Finite Group Databasebeta

← #13168550

Subgroups — #13168550

Order 1728.

1094 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723677C211yesmaximal, characteristic
2C4×#6293C211yesmaximal, characteristic, complemented
3#11723436C211yesmaximal, characteristic
4#11723410C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic
6C3×#63866C211yesmaximal, characteristic, complemented
7C3×#63843C211yesmaximal, characteristic, complemented
8#11723025C212yesmaximal, complemented
9#11723024C212yesmaximal, complemented
10#11722972C212yesmaximal, complemented
11#11722915C212yesmaximal, complemented
12#10595387—31nomaximal
13#10594335—31nomaximal
14#10593863—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6293C2211yescharacteristic
19C2×C3×#624C2212yes—
20C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C3×C4×C3⋊Dic3C2211yescharacteristic
22C32×C4⋊Dic3C2211yescharacteristic
23C32×C4×Dic3C2211yescharacteristic
24#88814C2212yes—
25#88814C2212yes—
26#88807C2211yescharacteristic
27#88807C2212yes—
28#88806C2211yescharacteristic
29Dic3⋊(C3⋊Dic3)C2211yescharacteristic
30#88803C2212yes—
31#88803C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×Dic32C2212yes—
38#64156—31no—
39#64096—31no—
40C4×#634—31no—
41C3×Q8×Dic3—31no—
42C3×#944—31no—
43C3×#893—31no—
44C3×#887—31no—
45C3×C4×D12—31no—
46C3×#869—31no—
47C4×#627—31no—
48C4×#627—31no—
49C4×#627—61no—
50#63895—32no—
51#63894D311yescharacteristic
52#63868—32no—
53#63866D311yescharacteristic, complemented
54#63864—31no—
55#63863—31no—
56#63863—31no—
57#63863—31no—
58#63863—61no—
59#63862—32no—
60#63860—31no—
61#63859—32no—
62#63858—32no—
63#63858—32no—
64#63857—32no—
65#63855—32no—
66#63851—32no—
67#63848—32no—
68#63843—31no—
69#63843—31no—
70#63843—61no—
71#63843D311yescharacteristic, complemented
72#63841—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2312yes—
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C3×C4⋊(C3⋊D3)—22no—
82C3×#634—22no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×Dic6—22no—
88#6293—22no—
89C3×#624—24no—
90#5732—91no—
91#5568—91no—
92#5542—91no—
93C2×C32×Q8—31no—
94C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
95C2×#634—31no—
96C2×#634C2×D311yescharacteristic
97C2×C3×D12—31no—
98C2×C3×D12—31no—
99C2×C3×D12—61no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3—32no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—31no—
104C2×C3×Dic6—31no—
105C2×C3×Dic6—61no—
106C2×C3×Dic6C2×D311yescharacteristic
107C2×C3×Dic6C2×D311yescharacteristic
108C2×#627—31no—
109C2×#627—31no—
110C2×#627—61no—
111C2×#624C2×D312yes—
112C32×C4⋊C4—31no—
113C32×C42—31no—
114#3752—32no—
115#3752—32no—
116C4⋊(C3⋊Dic3)—31no—
117#3750—31no—
118#3750—31no—
119#3750—32no—
120C4×C3⋊Dic3—31no—
121C4×C3⋊Dic3—31no—
122C4×C3⋊Dic3—31no—
123C4×C3⋊Dic3—32no—
124C4×C3⋊Dic3—61no—
125C4×C3⋊Dic3—61no—
126C4×C3⋊Dic3—61no—
127C4×C3⋊Dic3—121no—
