Finite Group Databasebeta

← #13168345

Subgroups — #13168345

Order 1728.

1126 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723674C211yesmaximal, characteristic
2#11723534C211yesmaximal, characteristic, complemented
3#11723435C211yesmaximal, characteristic
4Dic3×#634C211yesmaximal, characteristic, complemented
5C3×C4×#624C211yesmaximal, characteristic
6C3×#63866C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11723012C212yesmaximal, complemented
9#11722972C212yesmaximal
10#11722942C212yesmaximal, complemented
11#11722915C212yesmaximal
12#10595374—31nomaximal
13#10593873—31nomaximal
14#10593859—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6293C2212yes—
19C2×C3×#624C2211yescharacteristic
20C2×C3×#624C2211yescharacteristic
21C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C32×C4×Dic3C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25#88815C2212yes—
26#88814C2212yes—
27#88807C2212yes—
28#88806C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30#88803C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic32C2211yescharacteristic
36C3×Dic32C2212yes—
37C3×Dic32C2211yescharacteristic
38#64155—31no—
39#64078—31no—
40C4×#634—31no—
41C3×Q8×Dic3—31no—
42C3×#944—31no—
43C3×C42×D3—31no—
44C3×C42×D3—31no—
45C3×#869—31no—
46C3×C4×Dic6—31no—
47#63918—31no—
48#63918—31no—
49#63918—61no—
50C4×#627—32no—
51#63895—32no—
52C4×#624D311yescharacteristic
53#63871—31no—
54#63869—32no—
55#63867—32no—
56#63866D311yescharacteristic, complemented
57#63857—31no—
58#63857—32no—
59#63856—31no—
60#63856—31no—
61#63856—31no—
62#63856—61no—
63#63855—32no—
64#63851—32no—
65#63846—32no—
66#63844—32no—
67Dic3×Dic6—31no—
68Dic3×Dic6—31no—
69Dic3×Dic6—61no—
70Dic3×Dic6D311yescharacteristic, complemented
71#63841—32no—
72#63837—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2312yes—
77C2×C3×C3⋊Dic3C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C3×C4×C3⋊D3—22no—
81C3×#634—22no—
82C2×C32×Dic3C2311yescharacteristic
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×Dic6—22no—
88#6293—24no—
89C3×#624—22no—
90C3×#624Q814yescomplemented
91#5728—91no—
92#5578—91no—
93#5470—91no—
94C2×C32×Q8—31no—
95C2×C4×C3⋊D3C2×D311yescharacteristic
96C2×#634—32no—
97C2×#634C2×D311yescharacteristic
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—61no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6—31no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—61no—
109C2×C3×Dic6C2×D311yescharacteristic
110C2×C3×Dic6C2×D311yescharacteristic
111C2×#627—32no—
112C2×#627—32no—
113C2×#627—62no—
114C2×#624C2×D311yescharacteristic
115C2×#624C2×D311yescharacteristic
116C32×C42—31no—
117C32×C42—31no—
118#3752—32no—
119C4⋊(C3⋊Dic3)—31no—
120C4⋊(C3⋊Dic3)—31no—
121C4⋊(C3⋊Dic3)—31no—
122C4⋊(C3⋊Dic3)—32no—
123C4⋊(C3⋊Dic3)—61no—
124C4⋊(C3⋊Dic3)—61no—
125C4⋊(C3⋊Dic3)—61no—
126C4⋊(C3⋊Dic3)—121no—
127C4⋊(C3⋊Dic3)C2×D311yescharacteristic
128#3750—32no—
129#3750—32no—
130C4×C3⋊Dic3—32no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3—32no—
135C3×C4⋊Dic3—32no—
136C3×C4⋊Dic3—61no—
137C3×Dic3⋊C4—32no—
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×C4×Dic3—21no—
141C3×C4×Dic3—21no—
142C3×C4×Dic3—32no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—32no—
145C3×C4×Dic3—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3C2×D311yescharacteristic
149C3×C4×Dic3C2×D311yescharacteristic
150C3×C4×Dic3C2×D311yescharacteristic
151C3×C4×Dic3C2×D311yescharacteristic
152#3724—32no—
153#3724—32no—
