Finite Group Databasebeta

← #11808225

Subgroups — #11808225

Order 1152.

2017 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3805C211yesmaximal, characteristic, complemented
2C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#63902C211yesmaximal, characteristic, complemented
4C2×#63898C211yesmaximal, characteristic, complemented
5C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#4961C211yesmaximal, characteristic, complemented
7C3×#4960C211yesmaximal, characteristic, complemented
8#10591723C211yesmaximal, characteristic, complemented
9#10591708C211yesmaximal, characteristic, complemented
10#10591390C211yesmaximal, characteristic, complemented
11#10591389C211yesmaximal, characteristic, complemented
12#10591368C211yesmaximal, characteristic, complemented
13#10591368C211yesmaximal, characteristic, complemented
14#10591338C211yesmaximal, characteristic, complemented
15#10591293C211yesmaximal, characteristic, complemented
16#76889—31nomaximal
17#76665—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C2×#3805—24no—
27C2×#3805—24no—
28C2×#3805—24no—
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic
42#67⋊Dic3—24no—
43C2×#3724C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51#63902—24no—
52#63898—24no—
53#63658C2211yescharacteristic
54#63658C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57#63579C2211yescharacteristic
58#63579C2211yescharacteristic
59C22×#237—31no—
60C22×#237—31no—
61C2×D4×Dic3—31no—
62C2×D4×Dic3—31no—
63C2×#893—31no—
64C2×#67⋊C4—31no—
65C2×#67⋊C4—31no—
66C2×#67⋊C4—31no—
67C3×#394—31no—
68C3×#392—31no—
69#5223—31no—
70#5223—31no—
71#5223—31no—
72#5222—31no—
73#4979—31no—
74#4961—31no—
75#4961D311yescharacteristic, complemented
76#4960—31no—
77#4960D311yescharacteristic, complemented
78#4959—31no—
79#4959—31no—
80#4947—31no—
81Dic3×C22⋊C4—31no—
82Dic3×C22⋊C4—31no—
83Dic3×C22⋊C4—31no—
84Dic3×C22⋊C4—31no—
85Dic3×C22⋊C4—61no—
86#4673—31no—
87#4666—31no—
88#4666—31no—
89#4656—31no—
90C24×C32C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C23×C3×D3C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3—22no—
98C22×C3⋊Dic3D414yescomplemented
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—22no—
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×D12—22no—
118C2×C3×D12—22no—
119C2×C3×D12—22no—
120C2×#627—22no—
121C2×#627—22no—
122C2×#627—22no—
123C2×#625—22no—
124C2×#625—22no—
125C2×#625—22no—
126C2×#625—22no—
127C2×#625—22no—
128C2×#625—22no—
129#3805—232no—
130C2×D3×Dic3—22no—
131C2×D3×Dic3—22no—
132C2×D3×Dic3—22no—
133C2×D3×Dic3—22no—
134C2×D3×Dic3—22no—
135C2×D3×Dic3—22no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3D414yescomplemented
138C2×D3×Dic3D414yescomplemented
139C32×C22⋊C4—22no—
140#3757—22no—
141C4×C3⋊Dic3—22no—
142C4×C3⋊Dic3—22no—
143C3×#217—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—22no—
147C3×(C2×D3)⋊C4—22no—
148C3×C4⋊Dic3—22no—
149#3724—22no—
150Dic3⋊Dic3—22no—
151(C2×D3)⋊Dic3—22no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—22no—
155(C2×D3)⋊Dic3—22no—
156Dic32—22no—
157#2388—91noSylow
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67C2×D311yescharacteristic
167C22×#67C2×D311yescharacteristic
168C22×#67C2×D311yescharacteristic
169C23×Dic3—31no—
170C23×Dic3—31no—
171C23×Dic3—31no—
172C23×Dic3—31no—
173C23×Dic3—31no—
174C23×Dic3—61no—
175C2×#237—64no—
176C2×#237—64no—
177C2×#237—64no—
178C2×#237—64no—
179C2×#237—64no—
180C2×#237—64no—
181C22×D12C2×D311yescharacteristic
