Finite Group Databasebeta

← #13168521

Subgroups — #13168521

Order 1728.

1206 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723674C211yesmaximal, characteristic, complemented
2C4×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
3#11723450C211yesmaximal, characteristic, complemented
4#11723434C211yesmaximal, characteristic, complemented
5C3×#63916C211yesmaximal, characteristic
6C3×Dic3×D12C211yesmaximal, characteristic, complemented
7C3×#63844C211yesmaximal, characteristic, complemented
8#11723022C212yesmaximal, complemented
9#11722991C212yesmaximal, complemented
10Dic3×#626C212yesmaximal, complemented
11#11722913C212yesmaximal, complemented
12#10595172—31nomaximal
13#10594426—31nomaximal
14#10593875—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×Dic3×C3⋊D3C2211yescharacteristic
19C2×Dic3×C3⋊D3C2211yescharacteristic
20C2×C3×#626C2212yes—
21C2×C3×D3×Dic3C2212yes—
22C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25C32×C4×Dic3C2211yescharacteristic
26#88815C2212yes—
27#88814C2212yes—
28#88807C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30(C2×D3)⋊(C3⋊Dic3)C2212yes—
31(C2×D3)⋊(C3⋊Dic3)C2212yes—
32Dic3×C3⋊Dic3C2211yescharacteristic
33Dic3×C3⋊Dic3C2211yescharacteristic
34C3×#3724C2212yes—
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×Dic32C2212yes—
38#64145—31no—
39#64099—31no—
40C42×C3⋊D3—31no—
41C3×#938—31no—
42C3×D4×Dic3—31no—
43C3×#895—31no—
44C3×#887—31no—
45C3×C4×D12—31no—
46C3×C4×Dic6—31no—
47Dic3×#67—32no—
48#63969—32no—
49#63956—32no—
50#63955—32no—
51#63916D311yescharacteristic
52C4×#626—32no—
53Dic3×D12—32no—
54Dic3×D12D311yescharacteristic, complemented
55#63884—32no—
56#63877—32no—
57C4×D3×Dic3—31no—
58C4×D3×Dic3—31no—
59C4×D3×Dic3—61no—
60#63872—31no—
61#63872—31no—
62#63872—61no—
63#63871—31no—
64#63863—31no—
65#63863—31no—
66#63863—61no—
67#63862—32no—
68#63861—32no—
69#63857—31no—
70#63856—31no—
71#63855—32no—
72#63853—32no—
73#63844D311yescharacteristic, complemented
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C32×D3C2312yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4×C3⋊D3—22no—
83C3×#634—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×D12—22no—
88Dic3×C3⋊D3—22no—
89Dic3×C3⋊D3—22no—
90C3×#626—24no—
91C3×D3×Dic3—24no—
92#5600—91no—
93#5580—91no—
94#5557—91no—
95C2×C32×D4—31no—
96C2×C4×C3⋊D3—31no—
97C2×C4×C3⋊D3—31no—
98C2×C4×C3⋊D3C2×D311yescharacteristic
99C2×#634C2×D311yescharacteristic
100C2×C3×#67—32no—
101C22×C3×Dic3—32no—
102C2×C3×D12—21no—
103C2×C3×D12—32no—
104C2×C3×D12C2×D311yescharacteristic
105C2×C3×D12C2×D311yescharacteristic
106C2×C3×C4×D3—32no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—61no—
110C2×C3×Dic6—31no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—61no—
113C2×#626C2×D312yes—
114C2×D3×Dic3—31no—
115C2×D3×Dic3—31no—
116C2×D3×Dic3—31no—
117C2×D3×Dic3—31no—
118C2×D3×Dic3—61no—
119C2×D3×Dic3—61no—
120C2×D3×Dic3C2×D312yes—
121C32×C4⋊C4—31no—
122C32×C42—31no—
123#3757—32no—
124#3757—32no—
125C4⋊(C3⋊Dic3)—32no—
