Finite Group Databasebeta

← #13169283

Subgroups — #13169283

Order 1728.

1288 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6295C211yesmaximal, characteristic, complemented
2#11723526C211yesmaximal, characteristic, complemented
3#11723526C211yesmaximal, characteristic, complemented
4#11723494C211yesmaximal, characteristic, complemented
5C3×#63900C211yesmaximal, characteristic, complemented
6C3×#63872C211yesmaximal, characteristic, complemented
7C3×#63849C211yesmaximal, characteristic, complemented
8#11723021C212yesmaximal, complemented
9#11723000C212yesmaximal, complemented
10#11722961C212yesmaximal, complemented
11#11722933C212yesmaximal, complemented
12#10594578—31nomaximal
13#10594562—31nomaximal
14#10594559—31nomaximal
15C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×#6295C2211yescharacteristic
19C2×#6292C2212yes—
20C2×#6292C2212yes—
21C2×#6289C2212yes—
22C2×C3×#624C2212yes—
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26C32×C4⋊Dic3C2211yescharacteristic
27#88815C2211yescharacteristic
28#88814C2211yescharacteristic
29#88814C2211yescharacteristic
30#88804C2212yes—
31#88804C2212yes—
32#88804C2212yes—
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×Dic32C2212yes—
38#64104—31no—
39#64104—31no—
40#64102—31no—
41C3×#892—31no—
42C3×#892—31no—
43C3×D3×C4⋊C4—31no—
44C3×D3×C4⋊C4—31no—
45C3×#890—31no—
46C3×#890—31no—
47#63910—32no—
48#63909—31no—
49#63909—31no—
50#63909—31no—
51#63909—31no—
52#63909—32no—
53#63909—61no—
54#63909—61no—
55#63906—32no—
56#63904—32no—
57C4×#626—31no—
58C4×#626—31no—
59C4×#626—32no—
60C4×#625—31no—
61#63900D311yescharacteristic, complemented
62#63897—32no—
63#63894—32no—
64#63894—31no—
65#63894—31no—
66#63894—61no—
67#63872D311yescharacteristic, complemented
68#63868—32no—
69#63868—32no—
70#63854—32no—
71#63853—32no—
72#63849D311yescharacteristic, complemented
73#63848—32no—
74C22×C3⋊(C3⋊D3)C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C22×C3×C3⋊D3C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C4⋊(C3⋊(C3⋊D3))—22no—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3—22no—
84C3×C4×C3⋊D3—22no—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2312yes—
88#6295—22no—
89#6292—24no—
90#6292—42no—
91#6289—42no—
92C3×#624—42no—
93#5695—91no—
94#5530—91no—
95#5514—91no—
96C2×C4⋊(C3⋊D3)—32no—
97C2×C4⋊(C3⋊D3)—31no—
98C2×C4⋊(C3⋊D3)—31no—
99C2×C4⋊(C3⋊D3)—31no—
100C2×C4⋊(C3⋊D3)—32no—
101C2×C4⋊(C3⋊D3)—61no—
102C2×C4⋊(C3⋊D3)—61no—
103C2×C4⋊(C3⋊D3)—61no—
104C2×C4⋊(C3⋊D3)—121no—
105C2×C4×C3⋊D3—32no—
106C2×C4×C3⋊D3C2×D311yescharacteristic
107C2×C4×C3⋊D3C2×D311yescharacteristic
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—31no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3—61no—
115C2×C3×C4×D3—61no—
116C2×#626—31no—
117C2×#626—31no—
118C2×#626—32no—
119C2×#626—32no—
120C2×#626—32no—
121C2×#626—32no—
122C2×#626—62no—
123C2×#626—62no—
124C2×#625—31no—
125C2×#624—32no—
126C2×#624—32no—
127C2×#624—62no—
128C2×#624C2×D312yes—
129C32×C4⋊C4—31no—
130C32×C4⋊C4—31no—
131C32×C4⋊C4—31no—
132#3752—32no—
133#3752—32no—
134#3752—32no—
135C4×C3⋊Dic3C2×D311yescharacteristic
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4—32no—
