic
563C3⋊D3—22no—
564C3⋊D3—41no—
565C3×D3—62no—
566C3×D3—62no—
567C3×D3—122no—
568C3×D3—122no—
569C3×D3—121no—
570C3×D3—121no—
571C2×Q8—91no—
572C2×D4—271no—
573C22×C4—91no—
574C22×C4—91no—
575C22×C4—272no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—92no—
579C4⋊C4—92no—
580C4⋊C4—92no—
581C4⋊C4—272no—
582C4⋊C4—272no—
583C4⋊C4—271no—
584C4⋊C4—272no—
585C4⋊C4#111311yescharacteristic
586C22⋊C4—92no—
587C22⋊C4—92no—
588C22⋊C4—271no—
589C22⋊C4—271no—
590C22⋊C4—272no—
591C42—92no—
592C42—91no—
593C42—272no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—41no—
598C22×C3—92no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3—181no—
602C22×C3—181no—
603C22×C3—181no—
604C22×C3C22×D3211yescharacteristic
605C22×C3C22×D3211yescharacteristic
606C22×C3C22×D3211yescharacteristic
607C2×D3—32no—
608C2×D3—32no—
609C2×D3—62no—
610C2×D3—61no—
611C2×D3—61no—
612C2×D3—61no—
613C2×D3—61no—
614C2×D3—62no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—61no—
619C2×D3—61no—
620C2×D3—61no—
621C2×D3—121no—
622C2×D3—121no—
623C2×D3—121no—
624C2×D3—121no—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—42no—
632C3×C4—42no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—82no—
636C3×C4—181no—
637C3×C4—181no—
638C3×C4—182no—
639C3×C4—181no—
640C3×C4—182no—
641C3×C4—182no—
642C3×C4—181no—
643C3×C4#379512yes—
644C3×C4#379612yes—
645C3×C4#379912yes—
646Dic3—62no—
647Dic3—62no—
648Dic3—61no—
649Dic3—61no—
650Dic3—62no—
651Dic3—61no—
652Dic3—61no—
653Dic3—61no—
654Dic3—61no—
655Dic3—62no—
656Dic3—62no—
657Dic3—61no—
658Dic3—62no—
659Dic3—62no—
660Dic3—61no—
661Dic3—122no—
662Dic3—121no—
663Dic3—121no—
664Dic3—122no—
665Dic3—122no—
666Dic3—121no—
667C32—21no—
668C32—21no—
669C32—21no—
670C32—41no—
671C32#552911yescharacteristic, complemented
672C32#564211yescharacteristic, complemented
673C32#569411yescharacteristic, complemented
674C23—91no—
675C23—91no—
676Q8—182no—
677D4—542no—
678C2×C4—91no—
679C2×C4—91no—
680C2×C4—92no—
681C2×C4—91no—
682C2×C4—92no—
683C2×C4—92no—
684C2×C4—91no—
685C2×C4—182no—
686C2×C4—182no—
687C2×C4—544no—
688C2×C4C2×#111312yes—
689C2×C4C2×#111311yescharacteristic
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—182no—
703C2×C3—361no—
704C2×C3C2×#379511yescharacteristic
705C2×C3C2×#379611yescharacteristic
706C2×C3C2×#379911yescharacteristic
707C2×C3#6430911yescharacteristic
708C2×C3#6430911yescharacteristic
709C2×C3#6430911yescharacteristic
710C2×C3D3×#23911yescharacteristic
711C2×C3D3×#23911yescharacteristic
712C2×C3#6431911yescharacteristic
713D3—62no—
714D3—62no—
715D3—122no—
716D3—122no—
717D3—121no—
718D3—121no—
719C22—92no—
720C22—181no—
721C22—181no—
722C22—181no—
723C22—181no—
724C22—181no—
725C22C22×#111311yescharacteristic
726C4—22no—
727C4—181no—
728C4—181no—
729C4—182no—
730C4—181no—
731C4—182no—
732C4—182no—
733C4—181no—
734C4#8904112yes—
735C3—21no—
736C3—21no—
737C3—21no—
738C3—41no—
739C3#1059445611yescharacteristic, complemented
740C3#1059445711yescharacteristic, complemented
741C3#1059458411yescharacteristic, complemented
742C2—182no—
743C2—361no—
744C2C2×#8904111yescharacteristic
745C2#1172462011yescharacteristic
746C2#1172462611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC2×#6295C22
hypercenterC4⋊C4#1113
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64106C2semidirect
2. C3×#64101C2semidirect
3. C3×#64099C2semidirect
6. #11723689C2semidirect
7. #11723683C2semidirect
8. #11723680C2semidirect
9. #11723675C2semidirect
10. #11723674C2semidirect
11. #11723668C2semidirect
38. #64106D3semidirect
39. #64101D3semidirect
40. #64099D3semidirect
473. C33#552semidirect
671. C32#5529semidirect
672. C32#5642semidirect
673. C32#5694semidirect
739. C3#10594456semidirect
740. C3#10594457semidirect
741. C3#10594584semidirect

Maximal subgroups

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

subgroupindex
C3×#641062
C3×#641012
C3×#640992
C4×#62952
#117236902
#117236892
#117236832
#117236802
#117236752
#117236742
#117236682
#105945843
#105944573
#105944563