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×Dic6—31no—
186C22×Dic6—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C22⋊C4—21no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4C2×D311yescharacteristic
195C2×C3×C22⋊C4C2×D311yescharacteristic
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—61no—
204C2×#217C2×D311yescharacteristic
205D4×Dic3—64no—
206D4×Dic3—64no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×(C2×D3)⋊C4C2×D311yescharacteristic
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×(C2×D3)⋊C4C2×D311yescharacteristic
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3C2×D311yescharacteristic
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×C4×Dic3—31no—
222C2×C4×Dic3—31no—
223C2×C4×Dic3—31no—
224C2×C4×Dic3—31no—
225C2×C4×Dic3—31no—
226C2×C4×Dic3—31no—
227C2×C4×Dic3—61no—
228C2×C4×Dic3—61no—
229#893—64no—
230#67⋊C4—64no—
231#67⋊C4—64no—
232#67⋊C4—64no—
233C3×#95—31no—
234C3×#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—31no—
241C3⋊#95—31no—
242C3⋊#95—31no—
243C3⋊#95—61no—
244C3⋊#95—61no—
245C3⋊#95C2×D311yescharacteristic
246C3⋊#95C2×D311yescharacteristic
247C23×C32—21no—
248C23×C32—21no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32C2×D412yes—
254C23×C32C2411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3C2×D412yes—
274C22×C3×D3C2×D412yes—
275C22×C3×D3#4112yescomplemented
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4#4112yescomplemented
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—28no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3C2×D412yes—
291C2×C3⋊Dic3C2×D412yes—
292C2×C3⋊Dic3C2×D412yes—
293C2×C3⋊Dic3C2×D412yes—
294C2×C3⋊Dic3#4112yescomplemented
295C3×#67—28no—
296C3×#67—28no—
297C3×#67—28no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3C2×D412yes—
311C2×C3×Dic3C2×D412yes—
312C2×C3×Dic3#4112yescomplemented
313C3×D12—28no—
314#627—28no—
315#625—28no—
316#625—28no—
317D3×Dic3—28no—
318D3×Dic3—28no—
319D3×Dic3—44no—
320C22×#41—91no—
321C2×C4×D4—91no—
322C2×C4×D4—91no—
323C2×C4×D4—91no—
324#395—91no—
325#394—31no—
326#394—91no—
327#394—91no—
328#393—91no—
329#392—31no—
330#392—91no—
331#392—91no—
332C4×C22⋊C4—91no—
333C4×C22⋊C4—91no—
334C4×C22⋊C4—91no—
335C24×C3—21no—
336C24×C3—31no—
337C24×C3—31no—
338C24×C3—31no—
339C24×C3C22×D311yescharacteristic
340C24×C3C22×D311yescharacteristic
341C23×D3C22×D311yescharacteristic
342C23×D3C22×D311yescharacteristic
343C23×D3C22×D311yescharacteristic
344C2×C3×D4—62no—
345C2×C3×D4—62no—
346C2×C3×D4—62no—
347C2×C3×D4—62no—
348C2×C3×D4—62no—
349C2×C3×D4—62no—
350C2×C3×D4—62no—
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4—62no—
354C2×C3×D4—62no—
355C2×C3×D4—62no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C2×#67—22no—
368C2×#67—22no—
369C2×#67—22no—
370C2×#67—22no—
371C2×#67—22no—
372C2×#67—22no—
373C2×#67—22no—
374C2×#67—22no—
375C2×#67—22no—
376C2×#67—62no—
377C2×#67—62no—
378C2×#67—62no—
379C2×#67—62no—
380C2×#67—62no—
381C2×#67—62no—
382C2×#67—62no—
383C2×#67—62no—
384C2×#67—62no—
385C2×#67—62no—
386C2×#67—62no—
387C2×#67—62no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—34no—
391C22×Dic3—34no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—34no—
397C22×Dic3—34no—
398C22×Dic3—31no—
399C22×Dic3—31no—
400C22×Dic3—61no—
401C22×Dic3—61no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—64no—
405C22×Dic3—62no—
406C22×Dic3—62no—
407C22×Dic3—62no—
408C22×Dic3—62no—
409C22×Dic3—62no—
410C22×Dic3—62no—
411C22×Dic3—62no—
412C22×Dic3—62no—
413C22×Dic3—62no—
414C22×Dic3—62no—