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3—32no—
142C3×C4⋊Dic3—32no—
143C3×C4⋊Dic3C2×D311yescharacteristic
144C3×C4⋊Dic3C2×D311yescharacteristic
145C3×C4⋊Dic3C2×D311yescharacteristic
146C3×C4⋊Dic3C2×D311yescharacteristic
147C3×C4⋊Dic3C2×D311yescharacteristic
148C3×C4⋊Dic3C2×D311yescharacteristic
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—32no—
156C3×C4×Dic3—32no—
157C3×C4×Dic3—61no—
158#3724—31no—
159#3724C2×D312yes—
160Dic3⋊Dic3—31no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3C2×D312yes—
163Dic3⋊Dic3C2×D312yes—
164#3722—31no—
165#3722—31no—
166#3722—32no—
167#3722—32no—
168#3722—32no—
169#3722—32no—
170#3722—32no—
171#3722—32no—
172#3722—62no—
173#3722—62no—
174#3722—62no—
175#3722C2×D312yes—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—31no—
179(C2×D3)⋊Dic3—31no—
180Dic32C2×D312yes—
181C22×C33C2411yescharacteristic
182C2×C3⋊(C3⋊D3)—22no—
183C2×C3⋊(C3⋊D3)—22no—
184C2×C3⋊(C3⋊D3)—22no—
185C2×C3×C3⋊D3—21no—
186C2×C3×C3⋊D3—21no—
187C2×C3×C3⋊D3—21no—
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—21no—
190C2×C3×C3⋊D3#4112yes—
191C33×C4#4112yes—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—21no—
196C32×Dic3—22no—
197C32×Dic3—22no—
198C32×Dic3—22no—
199C3×#125—91no—
200C3×#117—91no—
201C2×C3×C4⋊C4—91no—
202#930—92no—
203#930—91no—
204#930—91no—
205C4×#67—92no—
206C4×#67—91no—
207C4×#67—91no—
208#898—92no—
209#898—92no—
210#895—92no—
211#895—91no—
212#895—91no—
213#895—91no—
214#895—91no—
215#895—181no—
216#895—181no—
217#894—92no—
218#894—92no—
219#893—91no—
220#893—91no—
221#893—92no—
222#893—181no—
223#892—31no—
224#892—31no—
225D3×C4⋊C4—31no—
226D3×C4⋊C4—31no—
227#890—31no—
228#890—31no—
229#884—92no—
230#883—92no—
231#876—92no—
232C4×D12—92no—
233C4×D12—91no—
234C4×D12—91no—
235C22×C3⋊D3—32no—
236C22×C3⋊D3—32no—
237C22×C3⋊D3—32no—
238C22×C3⋊D3—62no—
239C22×C3⋊D3—62no—
240C22×C3⋊D3—62no—
241C22×C3⋊D3—122no—
242C22×C3⋊D3C22×D311yescharacteristic
243C22×C3⋊D3C22×D311yescharacteristic
244C22×C3×D3—31no—
245C22×C3×D3—31no—
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—61no—
249C22×C3×D3—61no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—32no—
254C2×C32×C4—32no—
255C2×C32×C4—32no—
256C2×C32×C4—41no—
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D311yescharacteristic
264C4⋊(C3⋊D3)—62no—
265C4⋊(C3⋊D3)—64no—
266C4⋊(C3⋊D3)—64no—
267C4⋊(C3⋊D3)—62no—
268C4⋊(C3⋊D3)—62no—
269C4⋊(C3⋊D3)—122no—
270C4⋊(C3⋊D3)—122no—
271C4⋊(C3⋊D3)—124no—
272C4⋊(C3⋊D3)—122no—
273C4×C3⋊D3—22no—
274C4×C3⋊D3—22no—
275C4×C3⋊D3—122no—
276C2×C3×Dic3—22no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—61no—
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D312yes—
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C22×D312yes—
295C2×C3×Dic3C22×D312yes—
296C2×C3×Dic3C22×D312yes—
297C3×C4×D3—62no—
298C3×C4×D3—62no—
299C3×C4×D3—62no—
300C3×C4×D3—62no—
301C3×C4×D3—122no—
302C3×C4×D3—122no—
303C3×C4×D3—122no—
304C3×C4×D3—122no—
305#626—64no—
306#626—64no—
307#626—62no—
308#626—62no—
309#626—124no—
310#626—122no—
311#626—122no—
312#626—124no—
313#625—62no—
314#624—42no—
315#624—122no—
316#624—122no—
317#624—124no—