128C4×C3⋊Dic3C2×D311yescharacteristic
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—32no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3—32no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3—32no—
135C3×C4⋊Dic3C2×D311yescharacteristic
136C3×C4⋊Dic3C2×D311yescharacteristic
137C3×Dic3⋊C4—32no—
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×C4×Dic3—21no—
141C3×C4×Dic3—31no—
142C3×C4×Dic3—31no—
143C3×C4×Dic3—32no—
144C3×C4×Dic3—32no—
145C3×C4×Dic3—61no—
146C3×C4×Dic3C2×D311yescharacteristic
147C3×C4×Dic3C2×D311yescharacteristic
148#3724—31no—
149#3724—31no—
150#3724—61no—
151Dic3⋊Dic3—31no—
152Dic3⋊Dic3—32no—
153Dic3⋊Dic3—32no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156Dic3⋊Dic3—31no—
157Dic3⋊Dic3—61no—
158Dic3⋊Dic3—62no—
159Dic3⋊Dic3—61no—
160Dic3⋊Dic3C2×D312yes—
161Dic3⋊Dic3C2×D312yes—
162Dic3⋊Dic3C2×D312yes—
163#3722—32no—
164#3722—32no—
165#3722C2×D312yes—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—62no—
175(C2×D3)⋊Dic3—62no—
176Dic32—32no—
177Dic32—32no—
178Dic32—62no—
179Dic32C2×D312yes—
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3—22no—
183C2×C3×C3⋊D3—22no—
184C33×C4#4112yes—
185C3⋊(C3⋊Dic3)—21no—
186C3⋊(C3⋊Dic3)—21no—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—21no—
190C32×Dic3—22no—
191C32×Dic3—22no—
192C32×Dic3—21no—
193C32×Dic3#4112yes—
194C3×C4⋊Q8—91no—
195C3×C4×Q8—91no—
196C3×C4×D4—91no—
197#947—91no—
198#947—91no—
199#947—91no—
200#947—181no—
201Q8×Dic3—31no—
202Q8×Dic3—91no—
203#944—31no—
204#936—91no—
205#936—91no—
206#926—92no—
207#924—92no—
208#898—92no—
209#898—92no—
210#898—92no—
211#897—92no—
212#896—92no—
213#893—31no—
214#892—92no—
215#887—31no—
216#887—91no—
217#887—91no—
218#887—181no—
219#879—92no—
220#879—92no—
221#876—92no—
222#875—91no—
223C4×D12—31no—
224#872—92no—
225#869—31no—
226C4×Dic6—91no—
227C4×Dic6—91no—
228C4×Dic6—91no—
229C4×Dic6—181no—
230C22×C3⋊D3C22×D312yes—
231C22×C3×D3—32no—
232C22×C3×D3—32no—
233C22×C3×D3—62no—
234C32×Q8—62no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—31no—
239C2×C32×C4—32no—
240C2×C32×C4—32no—
241C2×C32×C4—31no—
242C2×C32×C4—41no—
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246C2×C3⋊Dic3—31no—
247C2×C3⋊Dic3—31no—
248C2×C3⋊Dic3—31no—
249C2×C3⋊Dic3—31no—
250C2×C3⋊Dic3—31no—
251C2×C3⋊Dic3—31no—
252C2×C3⋊Dic3—61no—
253C2×C3⋊Dic3—61no—
254C2×C3⋊Dic3—61no—
255C2×C3⋊Dic3—61no—
256C2×C3⋊Dic3—61no—
257C2×C3⋊Dic3—61no—
258C2×C3⋊Dic3—121no—
259C2×C3⋊Dic3—121no—
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D311yescharacteristic
263C4⋊(C3⋊D3)—22no—
264#634—22no—
265#634—62no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—62no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3C22×D312yes—
280C2×C3×Dic3C22×D312yes—
281C2×C3×Dic3C22×D312yes—
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C3×D12—62no—
288C3×D12—62no—
289C3×D12—122no—
