Finite Group Databasebeta

← C2×#10594263 #11900962

Subgroups — C2×#10594263 #11900962

Order 1152.

4139 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic, complemented
2C22×#3802C211yesmaximal, characteristic, complemented
3C2×#64092C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×#882C211yesmaximal, characteristic, complemented
6C2×#63983C211yesmaximal, characteristic, complemented
7C2×#63976C211yesmaximal, characteristic, complemented
8C2×#63970C211yesmaximal, characteristic, complemented
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63908C211yesmaximal, characteristic, complemented
12C2×#63891C211yesmaximal, characteristic, complemented
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63884C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594263C2116yesmaximal, direct product factor
17C2×#5605—31nomaximal
18C2×#5589—31nomaximal
19C24×C3×D3C2211yescharacteristic, complemented
20C23×D32C2211yescharacteristic
21C23×D32C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic, complemented
26C22×C3×#67C2211yescharacteristic, complemented
27C22×C3×D12C2211yescharacteristic
28C22×C3×D12C2211yescharacteristic, complemented
29C22×C3×D12C2211yescharacteristic, complemented
30C22×C3×C4×D3C2211yescharacteristic, complemented
31C2×D3×#67—28no—
32C2×D3×#67C2218yescomplemented
33C22×#626C2211yescharacteristic
34C22×#625C2211yescharacteristic
35C22×#625C2211yescharacteristic, complemented
36C22×#625C2211yescharacteristic, complemented
37C22×#625C2211yescharacteristic, complemented
38C22×D3×Dic3C2211yescharacteristic, complemented
39C22×D3×Dic3C2211yescharacteristic, complemented
40C2×#3802—28no—
41C2×#3802C2218yescomplemented
42C2×C32×C22⋊C4C2211yescharacteristic, complemented
43C2×#3757C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47#64092C2218yescomplemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C3×#884C2218yescomplemented
53C3×#882C2218yescomplemented
54#63983C2218yescomplemented
55#63976C2218yescomplemented
56#63970C2218yescomplemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64#63922C2218yescomplemented
65D3×(C2×D3)⋊C4C2218yescomplemented
66#63908C2218yescomplemented
67#63891C2218yescomplemented
68#63885C2218yescomplemented
69#63884C2218yescomplemented
70#63853C2218yescomplemented
71C23×#67—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C22×D3×D4—31no—
75C2×C3×#121—31no—
76C2×C3×#120—31no—
77C2×#953—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#938—31no—
81C2×#938—31no—
82C2×#937—31no—
83C2×#937—31no—
84C2×#937—31no—
85C2×#937—31no—
86C2×#935—31no—
87C2×#930—31no—
88C22×(C2×D3)⋊C4—31no—
89#5605—316no—
90#5589—316no—
91C2×#894—31no—
92C2×#894—31no—
93C2×#886—31no—
94C2×#884—31no—
95C2×#884D311yescharacteristic, complemented
96C2×#883—31no—
97C2×#883—31no—
98C2×#883—31no—
99C2×#883—31no—
100C2×#883—61no—
101C2×#882—31no—
102C2×#882D311yescharacteristic, complemented
103C2×D3×C22⋊C4—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3—24no—
107C23×C3×D3—42no—
108C23×C3×D3—42no—
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2314yescomplemented
115C22×D32—24no—
116C22×D32—42no—
117C22×D32—42no—
118C22×D32—42no—
119C22×D32—42no—
120C22×D32D418yescomplemented
121C22×D32C2314yes—
122C22×D32C2314yescomplemented
123C22×C32×C4C2311yescharacteristic
