Finite Group Databasebeta

← #13177479

Subgroups — #13177479

Order 1728.

2008 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723978C211yesmaximal, characteristic
2C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C32×#935C211yesmaximal, characteristic, complemented
4#11723641C211yesmaximal, characteristic, complemented
5#11723628C211yesmaximal, characteristic, complemented
6#11723627C211yesmaximal, characteristic, complemented
7#11723622C211yesmaximal, characteristic, complemented
8#11723608C211yesmaximal, characteristic, complemented
9C2×#88804C211yesmaximal, characteristic, complemented
10#11723594C211yesmaximal, characteristic, complemented
11#11723592C211yesmaximal, characteristic, complemented
12#11723485C211yesmaximal, characteristic, complemented
13#11723469C211yesmaximal, characteristic, complemented
14#11723446C211yesmaximal, characteristic, complemented
15#11723403C211yesmaximal, characteristic, complemented
16#10596129—31nomaximal
17#10595118—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C22×C32×Dic3C2211yescharacteristic
25C2×#6293C2211yescharacteristic, complemented
26C2×#6289C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28#88864C2211yescharacteristic
29#88859C2211yescharacteristic
30#88859C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic, complemented
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic, complemented
37C32×#217C2211yescharacteristic, complemented
38C32×Dic3⋊C4C2211yescharacteristic, complemented
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#123—31no—
54#64146—31no—
55#64146—34no—
56#64146—64no—
57D4×C3⋊Dic3D311yescharacteristic, complemented
58C2×#3752—31no—
59#64135—31no—
60#64107—31no—
61#64107—31no—
62#64106—31no—
63#64101—31no—
64#64095—31no—
65#64094—31no—
66#64092—31no—
67#64090—31no—
68C22⋊C4×C3⋊D3—31no—
69#64087—31no—
70C3×#935D314yescomplemented
71C3×D4×Dic3—34no—
72#63975—34no—
73#63974—34no—
74#63966—34no—
75#63964—34no—
76C2×#3722—34no—
77#63955—34no—
78#63953—34no—
79#63952—34no—
80#63895—34no—
81#63868—34no—
82#63848—34no—
83#63836—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)—22no—
87C22×C3⋊(C3⋊D3)—22no—
88C22×C3⋊(C3⋊D3)—41no—
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C33×D4—22no—
92C2×C33×C4C2311yescharacteristic
93#6312—22no—
94#6312—41no—
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3×C3⋊Dic3—41no—
98C2×C3×C3⋊Dic3—41no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C32×Dic3—22no—
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108#6293—41no—
109#6289—22no—
110#6289—41no—
111#5658—94no—
112#5556—91no—
113C23×C3⋊D3—31no—
114C23×C3⋊D3—34no—
115C23×C3⋊D3—64no—
116C2×C32×D4—24no—
117C2×C32×D4C2×D314yes—
118C2×C32×D4C2×D311yescharacteristic
119C22×C32×C4—31no—
120C2×#638—31no—
121C2×#638—34no—
122C2×#638—31no—
123C2×#638—34no—
124C2×#638—64no—
125C2×#638—64no—
126C22×C3⋊Dic3C2×D311yescharacteristic
127C22×C3⋊Dic3C2×D311yescharacteristic, complemented
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—31no—
130C2×#634—31no—
131C22×C3×Dic3—34no—
132C22×C3×Dic3—34no—
133C22×C3×Dic3C2×D314yes—
134C2×#627—34no—
135C2×#624—34no—
136C2×#624—34no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4—31no—
139C32×C22⋊C4—31no—
