Finite Group Databasebeta

← #11808445

Subgroups — #11808445

Order 1152.

1511 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63904C211yesmaximal, characteristic, complemented
2C2×#63904C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C2×#63836C211yesmaximal, characteristic, complemented
5#10592371C211yesmaximal, characteristic, complemented
6C3×#4666C211yesmaximal, characteristic, complemented
7C3×#4657C211yesmaximal, characteristic, complemented
8#10591395C211yesmaximal, characteristic
9#10591347C211yesmaximal, characteristic, complemented
10#10591308C211yesmaximal, characteristic, complemented
11#10591292C211yesmaximal, characteristic, complemented
12#10591291C211yesmaximal, characteristic, complemented
13#10591243C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591204C211yesmaximal, characteristic, complemented
16#77737—31nomaximal
17#73581—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63904—24no—
48#63904—24no—
49#63894—24no—
50#63836—24no—
51C32×#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C4×#67—31no—
58C2×C4×#67—31no—
59C2×#893—31no—
60C2×#893—31no—
61C2×#893—31no—
62C2×#892—31no—
63C2×C4×D12—31no—
64C2×#872—31no—
65C3×#398—31no—
66C3×C4×C22⋊C4—31no—
67#4994—31no—
68#4994—31no—
69#4992—31no—
70#4991—31no—
71#4960—31no—
72#4959—31no—
73#4959—31no—
74#4948—31no—
75C4×(C2×D3)⋊C4—31no—
76C4×Dic3⋊C4—31no—
77#4676—31no—
78#4675—31no—
79#4672—31no—
80#4672—31no—
81#4672—31no—
82#4672—61no—
83#4671—31no—
84#4666—31no—
85#4666D311yescharacteristic, complemented
86#4657D311yescharacteristic, complemented
87#4649—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—22no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×#626—22no—
110C2×#626—22no—
111C2×#626—22no—
112C2×#626—22no—
113C2×#626—22no—
114C2×#626—22no—
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—22no—
120C2×#624D414yescomplemented
121#3752—22no—
122#3752—22no—
123#3752—22no—
124#3752—22no—
125#3750—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×C4⋊Dic3—22no—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—22no—
131C3×Dic3⋊C4—22no—
132C3×C4×Dic3—22no—
133C3×C4×Dic3—22no—
134#3724—22no—
135Dic3⋊Dic3—22no—
136#3722—22no—
137#3722—22no—
138#3722—22no—
139#3722—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142Dic32—22no—
143Dic32D414yescomplemented
144#2392—91noSylow
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—61no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3C2×D311yescharacteristic
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C42—31no—
165C2×C3×C42—31no—
166C2×#217—31no—
167C2×#217—31no—
168C4×#67—64no—
169C4×#67—64no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—61no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4—61no—
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3C2×D311yescharacteristic
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—61no—
202C2×Dic3⋊C4C2×D311yescharacteristic
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×Dic3⋊C4C2×D311yescharacteristic
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3C2×D311yescharacteristic
210C2×C4×Dic3C2×D311yescharacteristic
211#893—64no—
212#893—64no—
213#893—64no—
214#892—64no—
215C4×D12—64no—
216#872—64no—
217C3×#95—21no—
218C3×#95—31no—
219C3×#95—31no—
220C3×#95—31no—
221C3×#95C2×D311yescharacteristic
222C3×#95C2×D311yescharacteristic
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C23×C32C2411yescharacteristic
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3C2×D412yes—
244C22×C3⋊D3#4112yes—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4#4112yes—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C2×D412yes—
267C4⋊(C3⋊D3)—28no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D412yes—
284C2×C3×Dic3C2×D412yes—
285C2×C3×Dic3C2×D412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3#4112yes—
288C2×C3×Dic3#4112yes—
289C3×C4×D3—44no—
290#626—28no—
291#626—28no—
292#624—28no—
293#624—44no—
294C2×C4×D4—91no—
295C2×C4×D4—91no—
296C2×C4×D4—91no—
297C2×#117—91no—
298#398—31no—
299#397—91no—
300#396—91no—
301#396—91no—
302#394—91no—
303#394—91no—
304#394—91no—
305#392—91no—
306C4×C4⋊C4—91no—
307C4×C22⋊C4—31no—
308C4×C22⋊C4—91no—
309C24×C3—31no—
310C23×D3—31no—
311C23×D3—31no—
312C23×D3—31no—
313C23×D3—31no—
314C23×D3—61no—
315C23×D3—61no—
316C23×D3C22×D311yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C2×D12—62no—
356C2×D12—62no—
357C2×D12—62no—
358C2×D12—62no—
