Finite Group Databasebeta

← #11808414

Subgroups — #11808414

Order 1152.

1553 conjugacy classes of subgroups.

The subgroup lattice has 1011 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63952C211yesmaximal, characteristic, complemented
2C2×#63952C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C2×#63836C211yesmaximal, characteristic, complemented
5#10592659C211yesmaximal, characteristic
6C3×#4948C211yesmaximal, characteristic, complemented
7C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
8#10591712C211yesmaximal, characteristic, complemented
9#10591712C211yesmaximal, characteristic, complemented
10#10591347C211yesmaximal, characteristic, complemented
11#10591345C211yesmaximal, characteristic, complemented
12#10591321C211yesmaximal, characteristic, complemented
13Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591216C211yesmaximal, characteristic, complemented
16#77281—31nomaximal
17#73581—31nomaximal
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63952—24no—
48#63952—24no—
49#63894—24no—
50#63836—24no—
51#63658C2211yescharacteristic
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×#892—31no—
61C2×#67⋊C4—31no—
62C2×#67⋊C4—31no—
63C2×C4×D12—31no—
64C2×#872—31no—
65C3×#396—31no—
66C3×C4×C22⋊C4—31no—
67#4994—31no—
68#4991—31no—
69#4982—31no—
70Dic3×C4⋊C4—31no—
71#4961—31no—
72#4961—31no—
73#4960—31no—
74#4960—31no—
75#4960—61no—
76#4959—31no—
77#4959—31no—
78#4948D311yescharacteristic, complemented
79Dic3×C22⋊C4D311yescharacteristic, complemented
80C4×(C2×D3)⋊C4—31no—
81C4×Dic3⋊C4—31no—
82#4676—31no—
83#4675—31no—
84#4675—31no—
85#4672—31no—
86#4666—31no—
87#4657—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—22no—
98C2×#638—22no—
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3—22no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—22no—
120C2×#624D414yescomplemented
121C32×C22⋊C4—22no—
122#3752—22no—
123#3752—22no—
124C3×#217—22no—
125C3×#217—22no—
126C3×#217—22no—
127C3×C4⋊Dic3—22no—
128C3×Dic3⋊C4—22no—
129C3×Dic3⋊C4—22no—
130C3×C4×Dic3—22no—
131C3×C4×Dic3—22no—
132#3724—22no—
133#3724—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—22no—
136#3722—22no—
137#3722—22no—
138#3722—22no—
139#3722—22no—
140#3722—22no—
141#3722—22no—
142Dic32—22no—
143Dic32D414yescomplemented
144#2392—91noSylow
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—61no—
151C22×#67—61no—
152C23×Dic3C2×D311yescharacteristic
153C22×D12—31no—
154C22×D12—31no—
155C22×D12—61no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C22⋊C4—21no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4C2×D311yescharacteristic
168C2×C3×C22⋊C4C2×D311yescharacteristic
169C2×C3×C42—31no—
170C2×C3×C42—31no—
171C2×#217C2×D311yescharacteristic
172C2×#217C2×D311yescharacteristic
173C2×#217C2×D311yescharacteristic
174C4×#67—64no—
175C4×#67—64no—
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—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—61no—
193C2×(C2×D3)⋊C4—61no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3C2×D311yescharacteristic
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
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#892—64no—
213#67⋊C4—64no—
214#67⋊C4—64no—
215C4×D12—64no—
216#872—64no—
217C3×#95—31no—
218C3×#95—31no—
219C3×#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—61no—
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32#4112yes—
237C23×C32C2411yescharacteristic