154#3724—32no—
155#3724—62no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—62no—
163Dic3⋊Dic3—62no—
164Dic3⋊Dic3C2×D312yes—
165Dic3⋊Dic3C2×D312yes—
166Dic3⋊Dic3C2×D312yes—
167#3722—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—62no—
173Dic32—32no—
174Dic32—32no—
175Dic32—62no—
176Dic32C2×D311yescharacteristic
177Dic32C2×D312yes—
178Dic32C2×D311yescharacteristic
179C22×C33C2411yescharacteristic
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3C2×Q812yes—
183C33×C4#4112yes—
184C3⋊(C3⋊Dic3)—22no—
185C3×C3⋊Dic3—22no—
186C3×C3⋊Dic3—22no—
187C3×C3⋊Dic3—21no—
188C32×Dic3—21no—
189C32×Dic3—22no—
190C32×Dic3C2×Q812yes—
191C32×Dic3C2×Q812yes—
192C32×Dic3#4112yes—
193C3×C4⋊Q8—91no—
194C3×C4×Q8—91no—
195C2×C3×C42—91no—
196#946—91no—
197#946—91no—
198#946—91no—
199#946—181no—
200Q8×Dic3—31no—
201Q8×Dic3—91no—
202#944—31no—
203#926—92no—
204#924—92no—
205#924—91no—
206#924—91no—
207#897—92no—
208#897—91no—
209#896—92no—
210#892—92no—
211#890—92no—
212#889—92no—
213#888—91no—
214#887—92no—
215#872—92no—
216C42×D3—31no—
217C42×D3—31no—
218#870—92no—
219#869—31no—
220#869—91no—
221#869—91no—
222#869—181no—
223C4×Dic6—31no—
224C4×Dic6—92no—
225C4×Dic6—92no—
226C4×Dic6—91no—
227C4×Dic6—91no—
228C4×Dic6—181no—
229C22×C3⋊D3C22×D311yescharacteristic
230C22×C3×D3—31no—
231C22×C3×D3—31no—
232C22×C3×D3—61no—
233C32×Q8—62no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—31no—
238C2×C32×C4—31no—
239C2×C32×C4—31no—
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—32no—
247C2×C3⋊Dic3—32no—
248C2×C3⋊Dic3—32no—
249C2×C3⋊Dic3—62no—
250C2×C3⋊Dic3—62no—
251C2×C3⋊Dic3—62no—
252C2×C3⋊Dic3—122no—
253C2×C3⋊Dic3C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D312yes—
255C2×C3⋊Dic3C22×D312yes—
256C4×C3⋊D3—22no—
257#634—22no—
258#634—64no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3C22×D312yes—
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D312yes—
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C3×C4×D3—34no—
284C3×C4×D3—34no—
285C3×C4×D3—62no—
286C3×C4×D3—62no—
287C3×C4×D3—62no—
288C3×C4×D3—62no—
289C3×C4×D3—122no—
290C3×Dic6—22no—
291C3×Dic6—22no—
292C3×Dic6—42no—
293C3×Dic6—64no—
294C3×Dic6—62no—
295C3×Dic6—62no—
296#627—64no—
297#627—64no—
298#627—124no—
299#624—22no—
300#624Dic614yescomplemented
301#533—271noSylow
302C2×C33C22×Q811yescharacteristic
303C2×C33C2×#4111yescharacteristic
304C2×C33C2×#4111yescharacteristic
305C3×C3⋊D3—22no—
306C2×C3×Q8—31no—
307C2×C3×Q8—31no—
308C2×C3×Q8—61no—
309C2×C3×Q8—91no—
310C22×C3×C4—91no—
311C22×C3×C4—91no—
312C22×C3×C4—91no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—61no—
323C2×Dic6—92no—
324C2×Dic6—92no—
325C2×Dic6—92no—
326C2×Dic6—182no—
327C2×Dic6D3211yescharacteristic
328C3×C4⋊C4—92no—
329C3×C4⋊C4—92no—
330C3×C4⋊C4—92no—
331C3×C4⋊C4—91no—
332C3×C42—31no—
333C3×C42—31no—
334C3×C42—31no—
335C3×C42—31no—
336C3×C42—61no—
337C3×C42—61no—
338C3×C42—91no—
339C3×C42—92no—
340C3×C42—91no—
341#217—92no—
342#217—92no—
343(C2×D3)⋊C4—92no—
344(C2×D3)⋊C4—92no—
345(C2×D3)⋊C4—92no—
346(C2×D3)⋊C4—92no—
347(C2×D3)⋊C4—182no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—32no—
351C4⋊Dic3—32no—
352C4⋊Dic3—32no—
353C4⋊Dic3—61no—
354C4⋊Dic3—92no—
355C4⋊Dic3—92no—
356C4⋊Dic3—92no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359C4⋊Dic3—91no—
360C4⋊Dic3—92no—
361C4⋊Dic3—182no—
362C4⋊Dic3—181no—
363C4⋊Dic3—181no—
364C4⋊Dic3—181no—
365C4⋊Dic3—361no—
366Dic3⋊C4—32no—
367Dic3⋊C4—32no—
368Dic3⋊C4—32no—
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—32no—