415C22×Dic3—62no—
416C22×Dic3—122no—
417C22×Dic3—122no—
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423#237—632no—
424#237—632no—
425C2×D12—22no—
426C2×D12—22no—
427C2×D12—22no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—62no—
431C2×C4×D3—62no—
432C2×C4×D3—62no—
433C2×C4×D3—62no—
434C2×C4×D3—62no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C2×Dic6—62no—
438C2×Dic6—62no—
439C2×Dic6—62no—
440C2×Dic6—62no—
441C2×Dic6—62no—
442C2×Dic6—62no—
443C3×C4⋊C4—62no—
444C3×C22⋊C4—24no—
445C3×C22⋊C4—22no—
446C3×C22⋊C4—22no—
447C3×C22⋊C4—62no—
448C3×C22⋊C4—62no—
449C3×C22⋊C4—62no—
450C3×C22⋊C4—62no—
451C3×C22⋊C4—62no—
452#217—22no—
453#217—62no—
454#217—62no—
455#217—62no—
456#217—62no—
457#217—62no—
458#217—64no—
459#217—62no—
460#217—62no—
461(C2×D3)⋊C4—22no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—62no—
466(C2×D3)⋊C4—62no—
467(C2×D3)⋊C4—62no—
468(C2×D3)⋊C4—62no—
469(C2×D3)⋊C4—62no—
470C4⋊Dic3—22no—
471C4⋊Dic3—62no—
472Dic3⋊C4—62no—
473Dic3⋊C4—62no—
474Dic3⋊C4—62no—
475C4×Dic3—62no—
476C4×Dic3—62no—
477C4×Dic3—62no—
478C4×Dic3—62no—
479C4×Dic3—62no—
480C4×Dic3—62no—
481C4×Dic3—122no—
482C4×Dic3—122no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32—41no—
489C22×C32—41no—
490C22×C32C22×D411yescharacteristic
491C22×C32C22×D411yescharacteristic
492C22×C32C22×D411yescharacteristic
493C22×C32C2×#4111yescharacteristic
494C22×C32C2×#4111yescharacteristic
495C22×C32C2×#4111yescharacteristic
496C22×C32C2×#4111yescharacteristic
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—41no—
507C2×C3×D3—41no—
508C2×C3×D3—41no—
509C2×C3×D3—41no—
510C2×C3×D3—41no—
511C2×C3×D3—41no—
512C2×C3×D3—41no—
513C2×C3×D3—41no—
514C2×C3×D3—41no—
515C2×C3×D3—41no—
516C2×C3×D3—41no—
517C2×C3×D3—41no—
518C32×C4—22no—
519C32×C4—41no—
520C3⋊Dic3—22no—
521C3⋊Dic3—22no—
522C3⋊Dic3—41no—
523C3⋊Dic3#12014yes—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—41no—
528C3×Dic3—41no—
529C2×#41—184no—
530C2×#41—184no—
531C2×#41—184no—
532C22×Q8—91no—
533C22×D4—31no—
534C22×D4—31no—
535C22×D4—31no—
536C22×D4—31no—
537C22×D4—91no—
538C22×D4—91no—
539C23×C4—91no—
540C23×C4—91no—
541C23×C4—91no—
542C23×C4—91no—
543C4×D4—184no—
544C4×D4—184no—
545C4×D4—184no—
546C2×C4⋊C4—31no—
547C2×C4⋊C4—91no—
548C2×C4⋊C4—91no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4D3211yescharacteristic
561C2×C42—91no—
562C2×C42—91no—
563C2×C42—91no—
564#95—31no—
565#95—31no—
566#95—91no—
567#95—91no—
568#95—91no—
569#95—91no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—22no—
586C23×C3—32no—
587C23×C3—32no—
588C23×C3—32no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—61no—
609C23×C3—61no—
610C23×C3—61no—
611C23×C3D3×D412yes—
612C23×C3D3×D412yes—
613C23×C3C23×D311yescharacteristic
614C23×C3C23×D311yescharacteristic
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3D3×D412yes—
634C22×D3D3×D412yes—
635C22×D3#23712yescomplemented
636C3×D4—68no—
637C3×D4—68no—
638C3×D4—68no—
639C3×D4—68no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—22no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—22no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4#23712yescomplemented
672C2×C3×C4#23712yescomplemented
673#67—28no—
674#67—28no—
675#67—28no—
676#67—68no—
677#67—68no—
678#67—68no—
679#67—68no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—32no—
696C2×Dic3—32no—
697C2×Dic3—32no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—32no—
701C2×Dic3—32no—
702C2×Dic3—62no—