124C22×C32×C4C2311yescharacteristic
125C2×#638—24no—
126C2×#638C2314yes—
127C22×C3⋊Dic3C2311yescharacteristic
128C22×C3⋊Dic3C2311yescharacteristic
129C22×C3⋊Dic3C2311yescharacteristic
130C2×C4×C3⋊D3—24no—
131C2×C4×C3⋊D3C2314yescomplemented
132C2×C3×#67—24no—
133C2×C3×#67—42no—
134C2×C3×#67—42no—
135C2×C3×#67C2314yescomplemented
136C2×C3×#67C2314yescomplemented
137C2×C3×#67C2314yescomplemented
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C2×C3×D12—24no—
142C2×C3×D12—24no—
143C2×C3×D12—42no—
144C2×C3×D12C2314yes—
145C2×C3×D12C2314yescomplemented
146C2×C3×D12C2314yescomplemented
147C2×C3×C4×D3—42no—
148C2×C3×C4×D3C2314yescomplemented
149D3×#67—232no—
150C2×#626—24no—
151C2×#626C2314yes—
152C2×#625—24no—
153C2×#625—24no—
154C2×#625—24no—
155C2×#625—42no—
156C2×#625C2314yes—
157C2×#625C2314yescomplemented
158C2×#625C2314yescomplemented
159C2×#625C2314yescomplemented
160C2×D3×Dic3—24no—
161C2×D3×Dic3—42no—
162C2×D3×Dic3C2314yescomplemented
163C2×D3×Dic3C2314yescomplemented
164#3802—232no—
165C32×C22⋊C4C2314yescomplemented
166#3757C2314yescomplemented
167#3752C2314yescomplemented
168C4⋊(C3⋊Dic3)C2314yescomplemented
169#3750C2314yescomplemented
170C3×(C2×D3)⋊C4C2314yescomplemented
171C3×(C2×D3)⋊C4C2314yescomplemented
172C3×(C2×D3)⋊C4C2314yescomplemented
173C3×Dic3⋊C4C2314yescomplemented
174Dic3⋊Dic3C2314yescomplemented
175#3722C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178(C2×D3)⋊Dic3C2314yescomplemented
179(C2×D3)⋊Dic3C2314yescomplemented
180(C2×D3)⋊Dic3C2314yescomplemented
181C2×#534—91noSylow
182C25×C3—31no—
183C24×D3—31no—
184C24×D3—31no—
185C24×D3—31no—
186C24×D3—31no—
187C24×D3C2×D311yescharacteristic, complemented
188C22×C3×D4—31no—
189C22×C3×D4—31no—
190C22×C3×D4—31no—
191C22×C3×D4—31no—
192C22×C3×D4—31no—
193C22×C3×D4—31no—
194C23×C3×C4—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—31no—
203C22×#67—31no—
204C22×#67—31no—
205C22×#67—38no—
206C22×#67—31no—
207C22×#67—61no—
208C22×#67—68no—
209C22×#67C2×D311yescharacteristic, complemented
210C22×#67C2×D311yescharacteristic, complemented
211C22×#67C2×D311yescharacteristic, complemented
212C23×Dic3—31no—
213C23×Dic3—31no—
214C2×D3×D4—38no—
215C2×D3×D4—38no—
216C2×D3×D4—38no—
217C2×D3×D4—68no—
218C2×D3×D4—68no—
219C2×D3×D4—68no—
220C22×D12—31no—
221C22×D12C2×D311yescharacteristic
222C22×D12C2×D311yescharacteristic, complemented
223C22×D12C2×D311yescharacteristic, complemented
224C22×C4×D3—31no—
225C22×C4×D3—31no—
226C22×C4×D3—31no—
227C22×C4×D3—31no—
228C22×C4×D3—61no—
229C22×C4×D3C2×D311yescharacteristic, complemented
230C3×#121—38no—
231C3×#120—38no—
232C2×C3×C4⋊C4—31no—
233C2×C3×C22⋊C4—21no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4—31no—
237C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
238C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
239#953—38no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—31no—
244C2×#217—31no—
245C2×#217—31no—
246C2×#217—31no—
247C2×#217—61no—
248#939—38no—
249#939—38no—
250#938—38no—
251#938—38no—
252#937—38no—
253#937—38no—
254#937—38no—
255#937—38no—
256#935—38no—
257#930—38no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—31no—
264C2×(C2×D3)⋊C4—31no—
265C2×(C2×D3)⋊C4—31no—
266C2×(C2×D3)⋊C4—31no—
267C2×(C2×D3)⋊C4—38no—
268C2×(C2×D3)⋊C4—61no—
269C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
