Finite Group Databasebeta

← #13168401

Subgroups — #13168401

Order 1728.

1112 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723680C211yesmaximal, characteristic, complemented
2#11723426C211yesmaximal, characteristic, complemented
3#11723426C211yesmaximal, characteristic, complemented
4#11723406C211yesmaximal, characteristic, complemented
5C3×C4×#625C211yesmaximal, characteristic
6C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63841C211yesmaximal, characteristic, complemented
8#11723019C212yesmaximal, complemented
9#11723014C212yesmaximal, complemented
10#11722985C212yesmaximal
11#11722913C212yesmaximal, complemented
12#10594939—31nomaximal
13#10594849—31nomaximal
14#10594550—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×C3×#625C2211yescharacteristic
19C2×C3×D3×Dic3C2212yes—
20C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4×C3⋊Dic3C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24#88815C2212yes—
25#88815C2212yes—
26#88807C2212yes—
27#88807C2212yes—
28#88806C2212yes—
29(C2×D3)⋊(C3⋊Dic3)C2212yes—
30(C2×D3)⋊(C3⋊Dic3)C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32C3×#3724C2211yescharacteristic
33C3×Dic3⋊Dic3C2212yes—
34C3×(C2×D3)⋊Dic3C2211yescharacteristic
35C3×(C2×D3)⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×Dic32C2212yes—
38#64133—31no—
39#64133—31no—
40#64096—31no—
41C3×C4×#67—31no—
42C3×C4×#67—31no—
43C3×#926—31no—
44C2×C3×C4⋊Dic3—31no—
45C3×#892—31no—
46C3×D3×C4⋊C4—31no—
47#63969—32no—
48#63961—32no—
49#63956—32no—
50#63955—32no—
51#63905—32no—
52C4×#625D311yescharacteristic
53D3×C4⋊Dic3D311yescharacteristic, complemented
54#63877—32no—
55#63872—31no—
56#63869—31no—
57#63869—31no—
58#63867—32no—
59#63867—32no—
60#63862—32no—
61#63858—32no—
62#63857—31no—
63#63857—31no—
64#63857—31no—
65#63857—31no—
66#63857—61no—
67#63857—61no—
68#63855—32no—
69#63847—32no—
70#63844—31no—
71#63844—31no—
72#63844—61no—
73#63841D311yescharacteristic, complemented
74C22×C32×D3C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78#6308—22no—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C32×C4×D3—22no—
87C32×C4×D3—22no—
88C3×#625—22no—
89C3×D3×Dic3—24no—
90#5541—91no—
91#5529—91no—
92#5513—91no—
93C22×C32×C4—31no—
94C22×C32×C4—31no—
95C2×#634—31no—
96C2×#634—31no—
97C2×#634—31no—
98C2×#634—61no—
99C2×#634—61no—
100C2×#634—61no—
101C2×#634—121no—
102C2×C3×#67—31no—
103C2×C3×#67—31no—
104C22×C3×Dic3—32no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3C2×D311yescharacteristic
109C2×C3×C4×D3C2×D311yescharacteristic
110C2×C3×C4×D3C2×D311yescharacteristic
111C2×C3×C4×D3C2×D311yescharacteristic
112C2×#625C2×D311yescharacteristic
113C2×D3×Dic3C2×D312yes—
114C32×C4⋊C4—31no—
115#3757—32no—
116#3757—32no—
117C4⋊(C3⋊Dic3)C2×D311yescharacteristic
118C4⋊(C3⋊Dic3)C2×D311yescharacteristic
119#3750—32no—
120#3750—32no—
121#3750—32no—
122C4×C3⋊Dic3—32no—
123C4×C3⋊Dic3C2×D311yescharacteristic
124C3×#217—32no—
125C3×#217—31no—
126C3×#217—31no—
127C3×(C2×D3)⋊C4—32no—
128C3×(C2×D3)⋊C4—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—31no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—32no—
136C3×C4⋊Dic3—61no—
137C3×C4⋊Dic3—61no—
138C3×C4⋊Dic3C2×D311yescharacteristic
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×Dic3⋊C4—32no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—31no—
145C3×C4×Dic3—32no—
146C3×C4×Dic3—32no—
147C3×C4×Dic3—61no—
148#3724—32no—
149#3724—32no—
150#3724—32no—
151#3724—32no—
152#3724—62no—
153#3724C2×D311yescharacteristic