126C4⋊(C3⋊Dic3)C2×D311yescharacteristic
127#3750—32no—
128C4×C3⋊Dic3—31no—
129C4×C3⋊Dic3—31no—
130C4×C3⋊Dic3—31no—
131C4×C3⋊Dic3—31no—
132C4×C3⋊Dic3—31no—
133C4×C3⋊Dic3—61no—
134C4×C3⋊Dic3—61no—
135C4×C3⋊Dic3—61no—
136C4×C3⋊Dic3—121no—
137C3×#217—32no—
138C3×#217—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—31no—
144C3×C4⋊Dic3—61no—
145C3×C4⋊Dic3C2×D311yescharacteristic
146C3×C4⋊Dic3C2×D311yescharacteristic
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×C4×Dic3—21no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—32no—
152C3×C4×Dic3C2×D311yescharacteristic
153C3×C4×Dic3C2×D311yescharacteristic
154#3724—32no—
155#3724C2×D312yes—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—62no—
163Dic3⋊Dic3—62no—
164#3722—32no—
165(C2×D3)⋊Dic3—32no—
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—62no—
172(C2×D3)⋊Dic3—62no—
173(C2×D3)⋊Dic3C2×D312yes—
174(C2×D3)⋊Dic3C2×D312yes—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178Dic32—31no—
179Dic32—61no—
180Dic32—61no—
181Dic32C2×D312yes—
182C22×C33C2411yescharacteristic
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3#4112yes—
186C2×C32×D3—22no—
187C2×C32×D3—22no—
188C2×C32×D3—22no—
189C33×C4#4112yes—
190C3⋊(C3⋊Dic3)—21no—
191C3⋊(C3⋊Dic3)—21no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—22no—
194C3×C3⋊Dic3—22no—
195C32×Dic3—21no—
196C32×Dic3—22no—
197C32×Dic3#4112yes—
198C3×#121—91no—
199C3×C4×Q8—91no—
200C3×C4×D4—91no—
201#947—91no—
202#946—91no—
203#938—31no—
204#936—91no—
205#936—91no—
206#936—181no—
207#935—92no—
208D4×Dic3—31no—
209D4×Dic3—92no—
210C4×#67—92no—
211#926—92no—
212#924—91no—
213C2×C4×Dic3—91no—
214#898—92no—
215#897—91no—
216#895—31no—
217#894—92no—
218#890—91no—
219#890—91no—
220#890—91no—
221#890—181no—
222#887—31no—
223#883—92no—
224#879—92no—
225#879—92no—
226#877—92no—
227C4×D12—31no—
228C4×D12—92no—
229#872—92no—
230C42×D3—91no—
231C42×D3—91no—
232C42×D3—181no—
233C4×Dic6—31no—
234C23×C32—32no—
235C22×C3⋊D3C22×D311yescharacteristic
236C22×C3×D3—22no—
237C22×C3×D3—31no—
238C22×C3×D3—31no—
239C22×C3×D3—61no—
240C22×C3×D3C22×D312yes—
241C22×C3×D3C22×D312yes—
242C32×D4—62no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—31no—
247C2×C32×C4—32no—
248C2×C32×C4—31no—
249C2×C32×C4—41no—
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—61no—
260C2×C3⋊Dic3—61no—
261C2×C3⋊Dic3—61no—
262C2×C3⋊Dic3—61no—
263C2×C3⋊Dic3—61no—
264C2×C3⋊Dic3—61no—
265C2×C3⋊Dic3—121no—
266C2×C3⋊Dic3—121no—
267C2×C3⋊Dic3C22×D312yes—
268C2×C3⋊Dic3C22×D312yes—
269C2×C3⋊Dic3C22×D311yescharacteristic
270C4×C3⋊D3—22no—
271C4×C3⋊D3—62no—
272C4×C3⋊D3—62no—
273#634—22no—
274C3×#67—64no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3—64no—
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D312yes—
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C3×D12—22no—
295C3×D12—22no—
296C3×D12—42no—
297C3×D12—64no—
298C3×C4×D3—64no—
299C3×C4×D3—64no—
300C3×C4×D3—62no—
301C3×C4×D3—62no—
302C3×Dic6—62no—
303C3×Dic6—62no—
304C3×Dic6—122no—
305#626—24no—