703C2×Dic3—62no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—68no—
708C2×Dic3—68no—
709C2×Dic3—68no—
710C2×Dic3—68no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—62no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—128no—
727C2×Dic3—121no—
728C2×Dic3—121no—
729C2×Dic3—121no—
730C2×Dic3—121no—
731C2×Dic3—121no—
732C2×Dic3—121no—
733C2×Dic3—124no—
734C2×Dic3D3×D412yes—
735C2×Dic3D3×D412yes—
736C2×Dic3#23712yescomplemented
737D12—28no—
738C4×D3—68no—
739C4×D3—68no—
740C4×D3—124no—
741Dic6—68no—
742Dic6—68no—
743C2×C32—42no—
744C2×C32C2×#12011yescharacteristic
745C2×C32#52511yescharacteristic
746C2×C32#52511yescharacteristic
747C2×C32#52511yescharacteristic
748C2×C32#53211yescharacteristic
749C2×C32#53211yescharacteristic
750C2×C32#53211yescharacteristic
751C3×D3—42no—
752C3×D3—42no—
753C3×D3—42no—
754C24—31no—
755C24—31no—
756C24—31no—
757C24C2×D3211yescharacteristic
758#41—1832no—
759C2×Q8—182no—
760C2×Q8—182no—
761C2×Q8—182no—
762C2×D4—62no—
763C2×D4—62no—
764C2×D4—62no—
765C2×D4—62no—
766C2×D4—62no—
767C2×D4—62no—
768C2×D4—62no—
769C2×D4—62no—
770C2×D4—62no—
771C2×D4—62no—
772C2×D4—62no—
773C2×D4—62no—
774C2×D4—182no—
775C2×D4—182no—
776C2×D4—182no—
777C2×D4—182no—
778C2×D4—182no—
779C2×D4—182no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—31no—
784C22×C4—31no—
785C22×C4—94no—
786C22×C4—94no—
787C22×C4—91no—
788C22×C4—91no—
789C22×C4—91no—
790C22×C4—94no—
791C22×C4—91no—
792C22×C4—182no—
793C22×C4—182no—
794C22×C4—182no—
795C22×C4—182no—
796C22×C4—182no—
797C22×C4—182no—
798C22×C4—182no—
799C22×C4—182no—
800C22×C4—182no—
801C22×C4C2×D3211yescharacteristic
802C22×C4C2×D3211yescharacteristic
803C4⋊C4—62no—
804C4⋊C4—182no—
805C4⋊C4—182no—
806C22⋊C4—22no—
807C22⋊C4—62no—
808C22⋊C4—62no—
809C22⋊C4—62no—
810C22⋊C4—62no—
811C22⋊C4—62no—
812C22⋊C4—182no—
813C22⋊C4—182no—
814C22⋊C4—182no—
815C22⋊C4—182no—
816C22⋊C4—182no—
817C22⋊C4—182no—
818C42—182no—
819C42—182no—
820C42—182no—
821C22×C3—24no—
822C22×C3—22no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—121no—
859C22×C3—121no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3—121no—
870C22×C3C2×D3×D411yescharacteristic
871C22×C3C2×D3×D411yescharacteristic
872C22×C3C2×D3×D411yescharacteristic
873C22×C3C2×D3×D411yescharacteristic
874C22×C3C2×D3×D411yescharacteristic
875C22×C3C2×D3×D411yescharacteristic
876C22×C3C2×#23711yescharacteristic
877C22×C3C2×#23711yescharacteristic
878C22×C3C2×#23711yescharacteristic
879C22×C3C2×#23711yescharacteristic
880C22×C3D3×#4111yescharacteristic
881C22×C3D3×#4111yescharacteristic
882C22×C3D3×#4111yescharacteristic
883C22×C3D3×#4111yescharacteristic
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—22no—
892C2×D3—22no—
893C2×D3—41no—
894C2×D3—41no—
895C2×D3—41no—
896C2×D3—41no—
897C2×D3—41no—
898C2×D3—41no—
899C2×D3—41no—
900C2×D3—41no—
901C2×D3—41no—
902C2×D3—41no—
903C2×D3—41no—
904C2×D3—41no—
905C3×C4—22no—
906C3×C4—22no—
907C3×C4—42no—
908C3×C4—42no—
909C3×C4—41no—
910C3×C4—41no—
911C3×C4—62no—
912C3×C4—62no—
913C3×C4—62no—
914C3×C4—121no—
915C3×C4—121no—
916Dic3—22no—
917Dic3—22no—
918Dic3—22no—
919Dic3—34no—
920Dic3—34no—
921Dic3—41no—
922Dic3—41no—
923Dic3—64no—
924Dic3—62no—
925Dic3—62no—
926Dic3—62no—
927Dic3—62no—
928Dic3—122no—
929Dic3—122no—
930Dic3—122no—
931Dic3—121no—
932Dic3—121no—
933C32#238811yescharacteristic, complemented, Sylow
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—32no—
941C23—32no—
942C23—32no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—61no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—61no—