270C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
271C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
272C2×C4⋊Dic3—31no—
273C2×C4⋊Dic3—31no—
274C2×C4⋊Dic3—31no—
275C2×C4⋊Dic3—61no—
276C2×Dic3⋊C4—31no—
277C2×Dic3⋊C4—31no—
278C2×Dic3⋊C4—31no—
279C2×Dic3⋊C4—61no—
280C2×Dic3⋊C4C2×D311yescharacteristic, complemented
281#894—38no—
282#894—38no—
283#886—38no—
284#884—38no—
285#884C2×D318yescomplemented
286#883—38no—
287#883—38no—
288#883—38no—
289#883—38no—
290#883—68no—
291#882—38no—
292#882C2×D318yescomplemented
293D3×C22⋊C4—38no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32C2412yes—
298C23×C32C2411yescharacteristic
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3C2×D414yes—
302C22×C3⋊D3C2412yes—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3—28no—
317C22×C3×D3—44no—
318C22×C3×D3—44no—
319C22×C3×D3—416no—
320C22×C3×D3C2×D414yes—
321C22×C3×D3C2×D414yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
324C22×C3×D3C2412yes—
325C22×C3×D3C2412yes—
326C22×C3×D3C2412yes—
327C2×D32—28no—
328C2×D32—416no—
329C2×D32—44no—
330C2×D32—44no—
331C2×D32—44no—
332C2×D32—44no—
333C2×D32—416no—
334C2×D32C2×D4116yescomplemented
335C2×C32×C4—22no—
336C2×C32×C4—22no—
337C2×C32×C4C2412yes—
338C2×C32×C4C2412yes—
339#638—28no—
340C2×C3⋊Dic3—22no—
341C2×C3⋊Dic3—22no—
342C2×C3⋊Dic3—22no—
343C2×C3⋊Dic3C2412yes—
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2412yes—
346C4×C3⋊D3—28no—
347C3×#67—28no—
348C3×#67—44no—
349C3×#67—44no—
350C2×C3×Dic3—22no—
351C2×C3×Dic3—22no—
352C2×C3×Dic3—22no—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C3×D12—28no—
357C3×D12—28no—
358C3×D12—44no—
359C3×C4×D3—44no—
360#626—28no—
361#625—28no—
362#625—28no—
363#625—28no—
364#625—44no—
365D3×Dic3—28no—
366D3×Dic3—44no—
367C23×D4—91no—
368C23×D4—91no—
369#534—916no—
370C2×#123—91no—
371C2×#123—91no—
372C2×#123—91no—
373C2×#123—91no—
374C2×#121—31no—
375C2×#121—91no—
376C2×#121—91no—
377C2×#121—91no—
378C2×#120—31no—
379C2×#120—91no—
380C2×#120—91no—
381C2×#120—91no—
382C22×C22⋊C4—91no—
383C24×C3—21no—
384C24×C3—31no—
385C24×C3—31no—
386C24×C3—31no—
387C24×C3—31no—
388C24×C3—31no—
389C24×C3—34no—
390C24×C3—64no—
391C24×C3—122no—
392C24×C3—122no—
393C24×C3C22×D311yescharacteristic
394C24×C3C22×D311yescharacteristic
395C23×D3—24no—
396C23×D3—31no—
397C23×D3—31no—
398C23×D3—38no—
399C23×D3—38no—
400C23×D3—34no—
401C23×D3—34no—
402C23×D3—34no—
403C23×D3—34no—
404C23×D3—42no—
405C23×D3—42no—
406C23×D3—61no—
407C23×D3—64no—
408C23×D3—64no—
409C23×D3—122no—
410C23×D3—122no—
411C23×D3—122no—
412C23×D3—122no—
413C23×D3—122no—
414C23×D3—122no—
415C23×D3—122no—
416C23×D3—122no—
417C23×D3C22×D311yescharacteristic
418C23×D3C22×D311yescharacteristic
419C23×D3C22×D311yescharacteristic
420C23×D3C22×D311yescharacteristic
421C23×D3C22×D311yescharacteristic
422C23×D3C22×D314yescomplemented
423C2×C3×D4—34no—
424C2×C3×D4—34no—
425C2×C3×D4—34no—
426C2×C3×D4—34no—
427C2×C3×D4—34no—
428C2×C3×D4—34no—
429C2×C3×D4—64no—
430C2×C3×D4—64no—
431C2×C3×D4—64no—
432C2×C3×D4—122no—
433C2×C3×D4—122no—
434C2×C3×D4—122no—
435C22×C3×C4—21no—
436C22×C3×C4—21no—
437C22×C3×C4—31no—
438C22×C3×C4—31no—
439C22×C3×C4—31no—
440C22×C3×C4—34no—
441C22×C3×C4—122no—
442C22×C3×C4C22×D311yescharacteristic
443C22×C3×C4C22×D311yescharacteristic