380C4×Dic3—31no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—32no—
385C4×Dic3—92no—
386C4×Dic3—92no—
387C4×Dic3—92no—
388C4×Dic3—182no—
389C4×Dic3D3211yescharacteristic
390C4×Dic3D3211yescharacteristic
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—41no—
395C22×C32C23×D311yescharacteristic
396C22×C32C23×D311yescharacteristic
397C22×C32C23×D311yescharacteristic
398C2×C3⋊D3—21no—
399C2×C3⋊D3—21no—
400C2×C3⋊D3C2×Dic612yes—
401C2×C3×D3—32no—
402C2×C3×D3—32no—
403C2×C3×D3—62no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3—61no—
407C2×C3×D3—61no—
408C2×C3×D3—121no—
409C2×C3×D3—121no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—32no—
414C32×C4—32no—
415C32×C4—32no—
416C32×C4—42no—
417C32×C4—62no—
418C32×C4—61no—
419C32×C4#23512yes—
420C32×C4#23512yes—
421C32×C4#23712yes—
422C3⋊Dic3—22no—
423C3⋊Dic3—21no—
424C3⋊Dic3—22no—
425C3⋊Dic3—62no—
426C3⋊Dic3—62no—
427C3⋊Dic3—62no—
428C3⋊Dic3—122no—
429C3⋊Dic3—122no—
430C3⋊Dic3—122no—
431C3⋊Dic3—242no—
432C3×Dic3—21no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—21no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—42no—
440C3×Dic3—41no—
441C3×Dic3—64no—
442C3×Dic3—62no—
443C3×Dic3—62no—
444C3×Dic3—62no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C3×Dic3—62no—
448C3×Dic3—122no—
449C3×Dic3—121no—
450C3×Dic3C2×Dic612yes—
451C3×Dic3C2×Dic612yes—
452C3×Dic3#23512yes—
453C3×Dic3D3×Q812yes—
454C3×Dic3D3×Q812yes—
455C3×Dic3#23912yes—
456C4⋊Q8—91no—
457C4⋊Q8—271no—
458#125—272no—
459C22⋊Q8—272no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462C4×Q8—91no—
463C4×Q8—271no—
464C4×Q8—272no—
465#117—272no—
466C2×C42—91no—
467C33#53311yescharacteristic, complemented, Sylow
468C23×C3—91no—
469C22×D3—31no—
470C22×D3—31no—
471C22×D3—61no—
472C3×Q8—62no—
473C3×Q8—62no—
474C3×Q8—122no—
475C3×Q8—182no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—32no—
487C2×C3×C4—31no—
488C2×C3×C4—32no—
489C2×C3×C4—41no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—62no—
495C2×C3×C4—94no—
496C2×C3×C4—92no—
497C2×C3×C4—91no—
498C2×C3×C4—92no—
499C2×C3×C4—182no—
500C2×C3×C4—182no—
501C2×C3×C4C2×D3211yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—32no—
509C2×Dic3—32no—
510C2×Dic3—62no—
511C2×Dic3—61no—
512C2×Dic3—62no—
513C2×Dic3—92no—
514C2×Dic3—92no—
515C2×Dic3—92no—
516C2×Dic3—182no—
517C2×Dic3—182no—
518C2×Dic3—182no—
519C2×Dic3—362no—
520C2×Dic3C2×D3211yescharacteristic
521C2×Dic3C2×D3212yes—
522C2×Dic3C2×D3211yescharacteristic
523C2×Dic3C2×D3211yescharacteristic
524C2×Dic3C2×D3211yescharacteristic
525C4×D3—34no—
526C4×D3—34no—
527C4×D3—62no—
528C4×D3—62no—
529C4×D3—62no—
530C4×D3—62no—
531C4×D3—122no—
532Dic6—22no—
533Dic6—64no—
534Dic6—62no—
535Dic6—62no—
536Dic6—184no—
537Dic6—184no—
538Dic6—184no—
539Dic6—364no—
540C2×C32—21no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—41no—
550C2×C32—41no—
551C2×C32—41no—
552C2×C32C22×Dic611yescharacteristic
553C2×C32C2×#23511yescharacteristic
554C2×C32C2×#23511yescharacteristic
555C2×C32C2×#23511yescharacteristic
556C2×C32C2×#23711yescharacteristic
557C2×C32C2×D3×Q811yescharacteristic
558C2×C32C2×D3×Q811yescharacteristic
559C2×C32C2×#23911yescharacteristic
560C2×C32D3×#4111yescharacteristic
561C3⋊D3—22no—
562C3×D3—62no—
563C3×D3—62no—
564C3×D3—122no—
565C2×Q8—31no—
566C2×Q8—91no—
567C2×Q8—272no—
568C22×C4—91no—
569C22×C4—91no—
570C22×C4—91no—
571C4⋊C4—92no—
572C4⋊C4—92no—
573C4⋊C4—92no—
574C4⋊C4—91no—
575C4⋊C4—272no—
576C4⋊C4—272no—