318#553—271noSylow
319C2×C33C2×#4111yescharacteristic
320C2×C33C2×#4111yescharacteristic
321C2×C33H(5,𝔽2)11yescharacteristic
322C3⋊(C3⋊D3)—42no—
323C3×C3⋊D3—22no—
324C3×C3⋊D3—41no—
325C22×C3×C4—92no—
326C22×C3×C4—91no—
327C22×C3×C4—91no—
328C2×#67—91no—
329C2×#67—91no—
330C2×#67—92no—
331C2×#67—92no—
332C2×D12—92no—
333C2×D12—92no—
334C2×D12—91no—
335C2×D12—91no—
336C2×D12—91no—
337C2×D12—91no—
338C2×D12—92no—
339C2×D12—92no—
340C2×D12—181no—
341C2×D12—181no—
342C2×D12—181no—
343C2×D12—182no—
344C2×D12—182no—
345C2×D12—361no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—32no—
351C2×C4×D3—32no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—92no—
355C2×C4×D3—92no—
356C2×C4×D3—92no—
357C2×C4×D3—182no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—92no—
368C3×C4⋊C4—92no—
369C3×C4⋊C4—92no—
370C3×C22⋊C4—92no—
371C3×C42—92no—
372C3×C42—91no—
373#217—91no—
374#217—91no—
375(C2×D3)⋊C4—32no—
376(C2×D3)⋊C4—32no—
377(C2×D3)⋊C4—92no—
378(C2×D3)⋊C4—92no—
379(C2×D3)⋊C4—92no—
380(C2×D3)⋊C4—92no—
381(C2×D3)⋊C4—92no—
382(C2×D3)⋊C4—92no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—92no—
388(C2×D3)⋊C4—92no—
389(C2×D3)⋊C4—92no—
390(C2×D3)⋊C4—182no—
391(C2×D3)⋊C4—182no—
392(C2×D3)⋊C4—182no—
393C4⋊Dic3—32no—
394C4⋊Dic3—32no—
395C4⋊Dic3—91no—
396C4⋊Dic3D3211yescharacteristic
397C4⋊Dic3D3211yescharacteristic
398C4⋊Dic3D3211yescharacteristic
399Dic3⋊C4—32no—
400Dic3⋊C4—32no—
401Dic3⋊C4—32no—
402Dic3⋊C4—32no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405C4×Dic3—31no—
406C4×Dic3—31no—
407C4×Dic3—32no—
408C4×Dic3—32no—
409C4×Dic3—61no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—41no—
414C22×C32C23×D311yescharacteristic
415C22×C32C23×D311yescharacteristic
416C22×C32C23×D311yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3—62no—
423C2×C3⋊D3—64no—
424C2×C3⋊D3—62no—
425C2×C3⋊D3—62no—
426C2×C3⋊D3—62no—
427C2×C3⋊D3—62no—
428C2×C3⋊D3—62no—
429C2×C3⋊D3—62no—
430C2×C3⋊D3—62no—
431C2×C3⋊D3—62no—
432C2×C3⋊D3—122no—
433C2×C3⋊D3—122no—
434C2×C3⋊D3—124no—
435C2×C3⋊D3—122no—
436C2×C3⋊D3—122no—
437C2×C3⋊D3—122no—
438C2×C3⋊D3—122no—
439C2×C3⋊D3—122no—
440C2×C3⋊D3—122no—
441C2×C3⋊D3—242no—
442C2×C3⋊D3—242no—
443C2×C3⋊D3#23912yes—
444C2×C3×D3—32no—
445C2×C3×D3—32no—
446C2×C3×D3—62no—
447C2×C3×D3—61no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C2×C3×D3—61no—
451C2×C3×D3—62no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—121no—
459C2×C3×D3—121no—
460C2×C3×D3—121no—
461C2×C3×D3—121no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—42no—
466C32×C4—62no—
467C32×C4—62no—
468C32×C4—62no—
469C32×C4#23512yes—
470C32×C4#23512yes—
471C32×C4#23912yes—
472C3⋊Dic3—21no—
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3⋊Dic3—21no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C3×Dic3—22no—
479C3×Dic3—22no—
480C3×Dic3—22no—
481C3×Dic3—22no—
482C3×Dic3—42no—
483C3×Dic3—42no—
484C3×Dic3—42no—
485C3×Dic3—62no—
486C3×Dic3—61no—
487C3×Dic3—61no—
488C3×Dic3—61no—
489C3×Dic3—61no—
490C3×Dic3—61no—
491C3×Dic3—61no—
492C3×Dic3—61no—
493C3×Dic3—61no—
494C3×Dic3—121no—
495C3×Dic3—121no—
496C3×Dic3—121no—
497#126—272no—
498#125—91no—
499#123—272no—
500#121—272no—