140C32×C22⋊C4—31no—
141C32×C22⋊C4—31no—
142#3757—31no—
143#3757—34no—
144#3757—64no—
145#3757C2×D311yescharacteristic
146#3757C2×D311yescharacteristic, complemented
147#3752—31no—
148#3752—31no—
149#3752—34no—
150#3752—34no—
151#3752—31no—
152#3752—31no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—64no—
158#3752—64no—
159C4⋊(C3⋊Dic3)—31no—
160C4⋊(C3⋊Dic3)—31no—
161C4⋊(C3⋊Dic3)—31no—
162C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
163#3750—31no—
164#3750—31no—
165C4×C3⋊Dic3—31no—
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3C2×D311yescharacteristic, complemented
168C3×#217—34no—
169C3×#217—34no—
170C3×#217C2×D314yes—
171C3×#217C2×D314yescomplemented
172C3×#217C2×D314yescomplemented
173C3×C4⋊Dic3—34no—
174C3×Dic3⋊C4C2×D314yescomplemented
175C3×Dic3⋊C4C2×D314yescomplemented
176C3×C4×Dic3—34no—
177#3724—34no—
178Dic3⋊Dic3—34no—
179Dic3⋊Dic3—34no—
180Dic3⋊Dic3—34no—
181Dic3⋊Dic3—34no—
182#3722—34no—
183#3722—34no—
184#3722—34no—
185#3722—34no—
186#3722—34no—
187#3722—34no—
188Dic32—34no—
189Dic32—34no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33#4112yes—
196C22×C33C2411yescharacteristic
197C2×C3⋊(C3⋊D3)—21no—
198C2×C3⋊(C3⋊D3)—21no—
199C2×C3⋊(C3⋊D3)—21no—
200C2×C3⋊(C3⋊D3)—21no—
201C2×C3⋊(C3⋊D3)—21no—
202C2×C3⋊(C3⋊D3)—44no—
203C2×C3⋊(C3⋊D3)#4112yes—
204C33×C4—21no—
205C3⋊(C3⋊Dic3)—21no—
206C3⋊(C3⋊Dic3)—21no—
207C3×C3⋊Dic3—21no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C3×#123—34no—
216C3×C4×D4—91no—
217#937—94no—
218#937—91no—
219#937—184no—
220#935C3⋊D311yescharacteristic, complemented
221D4×Dic3—34no—
222#929—91no—
223C4×#67—91no—
224C2×(C2×D3)⋊C4—94no—
225C2×(C2×D3)⋊C4—91no—
226#926—94no—
227#924—91no—
228#898—94no—
229#898—94no—
230#898—91no—
231#897—94no—
232#896—91no—
233#892—94no—
234#886—94no—
235#885—94no—
236#885—91no—
237#883—94no—
238#883—91no—
239#67⋊C4—94no—
240D3×C22⋊C4—94no—
241D3×C22⋊C4—91no—
242#878—94no—
243#877—91no—
244#876—91no—
245#872—91no—
246C23×C32—24no—
247C23×C32—24no—
248C23×C32C22×D314yes—
249C23×C32C22×D314yes—
250C23×C32C22×D311yescharacteristic
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3—31no—
253C22×C3⋊D3—31no—
254C22×C3⋊D3—34no—
255C22×C3⋊D3—34no—
256C22×C3⋊D3—64no—
257C22×C3⋊D3—64no—
258C22×C3⋊D3—62no—
259C22×C3⋊D3—62no—
260C22×C3⋊D3—68no—
261C22×C3⋊D3—68no—
262C22×C3⋊D3—128no—
263C22×C3⋊D3—128no—
264C22×C3⋊D3—121no—
265C22×C3⋊D3—124no—
266C22×C3⋊D3—128no—
267C32×D4—22no—
268C32×D4—28no—
269C32×D4—48no—
270C2×C32×C4—24no—
271C2×C32×C4—31no—
272C2×C32×C4—31no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—62no—
276C2×C32×C4C22×D314yes—
277C2×C32×C4C22×D311yescharacteristic
278#638—62no—
279#638—68no—
280#638—128no—
281#638—121no—
282#638—124no—
283#638—128no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—34no—
287C2×C3⋊Dic3—34no—
288C2×C3⋊Dic3—41no—
289C2×C3⋊Dic3—41no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D311yescharacteristic
296C4×C3⋊D3—62no—
297C4×C3⋊D3—121no—
298#634—121no—
299C2×C3×Dic3—28no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3—34no—
303C2×C3×Dic3—34no—
304C2×C3×Dic3—124no—
305C2×C3×Dic3—124no—
306C2×C3×Dic3C22×D314yes—
307C2×C3×Dic3C22×D314yes—
308C2×C3×Dic3C22×D314yes—
309C2×C3×Dic3C22×D314yes—
310#627—124no—
311#624—68no—
