Finite Group Databasebeta

← C2×C11×#3345 #14638430

Subgroups — C2×C11×#3345 #14638430

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic, complemented
2C2×C11×#547C211yesmaximal, characteristic, complemented
3C11×#3345C2116yesmaximal, direct product factor
4C2×C11×#501C211yesmaximal, characteristic, complemented
5C2×C11×#481C211yesmaximal, characteristic, complemented
6C2×C11×#481C211yesmaximal, characteristic, complemented
7C2×C11×#482C211yesmaximal, characteristic, complemented
8C2×C11×#480C211yesmaximal, characteristic, complemented
9C2×C11×#478C211yesmaximal, characteristic, complemented
10C2×C11×#476C211yesmaximal, characteristic, complemented
11C2×C11×#469C211yesmaximal, characteristic, complemented
12C2×C11×#466C211yesmaximal, characteristic, complemented
13C2×C11×#442C211yesmaximal, characteristic, complemented
14C2×C11×#435C211yesmaximal, characteristic, complemented
15C2×C11×#428C211yesmaximal, characteristic, complemented
16C22×C11×#106C211yesmaximal, characteristic, complemented
17C22×C11×#41—21no—
18C22×C11×D8C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C11×#553—24no—
22C11×#553C2218yescomplemented
23C11×#547—24no—
24C11×#547C2218yescomplemented
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#126—21no—
27C2×C11×#125C2211yescharacteristic
28C2×C11×#123—21no—
29C2×C11×#123—21no—
30C2×C11×#123—21no—
31C2×C11×C22⋊Q8—21no—
32C2×C11×#121—21no—
33C2×C11×#121C2211yescharacteristic
34C2×C11×#121C2211yescharacteristic
35C2×C11×#121C2211yescharacteristic
36C2×C11×#121C2211yescharacteristic
37C2×C4×D4×C11—21no—
38C2×C4×D4×C11C2211yescharacteristic
39C2×C4×D4×C11C2211yescharacteristic
40C2×C4×D4×C11C2211yescharacteristic
41C2×C11×#117C2211yescharacteristic
42C22×C11×C4⋊C4C2211yescharacteristic
43C22×C11×C4⋊C4C2211yescharacteristic
44C22×C11×C4⋊C4C2211yescharacteristic
45C11×#501C2218yescomplemented
46C11×#482C2218yescomplemented
47C11×#481C2218yescomplemented
48C11×#481C2218yescomplemented
49C11×#480C2218yescomplemented
50C11×#478C2218yescomplemented
51C11×#476C2218yescomplemented
52C11×#469C2218yescomplemented
53C11×#466C2218yescomplemented
54C11×#442C2218yescomplemented
55C11×#435C2218yescomplemented
56C11×#428C2218yescomplemented
57C2×C11×#107C2211yescharacteristic
58C2×C11×#107C2211yescharacteristic
59C2×C11×#107C2211yescharacteristic
60C2×C11×#106C2211yescharacteristic
61C2×C11×#106C2211yescharacteristic
62C2×C11×#106C2211yescharacteristic
63C2×C11×#106C2211yescharacteristic
64C2×C11×#106C2211yescharacteristic
65C2×C11×#106C2211yescharacteristic
66C2×C11×#106C2218yescomplemented
67C2×C11×C4⋊C8C2211yescharacteristic
68C2×C11×#102C2211yescharacteristic
69C2×C11×#102C2211yescharacteristic
70C2×C11×#102C2211yescharacteristic
71C2×C11×#102C2211yescharacteristic
72C2×C11×#102C2211yescharacteristic
73C2×C11×#102C2211yescharacteristic
74C2×C11×C22⋊C8C2211yescharacteristic
75C2×C11×C22⋊C8C2211yescharacteristic
76C2×C11×#97C2211yescharacteristic
77C2×C11×#41—28no—
78C2×C11×#41—48no—
79C22×Q8×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11D411yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C23×C4×C11—21no—
91C23×C4×C11—21no—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C2×C11×D8—24no—
95C2×C11×D8C2314yes—
96C2×C11×M16—24no—
97C2×C11×M16C2314yes—
98C22×C8×C11—24no—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2314yes—
