Finite Group Databasebeta

← #13178315

Subgroups — #13178315

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
1C3×#64106C211yesmaximal, characteristic
2C3×#64097C211yesmaximal, characteristic, complemented
3C3×#64096C211yesmaximal, characteristic, complemented
4#11723688C212yesmaximal
5#11723683C212yesmaximal
6C4×#6294C211yesmaximal, characteristic
7#11723678C211yesmaximal, characteristic, complemented
8#11723674C211yesmaximal, characteristic
9#11723669C212yesmaximal, complemented
10#11723668C211yesmaximal, characteristic, complemented
11#11723668C212yesmaximal, complemented
12#10594397—31nomaximal
13#10594387—31nomaximal
14#10594385—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C3×#634C2212yes—
18C2×C3×#634C2211yescharacteristic
19C2×#6294C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C33×C4⋊C4C2211yescharacteristic
22C3×#3752C2212yes—
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4⋊(C3⋊Dic3)C2212yes—
25C3×#3750C2212yes—
26C3×#3750C2212yes—
27C3×C4×C3⋊Dic3C2211yescharacteristic
28C3×C4×C3⋊Dic3C2212yes—
29C3×C4×C3⋊Dic3C2211yescharacteristic
30#88815C2212yes—
31#88815C2212yes—
32#88815C2212yes—
33#88815C2212yes—
34#88814C2212yes—
35#88813C2211yescharacteristic
36#88813C2212yes—
37#88813C2211yescharacteristic
38#64106D311yescharacteristic
39#64097D311yescharacteristic, complemented
40#64096D311yescharacteristic, complemented
41C3×#897—31no—
42C3×#897—31no—
43C3×#897—61no—
44C3×#888—31no—
45C3×#888—31no—
46C3×#888—61no—
47C3×#887—31no—
48C3×#887—31no—
49C3×#887—61no—
50#63896—32no—
51#63888—32no—
52#63887—32no—
53C4×#624—31no—
54#63878—32no—
55#63877—32no—
56C4×D3×Dic3—31no—
57C4×D3×Dic3—31no—
58#63873—31no—
59#63871—31no—
60#63866—31no—
61#63866—31no—
62#63857—31no—
63#63856—31no—
64#63847—32no—
65#63846—32no—
66#63845—32no—
67#63844—32no—
68#63844—31no—
69#63843—31no—
70#63843—32no—
71Dic3×Dic6—31no—
72Dic3×Dic6—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4×C3⋊D3—22no—
86C3×#634—22no—
87C3×#634—22no—
88C3×#634—24no—
89#6294—22no—
90#6294Q814yescomplemented
91#5728—91no—
92#5622—91no—
93#5578—91no—
94C2×C4×C3⋊D3C2×D311yescharacteristic
95C2×#634C2×D311yescharacteristic
96C2×#634C2×D312yes—
97C2×#634C2×D311yescharacteristic
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—61no—
101C2×C3×Dic6—31no—
102C2×C3×Dic6—31no—
103C2×C3×Dic6—32no—
104C2×C3×Dic6—32no—
105C2×C3×Dic6—31no—
106C2×C3×Dic6—31no—
107C2×C3×Dic6—61no—
108C2×C3×Dic6—62no—
109C2×C3×Dic6—61no—
110C2×#624—31no—
111C2×#624—31no—
112C2×D3×Dic3—31no—
113C2×D3×Dic3—31no—
114C2×D3×Dic3—31no—
115C2×D3×Dic3—31no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4—21no—
118C32×C4⋊C4—21no—
119C32×C4⋊C4—41no—
120C32×C4⋊C4C2×D311yescharacteristic
121C32×C4⋊C4C2×D311yescharacteristic
122C32×C4⋊C4C2×D311yescharacteristic
123#3752C2×D312yes—
124C4⋊(C3⋊Dic3)C2×D311yescharacteristic
125C4⋊(C3⋊Dic3)C2×D312yes—
126#3750C2×D312yes—
127#3750C2×D312yes—
128C4×C3⋊Dic3C2×D311yescharacteristic
129C4×C3⋊Dic3C2×D312yes—
130C4×C3⋊Dic3C2×D311yescharacteristic
131C3×(C2×D3)⋊C4—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—62no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—32no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—61no—
139C3×C4⋊Dic3—62no—
140C3×Dic3⋊C4—32no—