312#624—124no—
313#551—271noSylow
314C2×C33—22no—
315C2×C33—41no—
316C2×C33C2×#4111yescharacteristic
317C2×C33C2×#4111yescharacteristic
318C2×C33H(5,𝔽2)11yescharacteristic
319C3⋊(C3⋊D3)—22no—
320C3⋊(C3⋊D3)—41no—
321C23×D3—94no—
322C23×D3—91no—
323C23×D3—184no—
324C2×C3×D4—24no—
325C2×C3×D4D3214yes—
326C2×C3×D4C2×C3⋊D311yescharacteristic
327C22×C3×C4—34no—
328C22×C3×C4—91no—
329C22×C3×C4—91no—
330C2×#67—94no—
331C2×#67—91no—
332C2×#67—94no—
333C2×#67—91no—
334C2×#67—184no—
335C2×#67—184no—
336C22×Dic3—34no—
337C22×Dic3—34no—
338C22×Dic3C2×C3⋊D311yescharacteristic
339C2×C4×D3—94no—
340C2×C4×D3—91no—
341C2×C4×D3—94no—
342C2×C4×D3—91no—
343C2×Dic6—94no—
344C2×Dic6—91no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—34no—
347C3×C4⋊C4—91no—
348C3×C22⋊C4—34no—
349C3×C22⋊C4—34no—
350C3×C22⋊C4—34no—
351C3×C22⋊C4—91no—
352C3×C22⋊C4—91no—
353C3×C42—91no—
354#217—34no—
355#217—34no—
356#217—94no—
357#217—91no—
358#217—184no—
359#217C2×C3⋊D311yescharacteristic
360#217C2×C3⋊D311yescharacteristic, complemented
361#217C2×C3⋊D311yescharacteristic, complemented
362(C2×D3)⋊C4—94no—
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—94no—
365(C2×D3)⋊C4—94no—
366(C2×D3)⋊C4—94no—
367(C2×D3)⋊C4—94no—
368(C2×D3)⋊C4—94no—
369(C2×D3)⋊C4—94no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—184no—
379(C2×D3)⋊C4—184no—
380C4⋊Dic3—34no—
381C4⋊Dic3—94no—
382C4⋊Dic3—94no—
383C4⋊Dic3—94no—
384C4⋊Dic3—91no—
385Dic3⋊C4—94no—
386Dic3⋊C4—94no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
392Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
393C4×Dic3—34no—
394C4×Dic3—94no—
395C4×Dic3—94no—
396C4×Dic3—91no—
397C4×Dic3—91no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—24no—
404C22×C32—28no—
405C22×C32—24no—
406C22×C32—24no—
407C22×C32—24no—
408C22×C32—24no—
409C22×C32—24no—
410C22×C32—44no—
411C22×C32—44no—
412C22×C32—44no—
413C22×C32—44no—
414C22×C32—44no—
415C22×C32#23512yes—
416C22×C32#23718yes—
417C22×C32C23×D314yes—
418C22×C32C23×D311yescharacteristic
419C2×C3⋊D3—32no—
420C2×C3⋊D3—38no—
421C2×C3⋊D3—68no—
422C2×C3⋊D3—61no—
423C2×C3⋊D3—61no—
424C2×C3⋊D3—68no—
425C2×C3⋊D3—61no—
426C2×C3⋊D3—61no—
427C2×C3⋊D3—61no—
428C2×C3⋊D3—64no—
429C2×C3⋊D3—64no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—64no—
433C2×C3⋊D3—124no—
434C2×C3⋊D3—124no—
435C2×C3⋊D3—124no—
436C2×C3⋊D3—124no—
437C2×C3⋊D3—124no—
438C2×C3⋊D3—1216no—
439C2×C3⋊D3—1232no—
440C32×C4—21no—
441C32×C4—24no—
442C32×C4—44no—
443C32×C4—61no—
444C32×C4—61no—
445C32×C4—61no—
446C32×C4—61no—
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—21no—
450C3⋊Dic3—21no—
451C3⋊Dic3—61no—
452C3⋊Dic3—61no—
453C3⋊Dic3—64no—
454C3⋊Dic3—64no—
455C3⋊Dic3—124no—
456C3⋊Dic3—124no—
457C3×Dic3—24no—
458C3×Dic3—24no—
459C3×Dic3—24no—
460C3×Dic3—24no—
461C3×Dic3—64no—
462C3×Dic3—64no—
463C3×Dic3—64no—
464C3×Dic3—64no—
465#126—271no—
466#126—271no—
467#124—271no—
468#123—31no—
469#123—271no—
470#123—271no—
471C22⋊Q8—271no—
472C22⋊Q8—271no—
473#120—271no—
474C4×D4—91no—
475C4×D4—271no—
476#117—271no—
477#117—271no—
478C2×C22⋊C4—271no—
479C2×C22⋊C4—271no—
480C33#55111yescharacteristic, complemented, Sylow
481C23×C3—24no—
482C23×C3—24no—
483C23×C3C2×D3214yes—
484C23×C3C2×D3214yes—
485C23×C3C22×C3⋊D311yescharacteristic