444C22×C3×C4C22×D311yescharacteristic
445C22×C3×C4C22×D311yescharacteristic
446C2×#67—24no—
447C2×#67—34no—
448C2×#67—34no—
449C2×#67—34no—
450C2×#67—34no—
451C2×#67—34no—
452C2×#67—34no—
453C2×#67—34no—
454C2×#67—34no—
455C2×#67—34no—
456C2×#67—34no—
457C2×#67—34no—
458C2×#67—42no—
459C2×#67—42no—
460C2×#67—64no—
461C2×#67—64no—
462C2×#67—632no—
463C2×#67—64no—
464C2×#67—64no—
465C2×#67—64no—
466C2×#67—64no—
467C2×#67—64no—
468C2×#67—64no—
469C2×#67—64no—
470C2×#67—64no—
471C2×#67—124no—
472C2×#67—122no—
473C2×#67—122no—
474C2×#67C22×D314yescomplemented
475C2×#67C22×D314yescomplemented
476C2×#67C22×D314yescomplemented
477C22×Dic3—31no—
478C22×Dic3—31no—
479C22×Dic3—31no—
480C22×Dic3—31no—
481C22×Dic3—31no—
482C22×Dic3—31no—
483C22×Dic3—34no—
484C22×Dic3—34no—
485C22×Dic3—61no—
486C22×Dic3—61no—
487C22×Dic3—61no—
488C22×Dic3—64no—
489C22×Dic3—122no—
490C22×Dic3C22×D311yescharacteristic
491C22×Dic3C22×D311yescharacteristic
492C22×Dic3C22×D311yescharacteristic
493D3×D4—632no—
494D3×D4—632no—
495D3×D4—632no—
496C2×D12—24no—
497C2×D12—24no—
498C2×D12—34no—
499C2×D12—42no—
500C2×D12—64no—
501C2×D12C22×D314yes—
502C2×D12C22×D314yescomplemented
503C2×D12C22×D314yescomplemented
504C2×C4×D3—34no—
505C2×C4×D3—34no—
506C2×C4×D3—34no—
507C2×C4×D3—34no—
508C2×C4×D3—42no—
509C2×C4×D3—64no—
510C2×C4×D3—64no—
511C2×C4×D3—64no—
512C2×C4×D3—64no—
513C2×C4×D3—124no—
514C2×C4×D3—122no—
515C2×C4×D3C22×D314yescomplemented
516C3×C4⋊C4—34no—
517C3×C22⋊C4—24no—
518C3×C22⋊C4—34no—
519C3×C22⋊C4—34no—
520C3×C22⋊C4—34no—
521C3×C22⋊C4C22×D314yescomplemented
522C3×C22⋊C4C22×D314yescomplemented
523#217—34no—
524#217—34no—
525#217—34no—
526#217—34no—
527#217—34no—
528#217—34no—
529#217—34no—
530#217—64no—
531(C2×D3)⋊C4—34no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—34no—
534(C2×D3)⋊C4—34no—
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—34no—
540(C2×D3)⋊C4—64no—
541(C2×D3)⋊C4C22×D314yescomplemented
542(C2×D3)⋊C4C22×D314yescomplemented
543(C2×D3)⋊C4C22×D314yescomplemented
544C4⋊Dic3—34no—
545C4⋊Dic3—34no—
546C4⋊Dic3—34no—
547C4⋊Dic3—64no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—34no—
551Dic3⋊C4—64no—
552Dic3⋊C4C22×D314yescomplemented
553C22×C32—22no—
554C22×C32—22no—
555C22×C32—22no—
556C22×C32—44no—
557C22×C32C22×D412yes—
558C22×C32H(5,𝔽2)12yes—
559C22×C32H(5,𝔽2)12yes—
560C22×C32C2511yescharacteristic
561C2×C3⋊D3—28no—
562C2×C3⋊D3—22no—
563C2×C3⋊D3—22no—
564C2×C3⋊D3C22×D414yes—
565C2×C3×D3—28no—
566C2×C3×D3—28no—
567C2×C3×D3—22no—
568C2×C3×D3—22no—
569C2×C3×D3—22no—
570C2×C3×D3—22no—
571C2×C3×D3—22no—
572C2×C3×D3—22no—
573C2×C3×D3—22no—
574C2×C3×D3—22no—
575C2×C3×D3—22no—
576C2×C3×D3—22no—
577C2×C3×D3—22no—
578C2×C3×D3—22no—
579C2×C3×D3—22no—
580C2×C3×D3—416no—
581C2×C3×D3—44no—
582C2×C3×D3—44no—
583C2×C3×D3—44no—
584C2×C3×D3C22×D414yes—
585C2×C3×D3C22×D414yes—
586D32—416no—
587D32—416no—
588C32×C4—22no—
589C32×C4—22no—
590C3⋊Dic3—22no—
591C3⋊Dic3—22no—
592C3⋊Dic3—22no—
593C3×Dic3—22no—
594C3×Dic3—22no—
595C3×Dic3—22no—
596C25—31no—
597C25—91no—
598C25—91no—
599C22×D4—31no—
600C22×D4—31no—
601C22×D4—31no—
602C22×D4—31no—
603C22×D4—31no—
604C22×D4—31no—
605C22×D4—91no—
606C22×D4—98no—
607C22×D4—98no—
608C22×D4—91no—
609C22×D4—91no—
610C22×D4—91no—
611C22×D4—91no—
612C22×D4—91no—
613C22×D4—188no—
614C22×D4—188no—