141C3×Dic3⋊C4—32no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—62no—
145C3×Dic3⋊C4—62no—
146C3×C4×Dic3—32no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—32no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—62no—
153C3×C4×Dic3—61no—
154C3×C4×Dic3—61no—
155#3724—32no—
156#3724—32no—
157#3724—32no—
158#3724—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167#3722—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170Dic32—32no—
171Dic32—31no—
172Dic32—32no—
173Dic32—31no—
174Dic32—32no—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178Dic32—31no—
179C22×C33C2411yescharacteristic
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3C2×Q812yes—
183C33×C4—22no—
184C33×C4#4112yes—
185C3×C3⋊Dic3—22no—
186C3×C3⋊Dic3—21no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3C2×Q812yes—
191C3×C3⋊Dic3C2×Q812yes—
192C3×C3⋊Dic3#4112yes—
193C3×C4⋊Q8—91no—
194C3×C22⋊Q8—91no—
195C3×C4×Q8—91no—
196#946—92no—
197#946—91no—
198Q8×Dic3—92no—
199Q8×Dic3—91no—
200#944—91no—
201#944—91no—
202#924—91no—
203C2×C4×Dic3—91no—
204#897—31no—
205#897—31no—
206#897—61no—
207#897—91no—
208#896—92no—
209#892—92no—
210#890—92no—
211#889—92no—
212#889—92no—
213#888—31no—
214#888—31no—
215#888—61no—
216#887—31no—
217#887—31no—
218#887—61no—
219#887—91no—
220#887—92no—
221#878—92no—
222#877—92no—
223#872—92no—
224C42×D3—91no—
225C42×D3—91no—
226#869—91no—
227C4×Dic6—92no—
228C4×Dic6—91no—
229C22×C3⋊D3C22×D311yescharacteristic
230C22×C3×D3—31no—
231C22×C3×D3—31no—
232C22×C3×D3—61no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—22no—
237C2×C32×C4—22no—
238C2×C32×C4—22no—
239C2×C32×C4—41no—
240C2×C32×C4—42no—
241C2×C32×C4C22×D312yes—
242C2×C32×C4C22×D312yes—
243C2×C32×C4C22×D312yes—
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C3⋊Dic3C22×D311yescharacteristic
248C2×C3⋊Dic3C22×D312yes—
249C2×C3⋊Dic3C22×D312yes—
250C2×C3⋊Dic3C22×D311yescharacteristic
251C2×C3⋊Dic3C22×D312yes—
252C2×C3⋊Dic3C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D311yescharacteristic
255C4×C3⋊D3—22no—
256#634—22no—
257#634—22no—
258#634—24no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—62no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—62no—
283C3×C4×D3—62no—
284C3×C4×D3—62no—
285C3×C4×D3—122no—
286C3×Dic6—64no—
287C3×Dic6—64no—
288C3×Dic6—64no—
289C3×Dic6—62no—
290C3×Dic6—62no—
291C3×Dic6—62no—
292C3×Dic6—62no—
293C3×Dic6—124no—
294C3×Dic6—122no—
295#624—34no—
296#624—62no—
297D3×Dic3—34no—
298D3×Dic3—34no—
299D3×Dic3—62no—
300D3×Dic3—62no—
301#533—271noSylow
302C2×C33C22×Q811yescharacteristic
303C2×C33C2×#4111yescharacteristic
304C2×C33C2×#4111yescharacteristic
305C3×C3⋊D3—22no—
306C2×C3×Q8—91no—
307C2×C3×Q8—91no—
308C2×C3×Q8—92no—
309C22×C3×C4—91no—
310C22×Dic3—91no—
311C22×Dic3—91no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—61no—
315C2×C4×D3—91no—
316C2×C4×D3—91no—
317C2×C4×D3—91no—
318C2×C4×D3—91no—
319C2×Dic6—32no—
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—32no—
324C2×Dic6—31no—
325C2×Dic6—61no—
326C2×Dic6—62no—
327C2×Dic6—61no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—41no—
332C3×C4⋊C4—92no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—92no—
335C3×C4⋊C4—92no—
336C3×C4⋊C4D3211yescharacteristic
337C3×C4⋊C4D3211yescharacteristic