486C23×C3C22×C3⋊D311yescharacteristic
487C22×D3—94no—
488C22×D3—91no—
489C22×D3—94no—
490C22×D3—91no—
491C22×D3—184no—
492C22×D3—184no—
493C22×D3—182no—
494C22×D3—188no—
495C22×D3—188no—
496C22×D3—182no—
497C22×D3—368no—
498C22×D3—368no—
499C22×D3—364no—
500C22×D3—361no—
501C22×D3—368no—
502C3×D4—28no—
503C3×D4—22no—
504C3×D4—48no—
505C2×C3×C4—24no—
506C2×C3×C4—34no—
507C2×C3×C4—34no—
508C2×C3×C4—34no—
509C2×C3×C4—34no—
510C2×C3×C4—68no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—91no—
515C2×C3×C4—361no—
516C2×C3×C4—361no—
517C2×C3×C4C2×D3214yes—
518C2×C3×C4C22×C3⋊D311yescharacteristic
519#67—182no—
520#67—188no—
521#67—368no—
522#67—364no—
523#67—361no—
524#67—368no—
525C2×Dic3—22no—
526C2×Dic3—34no—
527C2×Dic3—34no—
528C2×Dic3—34no—
529C2×Dic3—34no—
530C2×Dic3—94no—
531C2×Dic3—94no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—124no—
535C2×Dic3—124no—
536C2×Dic3—184no—
537C2×Dic3—184no—
538C2×Dic3C22×C3⋊D311yescharacteristic
539C2×Dic3C22×C3⋊D311yescharacteristic
540C2×Dic3C22×C3⋊D311yescharacteristic
541C2×Dic3C22×C3⋊D311yescharacteristic
542C4×D3—182no—
543C4×D3—188no—
544C4×D3—361no—
545C4×D3—364no—
546Dic6—361no—
547Dic6—364no—
548C2×C32—22no—
549C2×C32—24no—
550C2×C32—24no—
551C2×C32—24no—
552C2×C32—28no—
553C2×C32—48no—
554C2×C32—41no—
555C2×C32—44no—
556C2×C32—84no—
557C2×C32C2×#23511yescharacteristic
558C2×C32C2×#23714yes—
559C2×C32#100411yescharacteristic
560C2×C32D3×#4114yes—
561C2×C32D3×#4111yescharacteristic
562C2×C32#100914yes—
563C3⋊D3—62no—
564C3⋊D3—68no—
565C3⋊D3—128no—
566C3⋊D3—128no—
567C3⋊D3—124no—
568C3⋊D3—121no—
569C24—271no—
570C2×Q8—271no—
571C2×D4—271no—
572C2×D4—271no—
573C2×D4D3×C3⋊D311yescharacteristic
574C22×C4—31no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4—271no—
578C22×C4—271no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—91no—
582C4⋊C4—271no—
583C4⋊C4—271no—
584C4⋊C4—271no—
585C4⋊C4—271no—
586C4⋊C4—271no—
587C22⋊C4—31no—
588C22⋊C4—31no—
589C22⋊C4—31no—
590C22⋊C4—91no—
591C22⋊C4—91no—
592C22⋊C4—271no—
593C22⋊C4—271no—
594C22⋊C4—271no—
595C22⋊C4—271no—
596C22⋊C4—271no—
597C22⋊C4—271no—
598C22⋊C4—271no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C42—91no—
602C42—271no—
603C42—271no—
604C22×C3—24no—
605C22×C3—24no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—24no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—24no—
615C22×C3—28no—
616C22×C3—44no—
617C22×C3—44no—
618C22×C3—44no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3#380418yes—
622C22×C3#383012yes—
623C22×C3C22×D3214yes—
624C22×C3C23×C3⋊D311yescharacteristic
625C2×D3—98no—
626C2×D3—92no—
627C2×D3—188no—
628C2×D3—184no—
629C2×D3—184no—
630C2×D3—181no—
631C2×D3—181no—
632C2×D3—188no—
633C2×D3—184no—
634C2×D3—184no—
635C2×D3—184no—
636C2×D3—181no—
637C2×D3—181no—
638C2×D3—181no—
639C2×D3—364no—
640C2×D3—364no—
641C2×D3—364no—
642C2×D3—364no—
643C2×D3—364no—
644C2×D3—3616no—
645C2×D3—3632no—
646C3×C4—24no—
647C3×C4—21no—
648C3×C4—44no—
649C3×C4—64no—
650C3×C4—64no—
651C3×C4—64no—
652C3×C4—64no—
653C3×C4—181no—
654C3×C4—181no—
655C3×C4—181no—
656C3×C4—181no—
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—21no—
661Dic3—64no—
662Dic3—64no—
663Dic3—64no—
664Dic3—64no—
665Dic3—184no—
666Dic3—184no—
667Dic3—181no—