306D3×Dic3—24no—
307D3×Dic3—62no—
308D3×Dic3—62no—
309D3×Dic3—64no—
310D3×Dic3—64no—
311D3×Dic3—62no—
312D3×Dic3—62no—
313#529—271noSylow
314C2×C33C2×#4111yescharacteristic
315C2×C33C2×#4111yescharacteristic
316C2×C33C2×#4111yescharacteristic
317C3×C3⋊D3—22no—
318C32×D3—42no—
319C2×C3×Q8—91no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—61no—
323C2×C3×D4—92no—
324C22×C3×C4—92no—
325C22×C3×C4—91no—
326C2×#67—32no—
327C22×Dic3—32no—
328C22×Dic3—91no—
329C22×Dic3—91no—
330C2×D12—32no—
331C2×D12D3211yescharacteristic
332C2×C4×D3—32no—
333C2×C4×D3—31no—
334C2×C4×D3—31no—
335C2×C4×D3—61no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—181no—
341C2×C4×D3—181no—
342C2×Dic6—31no—
343C2×Dic6—31no—
344C2×Dic6—61no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—92no—
349C3×C4⋊C4—91no—
350C3×C22⋊C4—92no—
351C3×C22⋊C4—92no—
352C3×C42—31no—
353C3×C42—31no—
354C3×C42—61no—
355C3×C42—92no—
356#217—32no—
357#217—32no—
358#217—92no—
359#217—92no—
360#217—92no—
361#217—92no—
362#217—92no—
363#217—182no—
364#217—182no—
365(C2×D3)⋊C4—32no—
366(C2×D3)⋊C4—32no—
367(C2×D3)⋊C4—92no—
368(C2×D3)⋊C4—92no—
369(C2×D3)⋊C4—92no—
370(C2×D3)⋊C4—92no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—92no—
375C4⋊Dic3—92no—
376C4⋊Dic3—92no—
377C4⋊Dic3—92no—
378C4⋊Dic3—182no—
379C4⋊Dic3D3211yescharacteristic
380Dic3⋊C4—32no—
381Dic3⋊C4—32no—
382Dic3⋊C4—92no—
383Dic3⋊C4—92no—
384Dic3⋊C4—92no—
385Dic3⋊C4—92no—
386Dic3⋊C4—92no—
387Dic3⋊C4—182no—
388C4×Dic3—32no—
389C4×Dic3—32no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C4×Dic3—91no—
398C4×Dic3—91no—
399C4×Dic3—181no—
400C4×Dic3—181no—
401C4×Dic3—181no—
402C4×Dic3—181no—
403C4×Dic3—181no—
404C4×Dic3—361no—
405C4×Dic3D3211yescharacteristic
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—41no—
410C22×C32—62no—
411C22×C32—62no—
412C22×C32—62no—
413C22×C32C23×D311yescharacteristic
414C22×C32C23×D311yescharacteristic
415C22×C32C23×D311yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3#23712yes—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—32no—
426C2×C3×D3—32no—
427C2×C3×D3—42no—
428C2×C3×D3—42no—
429C2×C3×D3—42no—
430C2×C3×D3—62no—
431C2×C3×D3—62no—
432C2×C3×D3—62no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C32×C4—22no—
438C32×C4—22no—
439C32×C4—22no—
440C32×C4—32no—
441C32×C4—42no—
442C32×C4—61no—
443C32×C4—62no—
444C32×C4#23512yes—
445C32×C4#23512yes—
446C32×C4#23712yes—
447C3⋊Dic3—21no—
448C3⋊Dic3—22no—
449C3⋊Dic3—22no—
450C3⋊Dic3—61no—
451C3⋊Dic3—61no—
452C3⋊Dic3—62no—
453C3⋊Dic3—62no—
454C3⋊Dic3—61no—
455C3⋊Dic3—61no—
456C3⋊Dic3—61no—
457C3⋊Dic3—61no—
458C3⋊Dic3—121no—
459C3⋊Dic3—121no—
460C3⋊Dic3—121no—
461C3⋊Dic3—121no—
462C3⋊Dic3—122no—
463C3⋊Dic3—122no—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—21no—
467C3×Dic3—21no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—42no—
471C3×Dic3—62no—
472C3×Dic3—62no—
473C3×Dic3—61no—
474C3×Dic3—61no—
475C3×Dic3—62no—
476C3×Dic3—62no—
477C3×Dic3—62no—
478C3×Dic3—122no—
479C3×Dic3—122no—
480C3×Dic3#23712yes—