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3C2×D412yes—
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#4112yes—
258#638—28no—
259#638—28no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3C2×D412yes—
265C2×C3⋊Dic3#4112yes—
266C4⋊(C3⋊D3)—28no—
267C2×C3×Dic3—21no—
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×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—44no—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3#4112yes—
292#624—28no—
293#624—44no—
294C2×C4×D4—91no—
295C2×C4×D4—91no—
296C2×C4×D4—91no—
297C2×#117—91no—
298#398—91no—
299#397—91no—
300#396—31no—
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—21no—
310C24×C3C22×D311yescharacteristic
311C24×C3C22×D311yescharacteristic
312C23×D3—31no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—61no—
317C23×D3—61no—
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—31no—
328C22×C3×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—62no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—122no—
348C2×#67—122no—
349C2×#67—122no—
350C2×#67—122no—
351C2×#67—122no—
352C2×#67—122no—
353C22×Dic3—22no—
354C22×Dic3—22no—
355C22×Dic3—22no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—62no—
373C2×D12—62no—
374C2×D12—62no—
375C2×D12—62no—
376C2×D12—122no—
377C2×D12—122no—
378C2×D12—122no—
379C2×C4×D3—34no—
380C2×C4×D3—34no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—62no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C3×C4⋊C4—62no—
392C3×C4⋊C4—62no—
393C3×C4⋊C4—62no—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—42no—
397C3×C22⋊C4—62no—
398C3×C22⋊C4—62no—
399C3×C22⋊C4—62no—
400C3×C42—62no—
401C3×C42—62no—
402#217—22no—
403#217—22no—
404#217—22no—
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—62no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—122no—
422(C2×D3)⋊C4—122no—
423C4⋊Dic3—22no—
424C4⋊Dic3—62no—
425C4⋊Dic3—62no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434C4×Dic3—22no—
435C4×Dic3—22no—
436C4×Dic3—34no—
437C4×Dic3—34no—
438C4×Dic3—62no—
439C4×Dic3—62no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32C22×D411yescharacteristic
448C22×C32C22×D411yescharacteristic
449C22×C32C2×#4111yescharacteristic
450C22×C32C2×#4111yescharacteristic
451C22×C32C2×#4111yescharacteristic
452C22×C32C2×#4111yescharacteristic
453C22×C32C2×#4111yescharacteristic
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
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—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C32×C4—22no—
469C32×C4—41no—
470C3⋊Dic3—22no—
471C3⋊Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3#12114yes—
480C22×D4—91no—
481C22×D4—91no—
482C22×D4—91no—
483C23×C4—31no—
484C23×C4—91no—
485C23×C4—91no—
486C4×D4—184no—
487C4×D4—184no—
488C4×D4—184no—
489#117—184no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4D3211yescharacteristic
509C2×C42—31no—
510C2×C42—31no—
511C2×C42—91no—
512C2×C42—91no—
513#95—31no—
514#95—31no—
515#95—31no—
516#95—91no—
517#95—91no—
518#95—91no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—22no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3#23512yes—
540C23×C3#23912yes—
541C23×C3C23×D311yescharacteristic
542C23×C3C23×D311yescharacteristic
543C22×D3—32no—
544C22×D3—32no—
545C22×D3—32no—
546C22×D3—32no—
547C22×D3—62no—
548C22×D3—62no—
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—61no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—121no—
574C22×D3—121no—
575C22×D3—121no—