290C3×C4×D3—64no—
291C3×C4×D3—64no—
292C3×Dic6—22no—
293C3×Dic6—22no—
294C3×Dic6—42no—
295C3×Dic6—64no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298#627—64no—
299#627—62no—
300#627—62no—
301#624—24no—
302#556—271noSylow
303C2×C33C2×#4111yescharacteristic
304C2×C33C2×#4111yescharacteristic
305C2×C332−1+411yescharacteristic
306C3×C3⋊D3—42no—
307C2×C3×Q8—31no—
308C2×C3×Q8—31no—
309C2×C3×Q8—61no—
310C2×C3×Q8—91no—
311C2×C3×D4—91no—
312C22×C3×C4—92no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×C4×D3—32no—
317C2×C4×D3—32no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—61no—
321C2×Dic6—91no—
322C2×Dic6—91no—
323C2×Dic6—91no—
324C2×Dic6—181no—
325C2×Dic6D3211yescharacteristic
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—92no—
330C3×C4⋊C4—92no—
331C3×C4⋊C4—92no—
332C3×C22⋊C4—92no—
333C3×C42—31no—
334C3×C42—31no—
335C3×C42—61no—
336C3×C42—92no—
337C3×C42—91no—
338#217—92no—
339#217—92no—
340#217—92no—
341#217—92no—
342(C2×D3)⋊C4—32no—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4—92no—
345(C2×D3)⋊C4—92no—
346(C2×D3)⋊C4—92no—
347(C2×D3)⋊C4—92no—
348(C2×D3)⋊C4—92no—
349(C2×D3)⋊C4—92no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—92no—
352(C2×D3)⋊C4—182no—
353(C2×D3)⋊C4—182no—
354C4⋊Dic3—32no—
355C4⋊Dic3—32no—
356C4⋊Dic3—32no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359C4⋊Dic3—91no—
360C4⋊Dic3—92no—
361C4⋊Dic3—181no—
362C4⋊Dic3D3211yescharacteristic
363Dic3⋊C4—32no—
364Dic3⋊C4—32no—
365Dic3⋊C4—32no—
366Dic3⋊C4—91no—
367Dic3⋊C4—91no—
368Dic3⋊C4—91no—
369Dic3⋊C4—91no—
370Dic3⋊C4—92no—
371Dic3⋊C4—92no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—181no—
375Dic3⋊C4—181no—
376Dic3⋊C4—182no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—32no—
380C4×Dic3—32no—
381C4×Dic3—61no—
382C4×Dic3—92no—
383C4×Dic3—92no—
384C4×Dic3—91no—
385C4×Dic3—91no—
386C4×Dic3—91no—
387C4×Dic3—92no—
388C4×Dic3—182no—
389C4×Dic3—181no—
390C4×Dic3—181no—
391C4×Dic3—181no—
392C4×Dic3—361no—
393C4×Dic3D3211yescharacteristic
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—41no—
398C22×C32C23×D311yescharacteristic
399C22×C32C23×D311yescharacteristic
400C22×C32C23×D311yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—22no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—62no—
408C2×C3×D3—62no—
409C2×C3×D3—62no—
410C2×C3×D3—122no—
411C2×C3×D3—122no—
412C2×C3×D3—122no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—22no—
416C32×C4—32no—
417C32×C4—42no—
418C32×C4—62no—
419C32×C4—62no—
420C32×C4—61no—
421C32×C4#23512yes—
422C32×C4#23512yes—
423C32×C4#23712yes—
424C3⋊Dic3—22no—
425C3⋊Dic3—21no—
426C3⋊Dic3—21no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3⋊Dic3—62no—
430C3⋊Dic3—62no—
431C3⋊Dic3—61no—
432C3⋊Dic3—61no—
433C3⋊Dic3—61no—
434C3⋊Dic3—61no—
435C3⋊Dic3—121no—
436C3⋊Dic3—121no—
437C3⋊Dic3—121no—
438C3⋊Dic3—121no—
439C3⋊Dic3—122no—