481C3×Dic3#23912yes—
482#126—272no—
483#125—271no—
484#124—271no—
485#123—272no—
486C22⋊Q8—271no—
487#121—91no—
488C4×Q8—91no—
489C4×D4—91no—
490C4×D4—272no—
491#117—272no—
492C2×C42—271no—
493C33#52911yescharacteristic, complemented, Sylow
494C23×C3—32no—
495C23×C3—32no—
496C23×C3—62no—
497C23×C3—91no—
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—61no—
501C22×D3C2×D3212yes—
502C3×Q8—182no—
503C3×D4—62no—
504C3×D4—62no—
505C3×D4—122no—
506C3×D4—184no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—32no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—32no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—62no—
520C2×C3×C4—91no—
521C2×C3×C4—92no—
522C2×C3×C4—92no—
523C2×C3×C4—184no—
524C2×C3×C4—182no—
525C2×C3×C4C2×D3211yescharacteristic
526C2×C3×C4C2×D3211yescharacteristic
527C2×C3×C4C2×D3211yescharacteristic
528#67—64no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—61no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—64no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—181no—
546C2×Dic3—181no—
547C2×Dic3—181no—
548C2×Dic3—181no—
549C2×Dic3—181no—
550C2×Dic3—181no—
551C2×Dic3—182no—
552C2×Dic3—182no—
553C2×Dic3—361no—
554C2×Dic3—361no—
555C2×Dic3C2×D3212yes—
556C2×Dic3C2×D3211yescharacteristic
557C2×Dic3C2×D3211yescharacteristic
558D12—22no—
559D12—64no—
560C4×D3—64no—
561C4×D3—64no—
562C4×D3—62no—
563C4×D3—62no—
564C4×D3—182no—
565C4×D3—182no—
566C4×D3—182no—
567C4×D3—182no—
568C4×D3—184no—
569C4×D3—184no—
570Dic6—62no—
571Dic6—62no—
572Dic6—122no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—41no—
583C2×C32—41no—
584C2×C32—41no—
585C2×C32—122no—
586C2×C32C2×#23511yescharacteristic
587C2×C32C2×#23511yescharacteristic
588C2×C32C2×#23711yescharacteristic
589C2×C32C2×#23711yescharacteristic
590C2×C32C2×#23711yescharacteristic
591C2×C32C2×#23911yescharacteristic
592C2×C32D3×#4111yescharacteristic
593C2×C32D3×#4111yescharacteristic
594C2×C32D3×#4111yescharacteristic
595C3⋊D3—22no—
596C3×D3—42no—
597C3×D3—42no—
598C3×D3—64no—
599C3×D3—62no—
600C3×D3—62no—
601C3×D3—82no—
602C2×Q8—91no—
603C2×D4—31no—
604C2×D4—92no—
605C22×C4—92no—
606C22×C4—91no—
607C22×C4—271no—
608C22×C4—271no—
609C4⋊C4—31no—
610C4⋊C4—92no—
611C4⋊C4—91no—
612C4⋊C4—272no—
613C4⋊C4—272no—
614C4⋊C4—272no—
615C22⋊C4—92no—
616C22⋊C4—92no—
617C22⋊C4—272no—
618C22⋊C4—272no—
619C22⋊C4—272no—
620C42—31no—
621C42—92no—
622C42—271no—
623C42—271no—
624C42—271no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—41no—
629C22×C3—62no—
630C22×C3—62no—
631C22×C3—62no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—92no—
636C22×C3—122no—
637C22×C3—122no—
638C22×C3—122no—
639C22×C3—181no—
640C22×C3—181no—
641C22×C3C22×D3211yescharacteristic
642C22×C3C22×D3211yescharacteristic
643C22×C3C22×D3211yescharacteristic
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—32no—
648C2×D3—32no—
649C2×D3—62no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—32no—
660C3×C4—32no—