615C23×C4—31no—
616C23×C4—91no—
617C23×C4—91no—
618C23×C4—91no—
619#123—98no—
620#123—98no—
621#123—98no—
622#123—98no—
623#121—38no—
624#121—98no—
625#121—98no—
626#121—98no—
627#120—38no—
628#120—98no—
629#120—98no—
630#120—98no—
631C2×C4⋊C4—31no—
632C2×C4⋊C4—91no—
633C2×C4⋊C4—91no—
634C2×C4⋊C4—91no—
635C2×C22⋊C4—31no—
636C2×C22⋊C4—31no—
637C2×C22⋊C4—31no—
638C2×C22⋊C4—98no—
639C2×C22⋊C4—91no—
640C2×C22⋊C4—91no—
641C2×C22⋊C4—91no—
642C2×C22⋊C4—91no—
643C2×C22⋊C4—91no—
644C2×C22⋊C4—91no—
645C2×C22⋊C4—91no—
646C2×C22⋊C4—91no—
647C2×C22⋊C4D3211yescharacteristic, complemented
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—22no—
651C23×C3—22no—
652C23×C3—22no—
653C23×C3—22no—
654C23×C3—22no—
655C23×C3—21no—
656C23×C3—34no—
657C23×C3—34no—
658C23×C3—32no—
659C23×C3—32no—
660C23×C3—32no—
661C23×C3—32no—
662C23×C3—32no—
663C23×C3—42no—
664C23×C3—42no—
665C23×C3—42no—
666C23×C3—68no—
667C23×C3—62no—
668C23×C3—62no—
669C23×C3—62no—
670C23×C3—62no—
671C23×C3—62no—
672C23×C3—62no—
673C23×C3—62no—
674C23×C3—62no—
675C23×C3—62no—
676C23×C3—62no—
677C23×C3—62no—
678C23×C3—62no—
679C23×C3—62no—
680C23×C3—124no—
681C23×C3—124no—
682C23×C3—1216no—
683C23×C3C23×D312yes—
684C23×C3C23×D312yes—
685C23×C3C23×D311yescharacteristic
686C23×C3C23×D311yescharacteristic
687C22×D3—22no—
688C22×D3—22no—
689C22×D3—22no—
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—22no—
693C22×D3—22no—
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—22no—
698C22×D3—22no—
699C22×D3—22no—
700C22×D3—28no—
701C22×D3—34no—
702C22×D3—34no—
703C22×D3—32no—
704C22×D3—32no—
705C22×D3—316no—
706C22×D3—316no—
707C22×D3—44no—
708C22×D3—44no—
709C22×D3—416no—
710C22×D3—64no—
711C22×D3—62no—
712C22×D3—68no—
713C22×D3—68no—
714C22×D3—62no—
715C22×D3—62no—
716C22×D3—62no—
717C22×D3—62no—
718C22×D3—122no—
719C22×D3—122no—
720C22×D3—124no—
721C22×D3—124no—
722C22×D3—124no—
723C22×D3—124no—
724C22×D3—1216no—
725C22×D3—1216no—
726C22×D3—124no—
727C22×D3—124no—
728C22×D3—124no—
729C22×D3—124no—
730C22×D3—1216no—
731C22×D3—1216no—
732C22×D3D3×D414yes—
733C22×D3D3×D414yes—
734C22×D3C23×D312yes—
735C22×D3C23×D312yes—
736C22×D3C23×D312yes—
737C22×D3C23×D312yes—
738C22×D3C23×D312yes—
739C3×D4—68no—
740C3×D4—68no—
741C3×D4—68no—
742C3×D4—124no—
743C3×D4—124no—
744C3×D4—124no—
745C2×C3×C4—22no—
746C2×C3×C4—22no—
747C2×C3×C4—22no—
748C2×C3×C4—22no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—32no—
752C2×C3×C4—32no—
753C2×C3×C4—32no—
754C2×C3×C4—42no—
755C2×C3×C4—42no—
756C2×C3×C4—62no—
757C2×C3×C4—62no—
758C2×C3×C4—62no—
759C2×C3×C4—124no—
760C2×C3×C4C23×D312yes—
761C2×C3×C4C23×D312yes—
762C2×C3×C4C23×D312yes—
763C2×C3×C4C23×D312yes—
764#67—28no—
765#67—44no—
766#67—44no—
767#67—68no—
768#67—68no—
769#67—68no—
770#67—68no—
771#67—68no—
772#67—68no—
773#67—68no—
774#67—68no—
775#67—68no—
776#67—128no—
777#67—124no—
778#67—124no—
779C2×Dic3—22no—
780C2×Dic3—22no—
781C2×Dic3—22no—
782C2×Dic3—32no—
783C2×Dic3—32no—
784C2×Dic3—32no—
785C2×Dic3—32no—
786C2×Dic3—32no—
787C2×Dic3—32no—
788C2×Dic3—62no—
789C2×Dic3—62no—
790C2×Dic3—62no—
791C2×Dic3—68no—
792C2×Dic3—62no—
793C2×Dic3—62no—
794C2×Dic3—62no—
795C2×Dic3—62no—
796C2×Dic3—62no—
797C2×Dic3—62no—
798C2×Dic3—122no—
799C2×Dic3—122no—
800C2×Dic3—122no—
801C2×Dic3—124no—
802C2×Dic3C23×D312yes—
803C2×Dic3C23×D312yes—