154Dic3⋊Dic3—32no—
155Dic3⋊Dic3—32no—
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—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—62no—
170(C2×D3)⋊Dic3—62no—
171(C2×D3)⋊Dic3C2×D312yes—
172(C2×D3)⋊Dic3C2×D311yescharacteristic
173(C2×D3)⋊Dic3C2×D311yescharacteristic
174Dic32—32no—
175Dic32—32no—
176Dic32—62no—
177Dic32C2×D312yes—
178C22×C33C2411yescharacteristic
179C2×C32×D3—21no—
180C2×C32×D3—21no—
181C2×C32×D3—21no—
182C2×C32×D3—21no—
183C2×C32×D3—21no—
184C2×C32×D3#4112yes—
185C33×C4#4112yes—
186C3⋊(C3⋊Dic3)—22no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—22no—
191C32×Dic3—22no—
192C32×Dic3—21no—
193C32×Dic3—21no—
194C3×C4×D4—91no—
195C3×#117—91no—
196C2×C3×C4⋊C4—91no—
197#935—92no—
198#929—92no—
199C4×#67—31no—
200C4×#67—31no—
201#926—31no—
202#926—92no—
203C2×C4⋊Dic3—31no—
204#924—91no—
205#924—91no—
206#924—91no—
207#924—91no—
208#924—181no—
209#924—181no—
210#898—92no—
211#897—91no—
212#897—91no—
213#892—31no—
214D3×C4⋊C4—31no—
215#890—91no—
216#890—91no—
217#889—92no—
218#889—92no—
219#887—91no—
220#887—91no—
221#887—181no—
222#883—92no—
223#879—92no—
224#879—92no—
225#877—92no—
226#872—92no—
227#870—92no—
228#870—91no—
229C4×Dic6—91no—
230C23×C32—31no—
231C23×C32—31no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3C22×D311yescharacteristic
235C22×C3×D3C22×D311yescharacteristic
236C22×C3×D3C22×D311yescharacteristic
237C22×C3×D3C22×D311yescharacteristic
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—31no—
242C2×C32×C4—32no—
243C2×C32×C4—31no—
244C2×C32×C4—41no—
245C2×C32×C4—62no—
246C2×C32×C4—62no—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C3⋊Dic3—32no—
251C2×C3⋊Dic3—32no—
252C2×C3⋊Dic3—32no—
253C2×C3⋊Dic3—62no—
254C2×C3⋊Dic3—62no—
255C2×C3⋊Dic3—62no—
256C2×C3⋊Dic3—122no—
257C2×C3⋊Dic3C22×D312yes—
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D312yes—
261#634—62no—
262#634—64no—
263#634—62no—
264#634—62no—
265#634—122no—
266#634—122no—
267#634—124no—
268C3×#67—62no—
269C3×#67—62no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—64no—
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C3×C4×D3—22no—
293C3×C4×D3—22no—
294C3×C4×D3—22no—
295C3×C4×D3—22no—
296C3×C4×D3—42no—
297C3×C4×D3—42no—
298C3×C4×D3—64no—
299#625—22no—
300D3×Dic3—24no—
301#552—271noSylow
302C2×C33C2×#4111yescharacteristic
303C2×C33C2×#4111yescharacteristic
304C2×C332−1+411yescharacteristic
305C32×D3—22no—
306C32×D3—41no—
307C2×C3×D4—91no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—92no—
315C2×#67—31no—
316C2×#67—31no—
317C22×Dic3—32no—
318C2×C4×D3—32no—
319C2×C4×D3D3211yescharacteristic
320C2×C4×D3D3211yescharacteristic
321C2×Dic6—91no—
322C2×Dic6—91no—
323C2×Dic6—91no—
324C2×Dic6—181no—
325C2×Dic6—181no—
326C2×Dic6—181no—
327C2×Dic6—361no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—92no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C22⋊C4—91no—
336C3×C22⋊C4—91no—
337C3×C22⋊C4—92no—
338C3×C42—92no—
339C3×C42—91no—
340#217—31no—
341#217—32no—
342#217—31no—
343#217—92no—
344#217—92no—
345#217—92no—
346#217—92no—
347#217—182no—
348#217—182no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—32no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—92no—
353(C2×D3)⋊C4—92no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—32no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—92no—
362C4⋊Dic3—92no—
363C4⋊Dic3—92no—
364C4⋊Dic3—92no—
365C4⋊Dic3D3211yescharacteristic
366Dic3⋊C4—31no—
367Dic3⋊C4—32no—
368Dic3⋊C4—31no—