501#121—271no—
502#121—271no—
503C4×D4—271no—
504C4×D4—272no—
505C4×D4—271no—
506#117—91no—
507C2×C4⋊C4—91no—
508C33#55311yescharacteristic, complemented, Sylow
509C23×C3—91no—
510C23×C3—91no—
511C22×D3—31no—
512C22×D3—31no—
513C22×D3—31no—
514C22×D3—31no—
515C22×D3—61no—
516C22×D3—61no—
517C22×D3—92no—
518C22×D3—92no—
519C22×D3—92no—
520C22×D3—182no—
521C22×D3—182no—
522C22×D3—182no—
523C22×D3—362no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—32no—
528C2×C3×C4—32no—
529C2×C3×C4—32no—
530C2×C3×C4—32no—
531C2×C3×C4—32no—
532C2×C3×C4—32no—
533C2×C3×C4—41no—
534C2×C3×C4—62no—
535C2×C3×C4—62no—
536C2×C3×C4—62no—
537C2×C3×C4—91no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—182no—
542C2×C3×C4—182no—
543C2×C3×C4—362no—
544C2×C3×C4C2×D3211yescharacteristic
545C2×C3×C4C2×D3211yescharacteristic
546C2×C3×C4C2×D3211yescharacteristic
547#67—184no—
548#67—182no—
549#67—182no—
550#67—362no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3C2×D3212yes—
564C2×Dic3C2×D3212yes—
565C2×Dic3C2×D3212yes—
566D12—184no—
567D12—184no—
568D12—184no—
569D12—182no—
570D12—182no—
571D12—182no—
572D12—182no—
573D12—362no—
574D12—362no—
575D12—364no—
576D12—364no—
577D12—362no—
578D12—362no—
579D12—364no—
580C4×D3—62no—
581C4×D3—62no—
582C4×D3—62no—
583C4×D3—62no—
584C4×D3—122no—
585C4×D3—122no—
586C4×D3—122no—
587C4×D3—122no—
588C4×D3—362no—
589C4×D3—362no—
590C4×D3—362no—
591C4×D3—364no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—21no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—41no—
602C2×C32—41no—
603C2×C32—41no—
604C2×C32C2×#23511yescharacteristic
605C2×C32C2×#23511yescharacteristic
606C2×C32#100411yescharacteristic
607C2×C32C2×#23911yescharacteristic
608C2×C32C2×#23911yescharacteristic
609C2×C32D3×#4111yescharacteristic
610C2×C32D3×#4111yescharacteristic
611C2×C32#100911yescharacteristic
612C2×C32#100911yescharacteristic
613C3⋊D3—22no—
614C3⋊D3—41no—
615C3⋊D3—122no—
616C3⋊D3—124no—
617C3⋊D3—122no—
618C3⋊D3—122no—
619C3⋊D3—242no—
620C3⋊D3—242no—
621C3⋊D3—244no—
622C3×D3—62no—
623C3×D3—62no—
624C3×D3—122no—
625C3×D3—122no—
626C3×D3—121no—
627C3×D3—121no—
628C2×D4—272no—
629C2×D4—272no—
630C2×D4—271no—
631C2×D4—271no—
632C22×C4—92no—
633C22×C4—91no—
634C22×C4—91no—
635C22×C4—272no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—92no—
640C4⋊C4—92no—
641C4⋊C4—92no—
642C4⋊C4—271no—
643C22⋊C4—92no—
644C22⋊C4—272no—
645C22⋊C4—272no—
646C22⋊C4—272no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C42—92no—
650C42—91no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—41no—
655C22×C3—92no—
656C22×C3—181no—
657C22×C3—181no—
658C22×C3—181no—
659C22×C3—181no—
660C22×C3—181no—
661C22×C3C22×D3211yescharacteristic
662C22×C3C22×D3211yescharacteristic
663C22×C3C22×D3211yescharacteristic
664C2×D3—32no—
665C2×D3—32no—
666C2×D3—62no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—62no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—184no—
683C2×D3—182no—
684C2×D3—182no—
685C2×D3—182no—
686C2×D3—182no—
687C2×D3—182no—
688C2×D3—182no—
689C2×D3—182no—
690C2×D3—182no—
691C2×D3—182no—
692C2×D3—362no—
693C2×D3—362no—
694C2×D3—362no—
695C2×D3—362no—
696C2×D3—362no—