661C3×C4—42no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4—62no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—62no—
668C3×C4—122no—
669C3×C4—181no—
670C3×C4—182no—
671C3×C4—182no—
672C3×C4#379512yes—
673C3×C4#379812yes—
674C3×C4#380412yes—
675Dic3—21no—
676Dic3—22no—
677Dic3—62no—
678Dic3—62no—
679Dic3—61no—
680Dic3—62no—
681Dic3—62no—
682Dic3—62no—
683Dic3—61no—
684Dic3—122no—
685Dic3—122no—
686Dic3—182no—
687Dic3—182no—
688Dic3—181no—
689Dic3—181no—
690Dic3—181no—
691Dic3—181no—
692Dic3—181no—
693Dic3—181no—
694Dic3—361no—
695Dic3—361no—
696Dic3—361no—
697Dic3—361no—
698Dic3—362no—
699Dic3—362no—
700Dic3#379612yes—
701C32—21no—
702C32—21no—
703C32—21no—
704C32—41no—
705C32#555711yescharacteristic, complemented
706C32#558011yescharacteristic, complemented
707C32#560011yescharacteristic, complemented
708C23—32no—
709C23—91no—
710Q8—182no—
711D4—62no—
712D4—184no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—32no—
716C2×C4—92no—
717C2×C4—91no—
718C2×C4—92no—
719C2×C4—184no—
720C2×C4—182no—
721C2×C4—271no—
722C2×C4—271no—
723C2×C4—542no—
724C2×C4—542no—
725C2×C4D3311yescharacteristic
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—41no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—122no—
739C2×C3—122no—
740C2×C3—182no—
741C2×C3—242no—
742C2×C3C2×#379511yescharacteristic
743C2×C3C2×#379611yescharacteristic
744C2×C3C2×#379811yescharacteristic
745C2×C3#6430611yescharacteristic
746C2×C3D3×#23711yescharacteristic
747C2×C3D3×#23711yescharacteristic
748C2×C3D3×#23711yescharacteristic
749C2×C3D3×#23911yescharacteristic
750C2×C3C2×#380411yescharacteristic
751D3—42no—
752D3—64no—
753D3—62no—
754D3—62no—
755C22—62no—
756C22—62no—
757C22—62no—
758C22—92no—
759C22—181no—
760C22—181no—
761C22C2×D3311yescharacteristic
762C4—32no—
763C4—61no—
764C4—62no—
765C4—182no—
766C4—181no—
767C4—182no—
768C4—541no—
769C4—541no—
770C4#8896012yes—
771C3—21no—
772C3—21no—
773C3—21no—
774C3—41no—
775C3#1059387511yescharacteristic, complemented
776C3#1059442611yescharacteristic, complemented
777C3#1059517211yescharacteristic, complemented
778C2—122no—
779C2—182no—
780C2D3×#379611yescharacteristic
781C2#1172437311yescharacteristic
782C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC3×#63916C2
hypercenterC2×C4D33
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723674C2semidirect
2. C4×Dic3×C3⋊D3C2semidirect
3. #11723450C2semidirect
4. #11723434C2semidirect
6. C3×Dic3×D12C2semidirect
7. C3×#63844C2semidirect
8. #11723022C2semidirect
9. #11722991C2semidirect
10. Dic3×#626C2semidirect
11. #11722913C2semidirect
54. Dic3×D12D3semidirect
73. #63844D3semidirect
493. C33#529semidirect
705. C32#5557semidirect
706. C32#5580semidirect
707. C32#5600semidirect
775. C3#10593875semidirect
776. C3#10594426semidirect
777. C3#10595172semidirect

Maximal subgroups

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

subgroupindex
#117236742
C4×Dic3×C3⋊D32
#117234502
#117234342
C3×#639162
C3×Dic3×D122
C3×#638442
#117230222
#117229912
Dic3×#6262
#117229132
#105951723
#105944263
#105938753