103C22×C8×C11C2311yescharacteristic
104C11×C4⋊Q8—22no—
105C11×C4⋊Q8C2314yes—
106C11×#126—28no—
107C11×#125—22no—
108C11×#125C2314yes—
109C11×#123—28no—
110C11×#123—28no—
111C11×#123—28no—
112C11×C22⋊Q8—28no—
113C11×#121—28no—
114C11×#121—22no—
115C11×#121—22no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121C2314yes—
119C11×#121C2314yes—
120C11×#121C2314yes—
121C11×#121C2314yes—
122C4×D4×C11—28no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C4×D4×C11D414yes—
126C4×D4×C11C2314yes—
127C4×D4×C11C2314yes—
128C4×D4×C11C2314yes—
129C11×#117—22no—
130C11×#117C2314yes—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—22no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4—22no—
137C2×C11×C4⋊C4—21no—
138C2×C11×C4⋊C4—21no—
139C2×C11×C4⋊C4—21no—
140C2×C11×C4⋊C4D411yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2314yes—
147C2×C11×C4⋊C4C2314yes—
148C2×C11×C4⋊C4C2314yes—
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C22⋊C4—21no—
151C2×C11×C22⋊C4—21no—
152C2×C11×C22⋊C4—21no—
153C2×C11×C22⋊C4—21no—
154C2×C11×C22⋊C4—21no—
155C2×C11×C22⋊C4—21no—
156C2×C11×C22⋊C4—21no—
157C2×C11×C22⋊C4D411yescharacteristic
158C2×C11×C22⋊C4D411yescharacteristic
159C2×C42×C11—21no—
160C2×C42×C11C2311yescharacteristic
161C11×#107C2314yes—
162C11×#107C2314yes—
163C11×#107C2314yes—
164C11×#106C2314yes—
165C11×#106C2314yes—
166C11×#106C2314yes—
167C11×#106C2314yes—
168C11×#106C2314yes—
169C11×#106C2314yes—
170C11×C4⋊C8C2314yes—
171C11×#102C2314yes—
172C11×#102C2314yes—
173C11×#102C2314yes—
174C11×#102C2314yes—
175C11×#102C2314yes—
176C11×#102C2314yes—
177C11×C22⋊C8C2314yes—
178C11×C22⋊C8C2314yes—
179C11×#97C2314yes—
180C2×#3345C1111yesmaximal, characteristic, direct product factor, Sylow
181C24×C11—21no—
182C24×C11—21no—
183C24×C11C2×D411yescharacteristic
184C24×C11C2×D411yescharacteristic
185C11×#41—432no—
186C2×Q8×C11—24no—
187C2×Q8×C11—44no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—44no—
200C2×D4×C11—44no—
201C2×D4×C11—44no—
202C2×D4×C11—82no—
203C2×D4×C11C2×D414yes—
204C2×D4×C11C2412yes—
205C2×D4×C11C2412yes—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—24no—
211C22×C4×C11—24no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—24no—
219C22×C4×C11—24no—
220C22×C4×C11—24no—
221C22×C4×C11—44no—
222C22×C4×C11—44no—
223C22×C4×C11—44no—
224C22×C4×C11—82no—
225C22×C4×C11—82no—
226C22×C4×C11C2×D412yes—
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C22×C4×C11C2411yescharacteristic
235C11×D8—28no—
236C11×M16—28no—
237C2×C8×C11—28no—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11—22no—
241C2×C8×C11#4114yescomplemented
242C2×C8×C11C2412yes—
243C2×C8×C11C2412yes—
244C2×C8×C11C2412yes—
245C2×C8×C11C2412yes—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—24no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4C2×D414yes—
259C11×C4⋊C4C2412yes—
260C11×C4⋊C4C2412yes—
261C11×C4⋊C4C2412yes—
262C11×C4⋊C4C2412yes—
263C11×C4⋊C4C2412yes—
264C11×C4⋊C4C2412yes—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4—24no—
269C11×C22⋊C4—24no—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—24no—
272C11×C22⋊C4C2×D414yes—
273C11×C22⋊C4C2×D414yes—
274C42×C11—24no—
275C42×C11C2×D412yes—
276C42×C11C2412yes—
277C2×#553C2×C1111yescharacteristic, complemented
278C2×#547C2×C1111yescharacteristic, complemented