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—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—182no—
381Dic3⋊C4—182no—
382Dic3⋊C4—182no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—32no—
386C4×Dic3—32no—
387C4×Dic3—61no—
388C4×Dic3—92no—
389C4×Dic3—92no—
390C4×Dic3—92no—
391C4×Dic3—182no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—32no—
396C22×C32—41no—
397C22×C32—61no—
398C22×C32—61no—
399C22×C32—61no—
400C22×C32—61no—
401C22×C32—61no—
402C22×C32C23×D311yescharacteristic
403C22×C32C23×D311yescharacteristic
404C22×C32C23×D311yescharacteristic
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—22no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3#23512yes—
422C2×C3×D3#23712yes—
423C32×C4—22no—
424C32×C4—22no—
425C32×C4—22no—
426C32×C4—42no—
427C32×C4—62no—
428C32×C4—61no—
429C32×C4—61no—
430C32×C4#23512yes—
431C32×C4#23512yes—
432C32×C4#23712yes—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—22no—
436C3⋊Dic3—22no—
437C3⋊Dic3—62no—
438C3⋊Dic3—64no—
439C3⋊Dic3—62no—
440C3⋊Dic3—62no—
441C3⋊Dic3—122no—
442C3⋊Dic3—122no—
443C3⋊Dic3—124no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—22no—
447C3×Dic3—21no—
448C3×Dic3—21no—
449C3×Dic3—22no—
450C3×Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—42no—
453C3×Dic3—62no—
454C3×Dic3—62no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—62no—
458C3×Dic3—62no—
459C3×Dic3—61no—
460C3×Dic3—62no—
461C3×Dic3—61no—
462C3×Dic3—122no—
463C3×Dic3—122no—
464C3×Dic3—121no—
465#126—272no—
466#125—272no—
467#125—271no—
468#123—272no—
469C22⋊Q8—271no—
470C22⋊Q8—271no—
471C4×Q8—271no—
472C4×D4—91no—
473#117—91no—
474#117—272no—
475C2×C4⋊C4—91no—
476C33#55211yescharacteristic, complemented, Sylow
477C23×C3—31no—
478C23×C3—31no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—61no—
482C23×C3—61no—
483C22×D3C2×D3211yescharacteristic
484C22×D3C2×D3211yescharacteristic
485C3×D4—182no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—31no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—62no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4—92no—
506C2×C3×C4—92no—
507C2×C3×C4—122no—
508C2×C3×C4—122no—
509C2×C3×C4—184no—
510C2×C3×C4C2×D3211yescharacteristic
511C2×C3×C4C2×D3211yescharacteristic
512C2×C3×C4C2×D3211yescharacteristic
513#67—62no—
514#67—62no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—32no—
522C2×Dic3—32no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3—64no—
528C2×Dic3—92no—
529C2×Dic3—92no—
530C2×Dic3—92no—
531C2×Dic3—182no—
532C2×Dic3—182no—
533C2×Dic3—182no—
534C2×Dic3—362no—
535C2×Dic3C2×D3211yescharacteristic
536C2×Dic3C2×D3212yes—
537C2×Dic3C2×D3211yescharacteristic
538C4×D3—22no—
539C4×D3—22no—
540C4×D3—64no—
541Dic6—184no—
542Dic6—182no—
543Dic6—182no—
544Dic6—182no—
545Dic6—362no—
546Dic6—362no—
547Dic6—364no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—41no—
558C2×C32—41no—
559C2×C32—41no—
560C2×C32—62no—
561C2×C32—121no—
562C2×C32C2×#23511yescharacteristic
563C2×C32C2×#23511yescharacteristic
564C2×C32C2×#23511yescharacteristic
565C2×C32C2×#23711yescharacteristic
566C2×C32C2×#23711yescharacteristic
567C2×C32#100711yescharacteristic
568C2×C32D3×#4111yescharacteristic
569C2×C32#101011yescharacteristic
570C2×C32#101011yescharacteristic
571C3×D3—22no—
572C3×D3—22no—
573C3×D3—42no—
574C3×D3—42no—
575C3×D3—41no—
576C3×D3—41no—
577C2×Q8—271no—
578C2×D4—91no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—92no—
582C4⋊C4—31no—
583C4⋊C4—92no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4—272no—