956C23—61no—
957C23—61no—
958C23—61no—
959C23—61no—
960C23—61no—
961C23#380212yes—
962C23C22×D3211yescharacteristic
963Q8—188no—
964D4—68no—
965D4—68no—
966D4—68no—
967D4—68no—
968D4—188no—
969D4—188no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—32no—
976C2×C4—32no—
977C2×C4—32no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—92no—
991C2×C4—92no—
992C2×C4—92no—
993C2×C4—92no—
994C2×C4—92no—
995C2×C4—188no—
996C2×C4—188no—
997C2×C4—188no—
998C2×C4—181no—
999C2×C4—181no—
1000C2×C4—181no—
1001C2×C4—181no—
1002C2×C4—181no—
1003C2×C4—181no—
1004C2×C4—181no—
1005C2×C4—364no—
1006C2×C4#380512yescomplemented
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—44no—
1015C2×C3—42no—
1016C2×C3—42no—
1017C2×C3—122no—
1018C2×C3—122no—
1019C2×C3—122no—
1020C2×C3#558611yescharacteristic
1021C2×C3#558611yescharacteristic
1022C2×C3D3×#12011yescharacteristic
1023C2×C3D3×#12011yescharacteristic
1024C2×C3#559611yescharacteristic
1025C2×C3#559611yescharacteristic
1026C2×C3#559611yescharacteristic
1027C2×C3#559611yescharacteristic
1028C2×C3#560611yescharacteristic
1029C2×C3#560611yescharacteristic
1030C2×C3#565611yescharacteristic
1031C2×C3#565611yescharacteristic
1032C2×C3#566811yescharacteristic
1033C2×C3#571611yescharacteristic
1034D3—42no—
1035D3—42no—
1036D3—42no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—62no—
1053C22—121no—
1054C22—121no—
1055C22—121no—
1056C22—121no—
1057C22—121no—
1058C22—121no—
1059C22—121no—
1060C22—121no—
1061C22—121no—
1062C22—121no—
1063C22—121no—
1064C22—121no—
1065C22C2×#380211yescharacteristic
1066C22#6430611yescharacteristic
1067C22D32×D411yescharacteristic
1068C22D32×D411yescharacteristic
1069C22D3×#23711yescharacteristic
1070C22D3×#23711yescharacteristic
1071C22C2×#380511yescharacteristic
1072C4—22no—
1073C4—41no—
1074C4—62no—
1075C4—62no—
1076C4—62no—
1077C4—94no—
1078C4—121no—
1079C4—121no—
1080C4—182no—
1081C4—182no—
1082C4—361no—
1083C3—21no—
1084C3#7666511yescharacteristic, complemented
1085C3#7688911yescharacteristic, complemented
1086C2—42no—
1087C2—122no—
1088C2—122no—
1089C2—122no—
1090C2#1059406111yescharacteristic
1091C2#1059408211yescharacteristic
1092C2#1059425811yescharacteristic
1093C2#1059426711yescharacteristic
1094C2#1059492911yescharacteristic
1095C2#1059513011yescharacteristic
1096C2#1059513311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3805C2semidirect
2. C2×#67⋊Dic3C2semidirect
3. C2×#63902C2semidirect
4. C2×#63898C2semidirect
5. C22⋊C4×C3⋊Dic3C2semidirect
6. C3×#4961C2semidirect
7. C3×#4960C2semidirect
8. #10591723C2semidirect
9. #10591708C2semidirect
10. #10591390C2semidirect
11. #10591389C2semidirect
12. #10591368C2semidirect
13. #10591368C2semidirect
14. #10591338C2semidirect
15. #10591293C2semidirect
75. #4961D3semidirect
77. #4960D3semidirect
98. C22×C3⋊Dic3D4semidirect
137. C2×D3×Dic3D4semidirect
138. C2×D3×Dic3D4semidirect
275. C22×C3×D3#41semidirect
281. C2×C32×C4#41semidirect
294. C2×C3⋊Dic3#41semidirect
312. C2×C3×Dic3#41semidirect
635. C22×D3#237semidirect
671. C2×C3×C4#237semidirect
672. C2×C3×C4#237semidirect
736. C2×Dic3#237semidirect
933. C32#2388semidirect
1006. C2×C4#3805semidirect
1084. C3#76665semidirect
1085. C3#76889semidirect

Maximal subgroups

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

subgroupindex
C22×#38052
C2×#67⋊Dic32
C2×#639022
C2×#638982
C22⋊C4×C3⋊Dic32
C3×#49612
C3×#49602
#105917232
#105917082
#105913902
#105913892
#105913682
#105913382
#105912932
#768893
#766653