338C3×C4⋊C4D3211yescharacteristic
339C3×C22⋊C4—92no—
340C3×C42—91no—
341C3×C42—92no—
342C3×C42—91no—
343#217—92no—
344(C2×D3)⋊C4—32no—
345(C2×D3)⋊C4—32no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—92no—
348(C2×D3)⋊C4—92no—
349C4⋊Dic3—31no—
350C4⋊Dic3—32no—
351C4⋊Dic3—31no—
352C4⋊Dic3—32no—
353C4⋊Dic3—61no—
354C4⋊Dic3—62no—
355C4⋊Dic3—92no—
356C4⋊Dic3—92no—
357C4⋊Dic3—92no—
358C4⋊Dic3—92no—
359Dic3⋊C4—32no—
360Dic3⋊C4—32no—
361Dic3⋊C4—32no—
362Dic3⋊C4—32no—
363Dic3⋊C4—62no—
364Dic3⋊C4—62no—
365Dic3⋊C4—92no—
366Dic3⋊C4—92no—
367Dic3⋊C4—92no—
368Dic3⋊C4—92no—
369Dic3⋊C4—92no—
370Dic3⋊C4—92no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—32no—
376C4×Dic3—32no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—61no—
380C4×Dic3—62no—
381C4×Dic3—61no—
382C4×Dic3—91no—
383C4×Dic3—92no—
384C4×Dic3—91no—
385C4×Dic3—91no—
386C4×Dic3—91no—
387C4×Dic3—92no—
388C4×Dic3—91no—
389C4×Dic3—92no—
390C4×Dic3—91no—
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⋊D3D3×Q812yes—
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—22no—
414C32×C4—22no—
415C32×C4—22no—
416C32×C4—42no—
417C32×C4—42no—
418C32×C4—42no—
419C32×C4—42no—
420C32×C4—82no—
421C32×C4#23512yes—
422C32×C4#23712yes—
423C32×C4#23912yes—
424C3⋊Dic3—22no—
425C3⋊Dic3—22no—
426C3⋊Dic3—22no—
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3#23712yes—
430C3⋊Dic3D3×Q812yes—
431C3⋊Dic3D3×Q812yes—
432C3×Dic3—32no—
433C3×Dic3—32no—
434C3×Dic3—32no—
435C3×Dic3—32no—
436C3×Dic3—32no—
437C3×Dic3—32no—
438C3×Dic3—62no—
439C3×Dic3—62no—
440C3×Dic3—62no—
441C3×Dic3—64no—
442C3×Dic3—62no—
443C3×Dic3—61no—
444C3×Dic3—61no—
445C3×Dic3—62no—
446C3×Dic3—62no—
447C3×Dic3—62no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—62no—
451C3×Dic3—62no—
452C3×Dic3—122no—
453C3×Dic3—122no—
454C3×Dic3—121no—
455C3×Dic3—121no—
456C4⋊Q8—91no—
457C4⋊Q8—271no—
458#125—272no—
459C22⋊Q8—91no—
460C22⋊Q8—272no—
461C22⋊Q8—271no—
462C4×Q8—91no—
463C4×Q8—271no—
464C4×Q8—272no—
465#117—272no—
466C2×C42—271no—
467C33#53311yescharacteristic, complemented, Sylow
468C23×C3—91no—
469C22×D3—31no—
470C22×D3—31no—
471C22×D3—61no—
472C3×Q8—184no—
473C3×Q8—182no—
474C3×Q8—182no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—41no—
482C2×C3×C4—42no—
483C2×C3×C4—91no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—91no—
487C2×C3×C4—92no—
488C2×C3×C4—91no—
489C2×C3×C4—92no—
490C2×C3×C4—92no—
491C2×C3×C4—182no—
492C2×C3×C4C2×D3212yes—
493C2×C3×C4C2×D3212yes—
494C2×C3×C4C2×D3212yes—
495C2×C3×C4C2×D3211yescharacteristic
496C2×C3×C4C2×D3211yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—62no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—62no—
520C2×Dic3—61no—
521C2×Dic3—62no—
522C2×Dic3—94no—
523C2×Dic3—182no—
524C4×D3—62no—
525C4×D3—62no—
526C4×D3—94no—
527C4×D3—94no—
528C4×D3—122no—
529C4×D3—182no—
530C4×D3—182no—
531Dic6—64no—
532Dic6—64no—
533Dic6—64no—
534Dic6—62no—
535Dic6—62no—
536Dic6—62no—
537Dic6—62no—
538Dic6—124no—
539Dic6—122no—
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×C32C2×#23511yescharacteristic
553C2×C32C2×#23711yescharacteristic
554C2×C32C2×#23711yescharacteristic
555C2×C32C2×D3×Q811yescharacteristic
556C2×C32C2×D3×Q811yescharacteristic
557C2×C32C2×D3×Q811yescharacteristic
558C2×C32C2×#23911yescharacteristic