359C2×D12—62no—
360C2×D12—62no—
361C2×D12—62no—
362C2×D12—62no—
363C2×D12—62no—
364C2×D12—62no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—122no—
368C2×D12—122no—
369C2×D12—122no—
370C2×C4×D3—22no—
371C2×C4×D3—22no—
372C2×C4×D3—22no—
373C2×C4×D3—34no—
374C2×C4×D3—34no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C4⋊C4—62no—
388C3×C4⋊C4—62no—
389C3×C22⋊C4—62no—
390C3×C22⋊C4—62no—
391C3×C42—62no—
392C3×C42—62no—
393#217—62no—
394#217—62no—
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—122no—
416(C2×D3)⋊C4—122no—
417(C2×D3)⋊C4—122no—
418(C2×D3)⋊C4—122no—
419C4⋊Dic3—22no—
420C4⋊Dic3—62no—
421Dic3⋊C4—22no—
422Dic3⋊C4—22no—
423Dic3⋊C4—22no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—122no—
430C4×Dic3—22no—
431C4×Dic3—22no—
432C4×Dic3—34no—
433C4×Dic3—34no—
434C4×Dic3—62no—
435C4×Dic3—62no—
436C22×C32C22×D411yescharacteristic
437C22×C32C22×D411yescharacteristic
438C22×C32C2×#4111yescharacteristic
439C22×C32C2×#4111yescharacteristic
440C22×C32C2×#4111yescharacteristic
441C22×C32C2×#4111yescharacteristic
442C22×C32C2×#4111yescharacteristic
443C2×C3⋊D3—22no—
444C2×C3⋊D3—22no—
445C2×C3⋊D3—22no—
446C2×C3⋊D3—22no—
447C2×C3⋊D3—22no—
448C2×C3⋊D3—22no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C32×C4—22no—
465C32×C4—41no—
466C32×C4—41no—
467C3⋊Dic3—22no—
468C3⋊Dic3—41no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—41no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3#12114yes—
476C22×D4—91no—
477C22×D4—91no—
478C22×D4—91no—
479C23×C4—31no—
480C23×C4—91no—
481C23×C4—91no—
482C4×D4—184no—
483C4×D4—184no—
484C4×D4—184no—
485#117—184no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C42—31no—
506C2×C42—31no—
507C2×C42—91no—
508C2×C42—91no—
509#95—31no—
510#95—31no—
511#95—31no—
512#95—91no—
513#95—91no—
514#95D3211yescharacteristic
515C23×C3—21no—
516C23×C3—32no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3C23×D311yescharacteristic
524C23×C3C23×D311yescharacteristic
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—32no—
532C22×D3—32no—
533C22×D3—32no—
534C22×D3—32no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—61no—
561C22×D3—121no—
562C22×D3—121no—
563C22×D3—121no—
564C22×D3—121no—
565C22×D3—121no—
566C22×D3—121no—
567C22×D3—121no—
568C22×D3—121no—
569C22×D3—121no—
570C22×D3—121no—
571C22×D3—121no—
572C22×D3—121no—
573C22×D3#23512yes—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—22no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—32no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—124no—
621C2×C3×C4#23512yes—
622C2×C3×C4#23912yes—
623#67—68no—
624#67—68no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—62no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3—121no—
656C2×Dic3—121no—
657C2×Dic3—121no—
658C2×Dic3#23512yes—
659C2×Dic3D3×D412yes—
660C2×Dic3D3×D412yes—
661C2×Dic3D3×D412yes—
662C2×Dic3D3×D412yes—
663C2×Dic3#23912yes—
664D12—68no—
665D12—68no—
666D12—68no—
667D12—68no—
668D12—128no—
669C4×D3—44no—
670C4×D3—68no—
671C4×D3—68no—
672C4×D3—124no—
673C4×D3—124no—
674C2×C32C2×#12111yescharacteristic
675C2×C32#52511yescharacteristic
676C2×C32#52511yescharacteristic
677C2×C32#52511yescharacteristic
678C2×C32#52911yescharacteristic
679C2×C32#52911yescharacteristic
680C2×C32#53211yescharacteristic
681C3⋊D3—42no—
682C3⋊D3—42no—
683C3×D3—42no—
684C24—31no—
685C24—91no—
686C24—91no—
687C2×D4—182no—
688C2×D4—182no—
689C2×D4—182no—
690C2×D4—182no—
691C2×D4—182no—
692C2×D4—182no—
693C2×D4—182no—
694C2×D4—182no—
695C2×D4—182no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—62no—
704C22×C4—62no—
705C22×C4—62no—
706C22×C4—94no—
707C22×C4—91no—
708C22×C4—91no—
709C22×C4—182no—
710C22×C4—182no—
711C22×C4—182no—
712C22×C4—182no—
713C22×C4—182no—
714C22×C4C2×D3211yescharacteristic
715C22×C4C2×D3211yescharacteristic
716C22×C4C2×D3211yescharacteristic
717C4⋊C4—62no—
718C4⋊C4—62no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—182no—
722C4⋊C4—182no—
723C4⋊C4—182no—
724C22⋊C4—62no—
725C22⋊C4—62no—
726C22⋊C4—182no—
727C22⋊C4—182no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—182no—
731C22⋊C4—182no—
732C22⋊C4—182no—
733C22⋊C4—182no—
734C22⋊C4—182no—
735C22⋊C4—182no—
736C42—62no—
737C42—62no—
738C42—94no—
739C42—182no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—62no—
748C22×C3—62no—
749C22×C3—62no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3C2×#23511yescharacteristic
755C22×C3C2×#23511yescharacteristic