804C2×Dic3C23×D312yes—
805D12—28no—
806D12—28no—
807D12—44no—
808D12—68no—
809C4×D3—44no—
810C4×D3—68no—
811C4×D3—68no—
812C4×D3—68no—
813C4×D3—128no—
814C4×D3—124no—
815C2×C32—42no—
816C2×C32#53414yescomplemented
817C2×C32C23×D411yescharacteristic
818C2×C32C2×H(5,𝔽2)11yescharacteristic
819C2×C32C2×H(5,𝔽2)11yescharacteristic
820C3⋊D3—24no—
821C3×D3—24no—
822C3×D3—24no—
823C3×D3—42no—
824C3×D3—42no—
825C3×D3—42no—
826C24—31no—
827C24—31no—
828C24—31no—
829C24—31no—
830C24—31no—
831C24—34no—
832C24—64no—
833C24—94no—
834C24—98no—
835C24—94no—
836C24—91no—
837C24—122no—
838C24—122no—
839C24—184no—
840C24—362no—
841C24—362no—
842C24—362no—
843C24—362no—
844C24C2×D3211yescharacteristic
845C2×D4—34no—
846C2×D4—34no—
847C2×D4—34no—
848C2×D4—34no—
849C2×D4—34no—
850C2×D4—34no—
851C2×D4—64no—
852C2×D4—64no—
853C2×D4—64no—
854C2×D4—94no—
855C2×D4—94no—
856C2×D4—94no—
857C2×D4—94no—
858C2×D4—94no—
859C2×D4—94no—
860C2×D4—122no—
861C2×D4—122no—
862C2×D4—122no—
863C2×D4—184no—
864C2×D4—1832no—
865C2×D4—1832no—
866C2×D4—184no—
867C2×D4—184no—
868C2×D4—184no—
869C2×D4—184no—
870C2×D4—362no—
871C22×C4—31no—
872C22×C4—31no—
873C22×C4—31no—
874C22×C4—34no—
875C22×C4—94no—
876C22×C4—94no—
877C22×C4—91no—
878C22×C4—91no—
879C22×C4—91no—
880C22×C4—94no—
881C22×C4—122no—
882C22×C4—184no—
883C22×C4—184no—
884C22×C4—362no—
885C22×C4C2×D3211yescharacteristic
886C22×C4C2×D3211yescharacteristic
887C4⋊C4—34no—
888C4⋊C4—94no—
889C4⋊C4—94no—
890C4⋊C4—94no—
891C22⋊C4—34no—
892C22⋊C4—34no—
893C22⋊C4—34no—
894C22⋊C4—94no—
895C22⋊C4—94no—
896C22⋊C4—94no—
897C22⋊C4—94no—
898C22⋊C4—94no—
899C22⋊C4—94no—
900C22⋊C4—94no—
901C22⋊C4—94no—
902C22⋊C4C2×D3214yescomplemented
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—22no—
907C22×C3—22no—
908C22×C3—22no—
909C22×C3—22no—
910C22×C3—22no—
911C22×C3—22no—
912C22×C3—21no—
913C22×C3—34no—
914C22×C3—34no—
915C22×C3—42no—
916C22×C3—42no—
917C22×C3—42no—
918C22×C3—44no—
919C22×C3—44no—
920C22×C3—62no—
921C22×C3—62no—
922C22×C3—62no—
923C22×C3—62no—
924C22×C3—68no—
925C22×C3—68no—
926C22×C3—62no—
927C22×C3—62no—
928C22×C3—62no—
929C22×C3—62no—
930C22×C3—62no—
931C22×C3—62no—
932C22×C3—62no—
933C22×C3—62no—
934C22×C3—62no—
935C22×C3—84no—
936C22×C3—1216no—
937C22×C3—124no—
938C22×C3—124no—
939C22×C3—124no—
940C22×C3C2×D3×D412yes—
941C22×C3C2×D3×D412yes—
942C22×C3#100412yes—
943C22×C3#100412yes—
944C22×C3#100412yes—
945C22×C3#100912yes—
946C22×C3C24×D311yescharacteristic
947C22×C3C24×D311yescharacteristic
948C2×D3—22no—
949C2×D3—22no—
950C2×D3—22no—
951C2×D3—22no—
952C2×D3—28no—
953C2×D3—28no—
954C2×D3—22no—
955C2×D3—22no—
956C2×D3—22no—
957C2×D3—22no—
958C2×D3—22no—
959C2×D3—22no—
960C2×D3—22no—
961C2×D3—22no—
962C2×D3—22no—
963C2×D3—34no—
964C2×D3—34no—
965C2×D3—416no—
966C2×D3—44no—
967C2×D3—44no—
968C2×D3—44no—
969C2×D3—64no—
970C2×D3—62no—
971C2×D3—62no—
972C2×D3—62no—
973C2×D3—62no—
974C2×D3—68no—
975C2×D3—68no—
976C2×D3—122no—
977C2×D3—122no—
978C2×D3—128no—
979C2×D3—1216no—
980C2×D3—1216no—
981C2×D3—1216no—
982C2×D3—1216no—
983C2×D3C2×D3×D414yes—
984C2×D3C2×D3×D414yes—
985C3×C4—22no—
986C3×C4—22no—
987C3×C4—22no—
988C3×C4—22no—
989C3×C4—42no—
990C3×C4—42no—
991C3×C4—62no—
992C3×C4—62no—
993C3×C4—62no—
994Dic3—22no—
995Dic3—22no—
996Dic3—22no—
997Dic3—62no—
998Dic3—62no—
999Dic3—62no—
1000Dic3—62no—