440C3⋊Dic3—122no—
441C3×Dic3—22no—
442C3×Dic3—22no—
443C3×Dic3—22no—
444C3×Dic3—21no—
445C3×Dic3—22no—
446C3×Dic3—21no—
447C3×Dic3—22no—
448C3×Dic3—42no—
449C3×Dic3—41no—
450C3×Dic3—42no—
451C3×Dic3—62no—
452C3×Dic3—64no—
453C3×Dic3—62no—
454C3×Dic3—62no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3—121no—
460C3×Dic3#23712yes—
461C3×Dic3#23912yes—
462C4⋊Q8—91no—
463#126—272no—
464#126—272no—
465#124—271no—
466#124—271no—
467C22⋊Q8—272no—
468C4×Q8—91no—
469C4×Q8—271no—
470C4×Q8—271no—
471C4×D4—91no—
472#117—272no—
473C33#55611yescharacteristic, complemented, Sylow
474C23×C3—92no—
475C22×D3—32no—
476C22×D3—32no—
477C22×D3—62no—
478C3×Q8—62no—
479C3×Q8—62no—
480C3×Q8—122no—
481C3×Q8—182no—
482C3×D4—182no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—41no—
495C2×C3×C4—61no—
496C2×C3×C4—62no—
497C2×C3×C4—61no—
498C2×C3×C4—62no—
499C2×C3×C4—92no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—184no—
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505C2×C3×C4C2×D3211yescharacteristic
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—61no—
513C2×Dic3—62no—
514C2×Dic3—61no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—181no—
522C2×Dic3—181no—
523C2×Dic3—181no—
524C2×Dic3—181no—
525C2×Dic3—181no—
526C2×Dic3—181no—
527C2×Dic3—361no—
528C2×Dic3—361no—
529C2×Dic3C2×D3212yes—
530C2×Dic3C2×D3212yes—
531C2×Dic3C2×D3211yescharacteristic
532C2×Dic3C2×D3211yescharacteristic
533D12—62no—
534D12—62no—
535D12—122no—
536C4×D3—64no—
537C4×D3—64no—
538Dic6—22no—
539Dic6—64no—
540Dic6—62no—
541Dic6—62no—
542Dic6—182no—
543Dic6—182no—
544Dic6—184no—
545Dic6—182no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—41no—
556C2×C32—41no—
557C2×C32—41no—
558C2×C32C2×#23511yescharacteristic
559C2×C32C2×#23511yescharacteristic
560C2×C32C2×#23711yescharacteristic
561C2×C32C2×#23711yescharacteristic
562C2×C32C2×#23911yescharacteristic
563C2×C32#100711yescharacteristic
564C2×C32#100711yescharacteristic
565C2×C32D3×#4111yescharacteristic
566C2×C32#101011yescharacteristic
567C3⋊D3—42no—
568C3×D3—122no—
569C3×D3—122no—
570C3×D3—242no—
571C2×Q8—31no—
572C2×Q8—91no—
573C2×Q8—271no—
574C2×D4—91no—
575C22×C4—92no—
576C4⋊C4—31no—
577C4⋊C4—92no—
578C4⋊C4—92no—
579C4⋊C4—92no—
580C4⋊C4—271no—
581C4⋊C4—272no—
582C4⋊C4—271no—
583C4⋊C4—271no—
584C22⋊C4—92no—
585C22⋊C4—272no—
586C22⋊C4—272no—
587C22⋊C4—272no—
588C22⋊C4—272no—
589C42—31no—
590C42—92no—
591C42—91no—
592C42—272no—
593C42—271no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—41no—
598C22×C3—182no—
599C22×C3—182no—
600C22×C3—182no—
601C22×C3C22×D3211yescharacteristic
602C22×C3C22×D3211yescharacteristic
603C22×C3C22×D3211yescharacteristic
604C2×D3—62no—
605C2×D3—62no—
606C2×D3—62no—
607C2×D3—62no—
608C2×D3—62no—
609C2×D3—62no—
610C2×D3—122no—
611C2×D3—122no—
612C2×D3—122no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—32no—