577C4⋊C4—272no—
578C4⋊C4—272no—
579C4⋊C4—271no—
580C22⋊C4—272no—
581C22⋊C4—272no—
582C42—31no—
583C42—31no—
584C42—91no—
585C42—91no—
586C42—92no—
587C42—272no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—41no—
592C22×C3—92no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3C22×D3211yescharacteristic
596C22×C3C22×D3211yescharacteristic
597C22×C3C22×D3211yescharacteristic
598C2×D3—32no—
599C2×D3—32no—
600C2×D3—62no—
601C2×D3—61no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—61no—
605C2×D3—121no—
606C2×D3—121no—
607C3×C4—22no—
608C3×C4—22no—
609C3×C4—22no—
610C3×C4—32no—
611C3×C4—32no—
612C3×C4—32no—
613C3×C4—32no—
614C3×C4—32no—
615C3×C4—32no—
616C3×C4—42no—
617C3×C4—62no—
618C3×C4—62no—
619C3×C4—62no—
620C3×C4—62no—
621C3×C4—62no—
622C3×C4—61no—
623C3×C4—61no—
624C3×C4—122no—
625C3×C4—121no—
626C3×C4—182no—
627C3×C4—182no—
628C3×C4—181no—
629C3×C4#379512yes—
630C3×C4#379812yes—
631C3×C4#380412yes—
632Dic3—21no—
633Dic3—22no—
634Dic3—64no—
635Dic3—62no—
636Dic3—61no—
637Dic3—61no—
638Dic3—62no—
639Dic3—62no—
640Dic3—62no—
641Dic3—122no—
642Dic3—121no—
643Dic3—182no—
644Dic3—182no—
645Dic3—182no—
646Dic3—362no—
647Dic3—362no—
648Dic3—362no—
649Dic3—722no—
650Dic3D3×Dic612yes—
651Dic3D3×Dic612yes—
652Dic3#379912yes—
653C32—21no—
654C32—21no—
655C32—21no—
656C32—41no—
657C32#547011yescharacteristic, complemented
658C32#557811yescharacteristic, complemented
659C32#572811yescharacteristic, complemented
660C23—91no—
661Q8—62no—
662Q8—182no—
663Q8—544no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—32no—
669C2×C4—94no—
670C2×C4—91no—
671C2×C4—92no—
672C2×C4—92no—
673C2×C4—182no—
674C2×C4—182no—
675C2×C4—272no—
676C2×C4D3311yescharacteristic
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—41no—
687C2×C3—41no—
688C2×C3—41no—
689C2×C3—182no—
690C2×C3C2×D3×Dic611yescharacteristic
691C2×C3C2×D3×Dic611yescharacteristic
692C2×C3C2×#379511yescharacteristic
693C2×C3C2×#379811yescharacteristic
694C2×C3C2×#379911yescharacteristic
695C2×C3D3×#23511yescharacteristic
696C2×C3D32×Q811yescharacteristic
697C2×C3D3×#23911yescharacteristic
698C2×C3C2×#380411yescharacteristic
699D3—62no—
700D3—62no—
701D3—122no—
702C22—92no—
703C22—181no—
704C22—181no—
705C22C2×D3311yescharacteristic
706C4—32no—
707C4—32no—
708C4—32no—
709C4—61no—
710C4—62no—
711C4—182no—
712C4—181no—
713C4—182no—
714C4—542no—
715C4#8896012yes—
716C3—21no—
717C3—21no—
718C3—21no—
719C3—41no—
720C3#1059385911yescharacteristic, complemented
721C3#1059387311yescharacteristic, complemented
722C3#1059537411yescharacteristic, complemented
723C2—182no—
724C2D32×Dic611yescharacteristic
725C2D3×#379911yescharacteristic
726C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×C3⋊D3C23
hypercenterC2×C4D33
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723534C2semidirect
4. Dic3×#634C2semidirect
6. C3×#63866C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11723012C2semidirect
10. #11722942C2semidirect
56. #63866D3semidirect
70. Dic3×Dic6D3semidirect
90. C3×#624Q8semidirect
300. #624Dic6semidirect
467. C33#533semidirect
657. C32#5470semidirect
658. C32#5578semidirect
659. C32#5728semidirect
720. C3#10593859semidirect
721. C3#10593873semidirect
722. C3#10595374semidirect

Maximal subgroups

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

subgroupindex
#117236742
#117235342
#117234352
Dic3×#6342
C3×C4×#6242
C3×#638662
C3×Dic3×Dic62
#117230122
#117229722
#117229422
#117229152
#105953743
#105938733
#105938593