279#3345C2×C11116yesdirect product factor
280C2×#501C2×C1111yescharacteristic, complemented
281C2×#481C2×C1111yescharacteristic, complemented
282C2×#481C2×C1111yescharacteristic, complemented
283C2×#482C2×C1111yescharacteristic, complemented
284C2×#480C2×C1111yescharacteristic, complemented
285C2×#478C2×C1111yescharacteristic, complemented
286C2×#476C2×C1111yescharacteristic, complemented
287C2×#469C2×C1111yescharacteristic, complemented
288C2×#466C2×C1111yescharacteristic, complemented
289C2×#442C2×C1111yescharacteristic, complemented
290C2×#435C2×C1111yescharacteristic, complemented
291C2×#428C2×C1111yescharacteristic, complemented
292C22×#106C2×C1111yescharacteristic, complemented
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11AGL(1,ℤ/8)14yes—
307C23×C11C22×D412yes—
308C23×C11C22×D412yes—
309C23×C11C22×D411yescharacteristic
310Q8×C11—48no—
311D4×C11—28no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—48no—
317D4×C11—48no—
318D4×C11—48no—
319D4×C11—42no—
320D4×C11—42no—
321D4×C11—84no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—24no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—48no—
339C2×C4×C11—48no—
340C2×C4×C11—42no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—48no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11—42no—
347C2×C4×C11—84no—
348C2×C4×C11—84no—
349C2×C4×C11C22×D412yes—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4112yes—
355C2×C4×C112−1+412yes—
356C2×C4×C11C2511yescharacteristic
357C8×C11—22no—
358C8×C11—22no—
359C8×C11—22no—
360C8×C11C2×#4114yescomplemented
361C22×#41—21no—
362C22×D8C22×C1111yescharacteristic
363C22×M16C22×C1111yescharacteristic
364C23×C8C22×C1111yescharacteristic
365#553—24no—
366#553C22×C1118yescomplemented
367#547—24no—
368#547C22×C1118yescomplemented
369C2×C4⋊Q8C22×C1111yescharacteristic
370C2×#126—21no—
371C2×#125C22×C1111yescharacteristic
372C2×#123—21no—
373C2×#123—21no—
374C2×#123—21no—
375C2×C22⋊Q8—21no—
376C2×#121—21no—
377C2×#121C22×C1111yescharacteristic
378C2×#121C22×C1111yescharacteristic
379C2×#121C22×C1111yescharacteristic
380C2×#121C22×C1111yescharacteristic
381C2×C4×D4—21no—
382C2×C4×D4C22×C1111yescharacteristic
383C2×C4×D4C22×C1111yescharacteristic
384C2×C4×D4C22×C1111yescharacteristic
385C2×#117C22×C1111yescharacteristic
386C22×C4⋊C4C22×C1111yescharacteristic
387C22×C4⋊C4C22×C1111yescharacteristic
388C22×C4⋊C4C22×C1111yescharacteristic
389#501C22×C1118yescomplemented
390#482C22×C1118yescomplemented
391#481C22×C1118yescomplemented
392#481C22×C1118yescomplemented
393#480C22×C1118yescomplemented
394#478C22×C1118yescomplemented
395#476C22×C1118yescomplemented
396#469C22×C1118yescomplemented
397#466C22×C1118yescomplemented
398#442C22×C1118yescomplemented
399#435C22×C1118yescomplemented
400#428C22×C1118yescomplemented
401C2×#107C22×C1111yescharacteristic
402C2×#107C22×C1111yescharacteristic
403C2×#107C22×C1111yescharacteristic
404C2×#106C22×C1111yescharacteristic
405C2×#106C22×C1111yescharacteristic
406C2×#106C22×C1111yescharacteristic
407C2×#106C22×C1111yescharacteristic
408C2×#106C22×C1111yescharacteristic
409C2×#106C22×C1111yescharacteristic
410C2×#106C22×C1118yescomplemented
411C2×C4⋊C8C22×C1111yescharacteristic
412C2×#102C22×C1111yescharacteristic
413C2×#102C22×C1111yescharacteristic
414C2×#102C22×C1111yescharacteristic
415C2×#102C22×C1111yescharacteristic