756C22×C3C2×#23511yescharacteristic
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C22×C3C2×#23911yescharacteristic
762C22×C3C2×#23911yescharacteristic
763C22×C3D3×#4111yescharacteristic
764C22×C3D3×#4111yescharacteristic
765C22×C3D3×#4111yescharacteristic
766C22×C3D3×#4111yescharacteristic
767C22×C3D3×#4111yescharacteristic
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—62no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—62no—
781C2×D3—62no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—122no—
788C2×D3—122no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—122no—
792C2×D3—122no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—241no—
810C2×D3—241no—
811C2×D3—241no—
812C2×D3—241no—
813C2×D3—241no—
814C2×D3—241no—
815C2×D3—241no—
816C2×D3—241no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—34no—
820C3×C4—42no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—41no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4—81no—
829C3×C4—81no—
830C3×C4—121no—
831C3×C4—121no—
832C3×C4—121no—
833Dic3—22no—
834Dic3—22no—
835Dic3—22no—
836Dic3—41no—
837Dic3—41no—
838Dic3—41no—
839Dic3—62no—
840Dic3—62no—
841Dic3—122no—
842Dic3—121no—
843Dic3—121no—
844Dic3—241no—
845Dic3#88414yes—
846C32#239211yescharacteristic, complemented, Sylow
847C23—32no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—92no—
855C23—92no—
856C23—181no—
857C23—181no—
858C23—181no—
859C23—181no—
860C23—181no—
861C23—181no—
862C23—181no—
863C23—181no—
864C23—181no—
865C23—181no—
866C23—181no—
867C23—181no—
868C23C22×D3211yescharacteristic
869D4—188no—
870D4—188no—
871D4—188no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—32no—
885C2×C4—32no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—92no—
902C2×C4—124no—
903C2×C4—188no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—364no—
910C2×C4#379912yes—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—122no—
919C2×C3#547911yescharacteristic
920C2×C3C2×#88411yescharacteristic
921C2×C3#552811yescharacteristic
922C2×C3#554711yescharacteristic
923C2×C3#554711yescharacteristic
924C2×C3#554711yescharacteristic
925C2×C3#554811yescharacteristic
926C2×C3D3×#12111yescharacteristic
927C2×C3#562711yescharacteristic
928C2×C3#562711yescharacteristic
929C2×C3#565611yescharacteristic
930C2×C3#569111yescharacteristic
931C2×C3#569111yescharacteristic
932C2×C3#572511yescharacteristic
933D3—42no—
934D3—122no—
935D3—122no—
936D3—122no—
937D3—122no—
938D3—242no—
939D3—242no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—121no—
944C22—121no—
945C22—121no—
946C22—121no—
947C22—182no—
948C22—182no—
949C22—182no—
950C22—182no—
951C22—182no—
952C22—182no—
953C22—361no—
954C22—361no—
955C22—361no—
956C22—361no—
957C22—361no—
958C22—361no—
959C22—361no—
960C22—361no—
961C22C2×#379911yescharacteristic
962C22D3×#23511yescharacteristic
963C22D3×#23511yescharacteristic
964C22D32×D411yescharacteristic
965C22D32×D411yescharacteristic
966C22#6431211yescharacteristic
967C22D3×#23911yescharacteristic
968C4—22no—
969C4—34no—
970C4—41no—
971C4—41no—
972C4—62no—
973C4—62no—
974C4—62no—
975C4—121no—
976C4—121no—
977C4—121no—
978C4—182no—
979C4—361no—
980C3—21no—
981C3#7358111yescharacteristic, complemented
982C3#7773711yescharacteristic, complemented
983C2—122no—
984C2—362no—
985C2—362no—
986C2#1059397611yescharacteristic
987C2#1059406611yescharacteristic
988C2D3×#88411yescharacteristic
989C2#1059426611yescharacteristic
990C2#1059442211yescharacteristic
991C2#1059451811yescharacteristic
992C2#1059462311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radical#10591395C2
hypercenter#95D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63904C2semidirect
2. C2×#63904C2semidirect
3. C2×#63894C2semidirect
4. C2×#63836C2semidirect
5. #10592371C2semidirect
6. C3×#4666C2semidirect
7. C3×#4657C2semidirect
9. #10591347C2semidirect
10. #10591308C2semidirect
11. #10591292C2semidirect
12. #10591291C2semidirect
13. #10591243C2semidirect
14. #10591233C2semidirect
15. #10591204C2semidirect
85. #4666D3semidirect
86. #4657D3semidirect
120. C2×#624D4semidirect
143. Dic32D4semidirect
846. C32#2392semidirect
981. C3#73581semidirect
982. C3#77737semidirect

Maximal subgroups

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

subgroupindex
C2×#639042
C2×#638942
C2×#638362
#105923712
C3×#46662
C3×#46572
#105913952
#105913472
#105913082
#105912922
#105912912
#105912432
#105912332
#105912042
#777373
#735813