668Dic3—181no—
669Dic3—364no—
670Dic3—364no—
671C32—24no—
672C32#555611yescharacteristic, complemented
673C32#565814yescomplemented
674C23—271no—
675C23—271no—
676C23—542no—
677C23—542no—
678C23—1081no—
679C23C2×D3×C3⋊D311yescharacteristic
680C23C2×D3×C3⋊D311yescharacteristic
681Q8—1081no—
682D4—22no—
683D4—542no—
684D4—1081no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—62no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—91no—
694C2×C4—271no—
695C2×C4—271no—
696C2×C4—361no—
697C2×C4—361no—
698C2×C4—542no—
699C2×C4—1081no—
700C2×C4C2×D3×C3⋊D311yescharacteristic
701C2×C3—22no—
702C2×C3—28no—
703C2×C3—24no—
704C2×C3—24no—
705C2×C3—24no—
706C2×C3—48no—
707C2×C3—41no—
708C2×C3—44no—
709C2×C3—84no—
710C2×C3#6431214yes—
711C2×C3#6431414yes—
712C2×C3C2×#380414yes—
713C2×C3C2×#383011yescharacteristic
714C2×C3#41×C3⋊D311yescharacteristic
715C2×C3#6436611yescharacteristic
716D3—182no—
717D3—188no—
718D3—368no—
719D3—368no—
720D3—361no—
721D3—364no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—272no—
728C22—541no—
729C22—541no—
730C22—541no—
731C22—541no—
732C22—541no—
733C22—1084no—
734C22#8902812yes—
735C22C22×D3×C3⋊D311yescharacteristic
736C4—21no—
737C4—61no—
738C4—61no—
739C4—61no—
740C4—61no—
741C4—181no—
742C4—181no—
743C4—181no—
744C4—181no—
745C4—541no—
746C4—541no—
747C3—24no—
748C3#1059511814yescomplemented
749C3#1059612911yescharacteristic, complemented
750C2—22no—
751C2—41no—
752C2—542no—
753C2—1081no—
754C2#1172458611yescharacteristic
755C2#1172458911yescharacteristic
756C2C2×#8902811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
prime radical#11723978C2
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C3×D4×C3⋊Dic3C2semidirect
3. C32×#935C2semidirect
4. #11723641C2semidirect
5. #11723628C2semidirect
6. #11723627C2semidirect
7. #11723622C2semidirect
8. #11723608C2semidirect
9. C2×#88804C2semidirect
10. #11723594C2semidirect
11. #11723592C2semidirect
12. #11723485C2semidirect
13. #11723469C2semidirect
14. #11723446C2semidirect
15. #11723403C2semidirect
23. C22×C3×C3⋊Dic3C22semidirect
25. C2×#6293C22semidirect
32. C3×#3757C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C3×C4×C3⋊Dic3C22semidirect
36. C32×#217C22semidirect
37. C32×#217C22semidirect
38. C32×Dic3⋊C4C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
42. Dic3⋊(C3⋊Dic3)C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
57. D4×C3⋊Dic3D3semidirect
70. C3×#935D3semidirect
127. C22×C3⋊Dic3C2×D3semidirect
146. #3757C2×D3semidirect
162. C4⋊(C3⋊Dic3)C2×D3semidirect
167. C4×C3⋊Dic3C2×D3semidirect
171. C3×#217C2×D3semidirect
172. C3×#217C2×D3semidirect
174. C3×Dic3⋊C4C2×D3semidirect
175. C3×Dic3⋊C4C2×D3semidirect
220. #935C3⋊D3semidirect
360. #217C2×C3⋊D3semidirect
361. #217C2×C3⋊D3semidirect
391. Dic3⋊C4C2×C3⋊D3semidirect
392. Dic3⋊C4C2×C3⋊D3semidirect
480. C33#551semidirect
672. C32#5556semidirect
673. C32#5658semidirect
748. C3#10595118semidirect
749. C3#10596129semidirect

Maximal subgroups

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

subgroupindex
#117239782
C3×D4×C3⋊Dic32
C32×#9352
#117236412
#117236282
#117236272
#117236222
#117236082
C2×#888042
#117235942
#117235922
#117234852
#117234692
#117234462
#117234032
#105961293
#105951183