576C22×D3—121no—
577C22×D3—121no—
578C22×D3—121no—
579C22×D3—121no—
580C22×D3—121no—
581C22×D3—121no—
582C22×D3—121no—
583C22×D3—121no—
584C22×D3—121no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—22no—
596C2×C3×C4—32no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—32no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
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—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—124no—
626C2×C3×C4#23512yes—
627C2×C3×C4#23712yes—
628#67—68no—
629#67—68no—
630#67—68no—
631#67—68no—
632#67—128no—
633#67—128no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—44no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3#23512yes—
673C2×Dic3D3×D412yes—
674C2×Dic3D3×D412yes—
675C2×Dic3D3×D412yes—
676C2×Dic3D3×D412yes—
677D12—68no—
678D12—68no—
679D12—128no—
680C4×D3—68no—
681C4×D3—68no—
682C4×D3—124no—
683C4×D3—124no—
684C2×C32—42no—
685C2×C32C2×#12111yescharacteristic
686C2×C32#52511yescharacteristic
687C2×C32#52511yescharacteristic
688C2×C32#52511yescharacteristic
689C2×C32#52911yescharacteristic
690C2×C32#52911yescharacteristic
691C2×C32#53211yescharacteristic
692C3⋊D3—42no—
693C3⋊D3—42no—
694C24—91no—
695C24—91no—
696C24C2×D3211yescharacteristic
697C2×D4—182no—
698C2×D4—182no—
699C2×D4—182no—
700C2×D4—182no—
701C2×D4—182no—
702C2×D4—182no—
703C2×D4—182no—
704C2×D4—182no—
705C2×D4—182no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—62no—
715C22×C4—62no—
716C22×C4—62no—
717C22×C4—94no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—182no—
723C22×C4—182no—
724C22×C4—182no—
725C22×C4C2×D3211yescharacteristic
726C22×C4C2×D3211yescharacteristic
727C4⋊C4—62no—
728C4⋊C4—62no—
729C4⋊C4—62no—
730C4⋊C4—182no—
731C4⋊C4—182no—
732C4⋊C4—182no—
733C4⋊C4—182no—
734C22⋊C4—22no—
735C22⋊C4—62no—
736C22⋊C4—62no—
737C22⋊C4—62no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C22⋊C4—182no—
742C22⋊C4—182no—
743C22⋊C4—182no—
744C22⋊C4—182no—
745C22⋊C4—182no—
746C42—62no—
747C42—62no—
748C42—94no—
749C42—182no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—81no—
775C22×C3—81no—
776C22×C3—81no—
777C22×C3—81no—
778C22×C3C2×#23511yescharacteristic
779C22×C3C2×#23511yescharacteristic
780C22×C3C2×#23511yescharacteristic
781C22×C3C2×D3×D411yescharacteristic
782C22×C3C2×D3×D411yescharacteristic
783C22×C3C2×D3×D411yescharacteristic
784C22×C3C2×D3×D411yescharacteristic
785C22×C3C2×#23711yescharacteristic
786C22×C3C2×#23911yescharacteristic
787C22×C3D3×#4111yescharacteristic
788C22×C3D3×#4111yescharacteristic
789C22×C3D3×#4111yescharacteristic
790C22×C3D3×#4111yescharacteristic
791C22×C3D3×#4111yescharacteristic
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—62no—
803C2×D3—62no—
804C2×D3—122no—
805C2×D3—122no—
806C2×D3—122no—
807C2×D3—122no—
808C2×D3—122no—
809C2×D3—122no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—121no—
813C2×D3—121no—
814C2×D3—121no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—121no—
818C2×D3—121no—
819C2×D3—121no—
820C2×D3—121no—
821C2×D3—121no—
822C2×D3—121no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—241no—
827C2×D3—241no—
828C2×D3—241no—
829C2×D3—241no—
830C2×D3—241no—
831C2×D3—241no—
832C2×D3—241no—
833C2×D3—241no—
834C3×C4—22no—
835C3×C4—22no—
836C3×C4—34no—
837C3×C4—42no—
838C3×C4—41no—
839C3×C4—41no—
840C3×C4—62no—
841C3×C4—62no—
842C3×C4—81no—
843C3×C4—121no—
844C3×C4—121no—
845C3×C4—121no—
846C3×C4—121no—
847C3×C4—121no—
848Dic3—22no—