559C2×C32D3×#4111yescharacteristic
560C2×C32D3×#4111yescharacteristic
561C3⋊D3—22no—
562C3×D3—62no—
563C3×D3—62no—
564C3×D3—122no—
565C2×Q8—91no—
566C2×Q8—91no—
567C2×Q8—92no—
568C22×C4—91no—
569C22×C4—271no—
570C22×C4—271no—
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#111311yescharacteristic
580C22⋊C4—92no—
581C22⋊C4—272no—
582C42—91no—
583C42—91no—
584C42—92no—
585C42—271no—
586C42—271no—
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—22no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—42no—
614C3×C4—42no—
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—82no—
618C3×C4—92no—
619C3×C4—92no—
620C3×C4—92no—
621C3×C4—182no—
622C3×C4—181no—
623C3×C4—182no—
624C3×C4—181no—
625C3×C4—182no—
626C3×C4#379512yes—
627C3×C4#379612yes—
628C3×C4#379912yes—
629Dic3—32no—
630Dic3—32no—
631Dic3—32no—
632Dic3—32no—
633Dic3—32no—
634Dic3—32no—
635Dic3—62no—
636Dic3—62no—
637Dic3—62no—
638Dic3—64no—
639Dic3—62no—
640Dic3—62no—
641Dic3—61no—
642Dic3—62no—
643Dic3—61no—
644Dic3—62no—
645Dic3—62no—
646Dic3—62no—
647Dic3—61no—
648Dic3—61no—
649Dic3—122no—
650Dic3—122no—
651Dic3—121no—
652Dic3—121no—
653C32—21no—
654C32—21no—
655C32—21no—
656C32—41no—
657C32#557811yescharacteristic, complemented
658C32#562211yescharacteristic, complemented
659C32#572811yescharacteristic, complemented
660C23—91no—
661Q8—184no—
662Q8—182no—
663Q8—182no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—92no—
669C2×C4—91no—
670C2×C4—92no—
671C2×C4—92no—
672C2×C4—182no—
673C2×C4—274no—
674C2×C4—542no—
675C2×C4C2×#111312yes—
676C2×C4C2×#111311yescharacteristic
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×#379511yescharacteristic
691C2×C3C2×#379611yescharacteristic
692C2×C3C2×#379911yescharacteristic
693C2×C3D3×#23711yescharacteristic
694C2×C3D3×#23711yescharacteristic
695C2×C3#6431211yescharacteristic
696C2×C3D32×Q811yescharacteristic
697C2×C3D32×Q811yescharacteristic
698C2×C3D32×Q811yescharacteristic
699D3—62no—
700D3—62no—
701D3—122no—
702C22—92no—
703C22—181no—
704C22—181no—
705C22C22×#111311yescharacteristic
706C4—22no—
707C4—92no—
708C4—92no—
709C4—92no—
710C4—181no—
711C4—182no—
712C4—182no—
713C4—181no—
714C4—182no—
715C4#8904112yes—
716C3—21no—
717C3—21no—
718C3—21no—
719C3—41no—
720C3#1059438511yescharacteristic, complemented
721C3#1059438711yescharacteristic, complemented
722C3#1059439711yescharacteristic, complemented
723C2—182no—
724C2C2×#8904111yescharacteristic
725C2#1172462211yescharacteristic
726C2Q8×#111311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC22×C3×C3⋊D3C23
hypercenterC4⋊C4#1113
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#64097C2semidirect
3. C3×#64096C2semidirect
7. #11723678C2semidirect
9. #11723669C2semidirect
10. #11723668C2semidirect
11. #11723668C2semidirect
39. #64097D3semidirect
40. #64096D3semidirect
90. #6294Q8semidirect
467. C33#533semidirect
657. C32#5578semidirect
658. C32#5622semidirect
659. C32#5728semidirect
720. C3#10594385semidirect
721. C3#10594387semidirect
722. C3#10594397semidirect

Maximal subgroups

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

subgroupindex
C3×#641062
C3×#640972
C3×#640962
#117236882
#117236832
C4×#62942
#117236782
#117236742
#117236692
#117236682
#105943973
#105943873
#105943853