617C3×C4—32no—
618C3×C4—42no—
619C3×C4—62no—
620C3×C4—62no—
621C3×C4—62no—
622C3×C4—62no—
623C3×C4—61no—
624C3×C4—61no—
625C3×C4—62no—
626C3×C4—122no—
627C3×C4—122no—
628C3×C4—121no—
629C3×C4—181no—
630C3×C4—181no—
631C3×C4—182no—
632C3×C4#379512yes—
633C3×C4#379812yes—
634C3×C4#380412yes—
635Dic3—21no—
636Dic3—22no—
637Dic3—22no—
638Dic3—64no—
639Dic3—62no—
640Dic3—62no—
641Dic3—61no—
642Dic3—61no—
643Dic3—61no—
644Dic3—61no—
645Dic3—62no—
646Dic3—121no—
647Dic3—182no—
648Dic3—182no—
649Dic3—181no—
650Dic3—181no—
651Dic3—181no—
652Dic3—181no—
653Dic3—181no—
654Dic3—181no—
655Dic3—361no—
656Dic3—361no—
657Dic3—361no—
658Dic3—361no—
659Dic3—362no—
660Dic3—362no—
661Dic3#379612yes—
662C32—21no—
663C32—21no—
664C32—21no—
665C32—41no—
666C32#554211yescharacteristic, complemented
667C32#556811yescharacteristic, complemented
668C32#573211yescharacteristic, complemented
669C23—92no—
670Q8—62no—
671Q8—182no—
672Q8—542no—
673D4—182no—
674C2×C4—31no—
675C2×C4—31no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—91no—
679C2×C4—91no—
680C2×C4—92no—
681C2×C4—184no—
682C2×C4—271no—
683C2×C4—271no—
684C2×C4D3311yescharacteristic
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—41no—
697C2×C3—362no—
698C2×C3C2×#379511yescharacteristic
699C2×C3C2×#379611yescharacteristic
700C2×C3#6429711yescharacteristic
701C2×C3C2×#379811yescharacteristic
702C2×C3D3×#23711yescharacteristic
703C2×C3#6431511yescharacteristic
704C2×C3#6431611yescharacteristic
705C2×C3D3×#23911yescharacteristic
706C2×C3C2×#380411yescharacteristic
707D3—122no—
708D3—122no—
709D3—242no—
710C22—182no—
711C22—182no—
712C22—182no—
713C22C2×D3311yescharacteristic
714C4—32no—
715C4—62no—
716C4—61no—
717C4—62no—
718C4—181no—
719C4—181no—
720C4—182no—
721C4—541no—
722C4—541no—
723C4#8896012yes—
724C3—21no—
725C3—21no—
726C3—21no—
727C3—41no—
728C3#1059386311yescharacteristic, complemented
729C3#1059433511yescharacteristic, complemented
730C3#1059538711yescharacteristic, complemented
731C2—362no—
732C2D3×#379611yescharacteristic
733C2#1172439711yescharacteristic
734C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×C4⋊(C3⋊D3)C22
hypercenterC2×C4D33
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6293C2semidirect
4. #11723410C2semidirect
6. C3×#63866C2semidirect
7. C3×#63843C2semidirect
8. #11723025C2semidirect
9. #11723024C2semidirect
10. #11722972C2semidirect
11. #11722915C2semidirect
53. #63866D3semidirect
71. #63843D3semidirect
473. C33#556semidirect
666. C32#5542semidirect
667. C32#5568semidirect
668. C32#5732semidirect
728. C3#10593863semidirect
729. C3#10594335semidirect
730. C3#10595387semidirect

Maximal subgroups

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

subgroupindex
#117236772
C4×#62932
#117234362
#117234102
C3×#638942
C3×#638662
C3×#638432
#117230252
#117230242
#117229722
#117229152
#105953873
#105943353
#105938633