1001Dic3—62no—
1002Dic3—62no—
1003Dic3—122no—
1004Dic3—122no—
1005Dic3—122no—
1006C32C2×#53411yescharacteristic, complemented, Sylow
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—34no—
1011C23—34no—
1012C23—32no—
1013C23—32no—
1014C23—32no—
1015C23—32no—
1016C23—32no—
1017C23—68no—
1018C23—62no—
1019C23—62no—
1020C23—62no—
1021C23—62no—
1022C23—62no—
1023C23—62no—
1024C23—62no—
1025C23—62no—
1026C23—62no—
1027C23—62no—
1028C23—62no—
1029C23—62no—
1030C23—62no—
1031C23—916no—
1032C23—94no—
1033C23—92no—
1034C23—124no—
1035C23—124no—
1036C23—1216no—
1037C23—188no—
1038C23—182no—
1039C23—182no—
1040C23—364no—
1041C23—364no—
1042C23—3616no—
1043C23—364no—
1044C23—364no—
1045C23—3616no—
1046C23C22×D3212yes—
1047C23C22×D3211yescharacteristic
1048D4—68no—
1049D4—68no—
1050D4—68no—
1051D4—124no—
1052D4—124no—
1053D4—124no—
1054D4—188no—
1055D4—188no—
1056D4—188no—
1057D4—188no—
1058D4—188no—
1059D4—364no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—32no—
1063C2×C4—32no—
1064C2×C4—32no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—92no—
1069C2×C4—92no—
1070C2×C4—92no—
1071C2×C4—124no—
1072C2×C4—188no—
1073C2×C4—188no—
1074C2×C4—182no—
1075C2×C4—182no—
1076C2×C4—182no—
1077C2×C4—364no—
1078C2×C4C22×D3212yes—
1079C2×C4C22×D3212yes—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—24no—
1084C2×C3—42no—
1085C2×C3—42no—
1086C2×C3—64no—
1087C2×C3—64no—
1088C2×C3—82no—
1089C2×C3—122no—
1090C2×C3—122no—
1091C2×C3—122no—
1092C2×C3#558914yescomplemented
1093C2×C3#560514yescomplemented
1094C2×C3C22×D3×D411yescharacteristic
1095C2×C3C22×D3×D411yescharacteristic
1096C2×C3C2×#100411yescharacteristic
1097C2×C3C2×#100411yescharacteristic
1098C2×C3C2×#100411yescharacteristic
1099C2×C3C2×#100911yescharacteristic
1100D3—24no—
1101D3—24no—
1102D3—42no—
1103D3—42no—
1104D3—42no—
1105D3—64no—
1106D3—64no—
1107D3—124no—
1108C22—22no—
1109C22—22no—
1110C22—22no—
1111C22—34no—
1112C22—34no—
1113C22—44no—
1114C22—62no—
1115C22—62no—
1116C22—62no—
1117C22—62no—
1118C22—68no—
1119C22—68no—
1120C22—62no—
1121C22—62no—
1122C22—62no—
1123C22—62no—
1124C22—62no—
1125C22—62no—
1126C22—62no—
1127C22—62no—
1128C22—62no—
1129C22—94no—
1130C22—1216no—
1131C22—124no—
1132C22—124no—
1133C22—124no—
1134C22—182no—
1135C22—182no—
1136C22—188no—
1137C22—3616no—
1138C22—3616no—
1139C22#6430712yes—
1140C22D32×D412yes—
1141C22#6431312yes—
1142C22C23×D3211yescharacteristic
1143C4—22no—
1144C4—22no—
1145C4—62no—
1146C4—62no—
1147C4—62no—
1148C4—182no—
1149C4—182no—
1150C4—182no—
1151C3—21no—
1152C3C2×#558911yescharacteristic, complemented
1153C3C2×#560511yescharacteristic, complemented
1154C2—42no—
1155C2—64no—
1156C2—64no—
1157C2—122no—
1158C2—122no—
1159C2—122no—
1160C2—184no—
1161C2#1059426314yesdirect product factor
1162C2C2×#6430711yescharacteristic
1163C2C2×D32×D411yescharacteristic
1164C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×#67C2semidirect
2. C22×#3802C2semidirect
3. C2×#64092C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×#882C2semidirect
6. C2×#63983C2semidirect
7. C2×#63976C2semidirect
8. C2×#63970C2semidirect
9. C2×#63922C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63908C2semidirect
12. C2×#63891C2semidirect
13. C2×#63885C2semidirect
14. C2×#63884C2semidirect
15. C2×#63853C2semidirect
16. #10594263C2direct (N × H)