697C2×D3—362no—
698C2×D3—362no—
699C2×D3—362no—
700C2×D3—364no—
701C2×D3—722no—
702C2×D3—722no—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—42no—
707C3×C4—62no—
708C3×C4—62no—
709C3×C4—62no—
710C3×C4—62no—
711C3×C4—62no—
712C3×C4—62no—
713C3×C4—122no—
714C3×C4—122no—
715C3×C4—122no—
716C3×C4—181no—
717C3×C4—181no—
718C3×C4—181no—
719C3×C4—181no—
720C3×C4#379812yes—
721C3×C4#379912yes—
722C3×C4#379912yes—
723Dic3—22no—
724Dic3—22no—
725Dic3—22no—
726Dic3—62no—
727Dic3—61no—
728Dic3—61no—
729Dic3—61no—
730Dic3—61no—
731Dic3—61no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738C32—21no—
739C32—21no—
740C32—21no—
741C32—41no—
742C32#551411yescharacteristic, complemented
743C32#553011yescharacteristic, complemented
744C32#569511yescharacteristic, complemented
745C23—91no—
746C23—91no—
747C23—272no—
748D4—544no—
749D4—542no—
750D4—542no—
751D4—1082no—
752C2×C4—32no—
753C2×C4—32no—
754C2×C4—32no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—91no—
758C2×C4—91no—
759C2×C4—182no—
760C2×C4—182no—
761C2×C4—362no—
762C2×C4—1082no—
763C2×C4D3311yescharacteristic
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—41no—
774C2×C3—41no—
775C2×C3—41no—
776C2×C3—182no—
777C2×C3—361no—
778C2×C3C2×#379811yescharacteristic
779C2×C3C2×#379911yescharacteristic
780C2×C3C2×#379911yescharacteristic
781C2×C3#6431211yescharacteristic
782C2×C3#6431411yescharacteristic
783C2×C3#6431411yescharacteristic
784C2×C3D3×#23911yescharacteristic
785C2×C3D3×#23911yescharacteristic
786C2×C3#6432011yescharacteristic
787D3—62no—
788D3—62no—
789D3—122no—
790D3—122no—
791D3—121no—
792D3—121no—
793D3—364no—
794D3—362no—
795D3—362no—
796D3—362no—
797D3—722no—
798D3—722no—
799D3—724no—
800C22—92no—
801C22—181no—
802C22—181no—
803C22—181no—
804C22—181no—
805C22—181no—
806C22—542no—
807C22—542no—
808C22—542no—
809C22C2×D3311yescharacteristic
810C4—62no—
811C4—62no—
812C4—62no—
813C4—181no—
814C4—181no—
815C4—181no—
816C4—181no—
817C4#8896512yes—
818C3—21no—
819C3—21no—
820C3—21no—
821C3—41no—
822C3#1059455911yescharacteristic, complemented
823C3#1059456211yescharacteristic, complemented
824C3#1059457811yescharacteristic, complemented
825C2—182no—
826C2—361no—
827C2—1082no—
828C2#1172437711yescharacteristic
829C2#1172438611yescharacteristic
830C2C2×#8896511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#553
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C4×#6295C2semidirect
2. #11723526C2semidirect
3. #11723526C2semidirect
4. #11723494C2semidirect
5. C3×#63900C2semidirect
6. C3×#63872C2semidirect
7. C3×#63849C2semidirect
8. #11723021C2semidirect
9. #11723000C2semidirect
10. #11722961C2semidirect
11. #11722933C2semidirect
61. #63900D3semidirect
67. #63872D3semidirect
72. #63849D3semidirect
508. C33#553semidirect
742. C32#5514semidirect
743. C32#5530semidirect
744. C32#5695semidirect
822. C3#10594559semidirect
823. C3#10594562semidirect
824. C3#10594578semidirect

Maximal subgroups

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

subgroupindex
C4×#62952
#117235262
#117234942
C3×#639002
C3×#638722
C3×#638492
#117230212
#117230002
#117229612
#117229332
#105945783
#105945623
#105945593