416C2×#102C22×C1111yescharacteristic
417C2×#102C22×C1111yescharacteristic
418C2×C22⋊C8C22×C1111yescharacteristic
419C2×C22⋊C8C22×C1111yescharacteristic
420C2×#97C22×C1111yescharacteristic
421C22×C11—28no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—44no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—84no—
435C22×C11—84no—
436C22×C11#54712yes—
437C22×C11C2×AGL(1,ℤ/8)14yes—
438C22×C11C2×AGL(1,ℤ/8)12yes—
439C22×C11#57712yes—
440C22×C11C23×D411yescharacteristic
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—22no—
444C4×C11—22no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11#54712yes—
452C4×C11C22×#4111yescharacteristic
453C4×C11C2×2−1+411yescharacteristic
454C2×#41—28no—
455C2×#41—48no—
456C22×Q8—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4D4×C1111yescharacteristic
462C22×D4C23×C1111yescharacteristic
463C22×D4C23×C1111yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C1111yescharacteristic
470C23×C4C23×C1111yescharacteristic
471C2×D8—24no—
472C2×D8C23×C1114yes—
473C2×M16—24no—
474C2×M16C23×C1114yes—
475C22×C8—24no—
476C22×C8C23×C1111yescharacteristic
477C22×C8C23×C1114yes—
478C22×C8C23×C1111yescharacteristic
479C22×C8C23×C1111yescharacteristic
480C22×C8C23×C1111yescharacteristic
481C4⋊Q8—22no—
482C4⋊Q8C23×C1114yes—
483#126—28no—
484#125—22no—
485#125C23×C1114yes—
486#123—28no—
487#123—28no—
488#123—28no—
489C22⋊Q8—28no—
490#121—28no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—22no—
495#121C23×C1114yes—
496#121C23×C1114yes—
497#121C23×C1114yes—
498#121C23×C1114yes—
499C4×D4—28no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4D4×C1114yes—
503C4×D4C23×C1114yes—
504C4×D4C23×C1114yes—
505C4×D4C23×C1114yes—
506#117—22no—
507#117C23×C1114yes—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4D4×C1111yescharacteristic
518C2×C4⋊C4C23×C1111yescharacteristic
519C2×C4⋊C4C23×C1111yescharacteristic
520C2×C4⋊C4C23×C1111yescharacteristic
521C2×C4⋊C4C23×C1111yescharacteristic
522C2×C4⋊C4C23×C1111yescharacteristic
523C2×C4⋊C4C23×C1114yes—
524C2×C4⋊C4C23×C1114yes—
525C2×C4⋊C4C23×C1114yes—
526C2×C4⋊C4C23×C1111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4D4×C1111yescharacteristic
535C2×C22⋊C4D4×C1111yescharacteristic
536C2×C42—21no—
537C2×C42C23×C1111yescharacteristic
538#107C23×C1114yes—
539#107C23×C1114yes—
540#107C23×C1114yes—
541#106C23×C1114yes—
542#106C23×C1114yes—
543#106C23×C1114yes—
544#106C23×C1114yes—
545#106C23×C1114yes—
546#106C23×C1114yes—
547C4⋊C8C23×C1114yes—
548#102C23×C1114yes—
549#102C23×C1114yes—
550#102C23×C1114yes—
551#102C23×C1114yes—
552#102C23×C1114yes—
553#102C23×C1114yes—
554C22⋊C8C23×C1114yes—
555C22⋊C8C23×C1114yes—
556#97C23×C1114yes—
557C2×C11—24no—
558C2×C11—42no—
559C2×C11—82no—
560C2×C11—82no—
561C2×C11#334514yesdirect product factor
562C2×C11C2×#54711yescharacteristic
563C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
564C2×C11C2×#57711yescharacteristic
565C24—21no—
566C24—21no—
567C24C2×D4×C1111yescharacteristic
568C24C2×D4×C1111yescharacteristic
569#41—432no—
570C2×Q8—24no—
571C2×Q8—44no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—44no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—82no—
587C2×D4C2×D4×C1114yes—
588C2×D4C24×C1112yes—
589C2×D4C24×C1112yes—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4C2×D4×C1111yescharacteristic