849Dic3—22no—
850Dic3—41no—
851Dic3—41no—
852Dic3—41no—
853Dic3—41no—
854Dic3—41no—
855Dic3—62no—
856Dic3—62no—
857Dic3—62no—
858Dic3—62no—
859Dic3—122no—
860Dic3—122no—
861Dic3#88414yes—
862C32#239211yescharacteristic, complemented, Sylow
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—92no—
870C23—92no—
871C23—181no—
872C23—181no—
873C23—181no—
874C23—181no—
875C23—181no—
876C23—181no—
877C23—181no—
878C23—181no—
879C23—181no—
880C23—181no—
881C23—181no—
882C23—181no—
883C23#379912yes—
884C23C22×D3211yescharacteristic
885D4—188no—
886D4—188no—
887D4—188no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—32no—
894C2×C4—32no—
895C2×C4—32no—
896C2×C4—32no—
897C2×C4—32no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—92no—
918C2×C4—92no—
919C2×C4—124no—
920C2×C4—188no—
921C2×C4—181no—
922C2×C4—181no—
923C2×C4—181no—
924C2×C4—181no—
925C2×C4—364no—
926C2×C4#380412yes—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—42no—
935C2×C3—42no—
936C2×C3—82no—
937C2×C3#547911yescharacteristic
938C2×C3C2×#88411yescharacteristic
939C2×C3#552811yescharacteristic
940C2×C3#554711yescharacteristic
941C2×C3#554711yescharacteristic
942C2×C3#554711yescharacteristic
943C2×C3#554811yescharacteristic
944C2×C3#559611yescharacteristic
945C2×C3D3×#12111yescharacteristic
946C2×C3#560611yescharacteristic
947C2×C3#562411yescharacteristic
948C2×C3#562711yescharacteristic
949C2×C3#562711yescharacteristic
950C2×C3#570611yescharacteristic
951D3—122no—
952D3—122no—
953D3—122no—
954D3—122no—
955D3—242no—
956D3—242no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—182no—
965C22—182no—
966C22—182no—
967C22—182no—
968C22—182no—
969C22—182no—
970C22—361no—
971C22—361no—
972C22—361no—
973C22—361no—
974C22—361no—
975C22—361no—
976C22—361no—
977C22—361no—
978C22C2×#379911yescharacteristic
979C22D3×#23511yescharacteristic
980C22D32×D411yescharacteristic
981C22D32×D411yescharacteristic
982C22#6431211yescharacteristic
983C22#6431211yescharacteristic
984C22C2×#380411yescharacteristic
985C4—22no—
986C4—34no—
987C4—41no—
988C4—62no—
989C4—62no—
990C4—121no—
991C4—121no—
992C4—121no—
993C4—121no—
994C4—121no—
995C4—182no—
996C4—182no—
997C3—21no—
998C3#7358111yescharacteristic, complemented
999C3#7728111yescharacteristic, complemented
1000C2—42no—
1001C2—362no—
1002C2—362no—
1003C2#1059406611yescharacteristic
1004C2#1059406611yescharacteristic
1005C2#1059410611yescharacteristic
1006C2D3×#88411yescharacteristic
1007C2#1059495511yescharacteristic
1008C2#1059513111yescharacteristic
1009C2#1059513811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radical#10592659C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#63952C2semidirect
2. C2×#63952C2semidirect
3. C2×#63894C2semidirect
4. C2×#63836C2semidirect
6. C3×#4948C2semidirect
7. C3×Dic3×C22⋊C4C2semidirect
8. #10591712C2semidirect
9. #10591712C2semidirect
10. #10591347C2semidirect
11. #10591345C2semidirect
12. #10591321C2semidirect
13. Dic3×Dic3⋊C4C2semidirect
14. #10591233C2semidirect
15. #10591216C2semidirect
78. #4948D3semidirect
79. Dic3×C22⋊C4D3semidirect
120. C2×#624D4semidirect
143. Dic32D4semidirect
862. C32#2392semidirect
998. C3#73581semidirect
999. C3#77281semidirect

Maximal subgroups

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

subgroupindex
C2×#639522
C2×#638942
C2×#638362
#105926592
C3×#49482
C3×Dic3×C22⋊C42
#105917122
#105913472
#105913452
#105913212
Dic3×Dic3⋊C42
#105912332
#105912162
#772813
#735813