19. C24×C3×D3C22semidirect
21. C23×D32C22semidirect
23. C22×C4×C3⋊D3C22semidirect
24. C22×C3×#67C22semidirect
25. C22×C3×#67C22semidirect
26. C22×C3×#67C22semidirect
28. C22×C3×D12C22semidirect
29. C22×C3×D12C22semidirect
30. C22×C3×C4×D3C22semidirect
32. C2×D3×#67C22semidirect
35. C22×#625C22semidirect
36. C22×#625C22semidirect
37. C22×#625C22semidirect
38. C22×D3×Dic3C22semidirect
39. C22×D3×Dic3C22semidirect
41. C2×#3802C22semidirect
42. C2×C32×C22⋊C4C22semidirect
43. C2×#3757C22semidirect
44. C2×#3752C22semidirect
45. C2×C4⋊(C3⋊Dic3)C22semidirect
46. C2×#3750C22semidirect
47. #64092C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C3×#884C22semidirect
53. C3×#882C22semidirect
54. #63983C22semidirect
55. #63976C22semidirect
56. #63970C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63922C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. #63908C22semidirect
67. #63891C22semidirect
68. #63885C22semidirect
69. #63884C22semidirect
70. #63853C22semidirect
95. C2×#884D3semidirect
102. C2×#882D3semidirect
114. C23×C3×D3C23semidirect
120. C22×D32D4semidirect
122. C22×D32C23semidirect
131. C2×C4×C3⋊D3C23semidirect
135. C2×C3×#67C23semidirect
136. C2×C3×#67C23semidirect
137. C2×C3×#67C23semidirect
145. C2×C3×D12C23semidirect
146. C2×C3×D12C23semidirect
148. C2×C3×C4×D3C23semidirect
157. C2×#625C23semidirect
158. C2×#625C23semidirect
159. C2×#625C23semidirect
162. C2×D3×Dic3C23semidirect
163. C2×D3×Dic3C23semidirect
165. C32×C22⋊C4C23semidirect
166. #3757C23semidirect
167. #3752C23semidirect
168. C4⋊(C3⋊Dic3)C23semidirect
169. #3750C23semidirect
170. C3×(C2×D3)⋊C4C23semidirect
171. C3×(C2×D3)⋊C4C23semidirect
172. C3×(C2×D3)⋊C4C23semidirect
173. C3×Dic3⋊C4C23semidirect
174. Dic3⋊Dic3C23semidirect
175. #3722C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
178. (C2×D3)⋊Dic3C23semidirect
179. (C2×D3)⋊Dic3C23semidirect
180. (C2×D3)⋊Dic3C23semidirect
187. C24×D3C2×D3semidirect
209. C22×#67C2×D3semidirect
210. C22×#67C2×D3semidirect
211. C22×#67C2×D3semidirect
222. C22×D12C2×D3semidirect
223. C22×D12C2×D3semidirect
229. C22×C4×D3C2×D3semidirect
237. C2×C3×C22⋊C4C2×D3semidirect
238. C2×C3×C22⋊C4C2×D3semidirect
269. C2×(C2×D3)⋊C4C2×D3semidirect
270. C2×(C2×D3)⋊C4C2×D3semidirect
271. C2×(C2×D3)⋊C4C2×D3semidirect
280. C2×Dic3⋊C4C2×D3semidirect
285. #884C2×D3semidirect
292. #882C2×D3semidirect
334. C2×D32C2×D4semidirect
422. C23×D3C22×D3semidirect
474. C2×#67C22×D3semidirect
475. C2×#67C22×D3semidirect
476. C2×#67C22×D3semidirect
502. C2×D12C22×D3semidirect
503. C2×D12C22×D3semidirect
515. C2×C4×D3C22×D3semidirect
521. C3×C22⋊C4C22×D3semidirect
522. C3×C22⋊C4C22×D3semidirect
541. (C2×D3)⋊C4C22×D3semidirect
542. (C2×D3)⋊C4C22×D3semidirect
543. (C2×D3)⋊C4C22×D3semidirect
552. Dic3⋊C4C22×D3semidirect
647. C2×C22⋊C4D32semidirect
816. C2×C32#534semidirect
902. C22⋊C4C2×D32semidirect
1006. C32C2×#534semidirect
1092. C2×C3#5589semidirect
1093. C2×C3#5605semidirect
1152. C3C2×#5589semidirect
1153. C3C2×#5605semidirect
1161. C2#10594263direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#672
C22×#38022
C2×#640922
C2×C3×#8842
C2×C3×#8822
C2×#639832
C2×#639762
C2×#639702
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639082
C2×#638912
C2×#638852
C2×#638842
C2×#638532
#105942632
C2×#56053
C2×#55893