588C4⋊C4—272no—
589C4⋊C4—272no—
590C4⋊C4—272no—
591C4⋊C4—272no—
592C22⋊C4—92no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—272no—
596C22⋊C4—272no—
597C42—92no—
598C42—91no—
599C42—272no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—32no—
604C22×C3—32no—
605C22×C3—41no—
606C22×C3—62no—
607C22×C3—62no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3C22×D3211yescharacteristic
623C22×C3C22×D3211yescharacteristic
624C22×C3C22×D3211yescharacteristic
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3#379512yes—
631C3×C4—22no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—42no—
635C3×C4—62no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—62no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4—122no—
644C3×C4—182no—
645C3×C4—182no—
646C3×C4—181no—
647C3×C4—181no—
648C3×C4#379812yes—
649C3×C4#380412yes—
650C3×C4#380412yes—
651Dic3—22no—
652Dic3—21no—
653Dic3—21no—
654Dic3—62no—
655Dic3—62no—
656Dic3—61no—
657Dic3—61no—
658Dic3—61no—
659Dic3—62no—
660Dic3—61no—
661Dic3—62no—
662Dic3—62no—
663Dic3—122no—
664Dic3—121no—
665Dic3—122no—
666Dic3—184no—
667Dic3—182no—
668Dic3—182no—
669Dic3—182no—
670Dic3—362no—
671Dic3—362no—
672Dic3—364no—
673C32—21no—
674C32—21no—
675C32—21no—
676C32—41no—
677C32#551311yescharacteristic, complemented
678C32#552911yescharacteristic, complemented
679C32#554111yescharacteristic, complemented
680C23—31no—
681C23—31no—
682Q8—542no—
683D4—182no—
684C2×C4—31no—
685C2×C4—32no—
686C2×C4—31no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—91no—
690C2×C4—92no—
691C2×C4—91no—
692C2×C4—92no—
693C2×C4—184no—
694C2×C4—272no—
695C2×C4D3311yescharacteristic
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—62no—
709C2×C3—62no—
710C2×C3—122no—
711C2×C3—122no—
712C2×C3—121no—
713C2×C3—121no—
714C2×C3C2×#379511yescharacteristic
715C2×C3#6429711yescharacteristic
716C2×C3#6429811yescharacteristic
717C2×C3C2×#379811yescharacteristic
718C2×C3D3×#23511yescharacteristic
719C2×C3D3×#23711yescharacteristic
720C2×C3#6431511yescharacteristic
721C2×C3C2×#380411yescharacteristic
722C2×C3C2×#380411yescharacteristic
723D3—22no—
724D3—41no—
725C22—32no—
726C22—61no—
727C22—61no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22C2×D3311yescharacteristic
732C4—62no—
733C4—61no—
734C4—61no—
735C4—182no—
736C4—181no—
737C4—181no—
738C4—182no—
739C4—542no—
740C4#8895912yes—
741C3—21no—
742C3—21no—
743C3—21no—
744C3—41no—
745C3#1059455011yescharacteristic, complemented
746C3#1059484911yescharacteristic, complemented
747C3#1059493911yescharacteristic, complemented
748C2—62no—
749C2—121no—
750C2D3×#379511yescharacteristic
751C2#1172439611yescharacteristic
752C2C2×#8895911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#625C22
hypercenterC2×C4D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723680C2semidirect
2. #11723426C2semidirect
3. #11723426C2semidirect
4. #11723406C2semidirect
6. C3×D3×C4⋊Dic3C2semidirect
7. C3×#63841C2semidirect
8. #11723019C2semidirect
9. #11723014C2semidirect
11. #11722913C2semidirect
53. D3×C4⋊Dic3D3semidirect
73. #63841D3semidirect
476. C33#552semidirect
677. C32#5513semidirect
678. C32#5529semidirect
679. C32#5541semidirect
745. C3#10594550semidirect
746. C3#10594849semidirect
747. C3#10594939semidirect

Maximal subgroups

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

subgroupindex
#117236802
#117234262
#117234062
C3×C4×#6252
C3×D3×C4⋊Dic32
C3×#638412
#117230192
#117230142
#117229852
#117229132
#105949393
#105948493
#105945503