611C22×C4C2×D4×C1111yescharacteristic
612C22×C4C2×D4×C1111yescharacteristic
613C22×C4C2×D4×C1111yescharacteristic
614C22×C4C2×D4×C1112yes—
615C22×C4C2×D4×C1112yes—
616C22×C4C24×C1112yes—
617C22×C4C24×C1112yes—
618C22×C4C24×C1111yescharacteristic
619D8—28no—
620M16—28no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—28no—
625C2×C8C11×#4114yescomplemented
626C2×C8C24×C1112yes—
627C2×C8C24×C1112yes—
628C2×C8C24×C1112yes—
629C2×C8C24×C1112yes—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4C2×D4×C1114yes—
643C4⋊C4C24×C1112yes—
644C4⋊C4C24×C1112yes—
645C4⋊C4C24×C1112yes—
646C4⋊C4C24×C1112yes—
647C4⋊C4C24×C1112yes—
648C4⋊C4C24×C1112yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4C2×D4×C1114yes—
657C22⋊C4C2×D4×C1114yes—
658C42—24no—
659C42C2×D4×C1112yes—
660C42C24×C1112yes—
661C11C2×#334511yescharacteristic, direct product factor, Sylow
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23C11×AGL(1,ℤ/8)14yes—
676C23C22×D4×C1112yes—
677C23C22×D4×C1112yes—
678C23C22×D4×C1111yescharacteristic
679Q8—48no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—48no—
686D4—48no—
687D4—48no—
688D4—42no—
689D4—42no—
690D4—84no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—48no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4C22×D4×C1112yes—
719C2×C4C22×D4×C1112yes—
720C2×C4C22×D4×C1112yes—
721C2×C4C22×D4×C1112yes—
722C2×C4C22×D4×C1111yescharacteristic
723C2×C4C2×C11×#4112yes—
724C2×C4C11×2−1+412yes—
725C2×C4C25×C1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8C2×C11×#4114yescomplemented
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—84no—
745C22C11×#54712yes—
746C22C2×C11×AGL(1,ℤ/8)14yes—
747C22C2×C11×AGL(1,ℤ/8)12yes—
748C22C11×#57712yes—
749C22C23×D4×C1111yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4C11×#54712yes—
761C4C22×C11×#4111yescharacteristic
762C4C2×C11×2−1+411yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—82no—
767C2C11×#334514yesdirect product factor
768C2C2×C11×#54711yescharacteristic
769C2C22×C11×AGL(1,ℤ/8)11yescharacteristic
770C2C2×C11×#57711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#553C2semidirect
2. C2×C11×#547C2semidirect
3. C11×#3345C2direct (N × H)
4. C2×C11×#501C2semidirect
5. C2×C11×#481C2semidirect
6. C2×C11×#481C2semidirect
7. C2×C11×#482C2semidirect
8. C2×C11×#480C2semidirect
9. C2×C11×#478C2semidirect
10. C2×C11×#476C2semidirect
11. C2×C11×#469C2semidirect
12. C2×C11×#466C2semidirect
13. C2×C11×#442C2semidirect
14. C2×C11×#435C2semidirect
15. C2×C11×#428C2semidirect
16. C22×C11×#106C2semidirect
22. C11×#553C22semidirect
24. C11×#547C22semidirect
45. C11×#501C22semidirect
46. C11×#482C22semidirect
47. C11×#481C22semidirect
48. C11×#481C22semidirect
49. C11×#480C22semidirect
50. C11×#478C22semidirect
51. C11×#476C22semidirect
52. C11×#469C22semidirect
53. C11×#466C22semidirect
54. C11×#442C22semidirect
55. C11×#435C22semidirect
56. C11×#428C22semidirect
66. C2×C11×#106C22semidirect
180. C2×#3345C11direct (N × H)
241. C2×C8×C11#41semidirect
277. C2×#553C2×C11semidirect
278. C2×#547C2×C11semidirect
279. #3345C2×C11direct (N × H)
280. C2×#501C2×C11semidirect
281. C2×#481C2×C11semidirect
282. C2×#481C2×C11semidirect
283. C2×#482C2×C11semidirect
284. C2×#480C2×C11semidirect
285. C2×#478C2×C11semidirect
286. C2×#476C2×C11semidirect
287. C2×#469C2×C11semidirect
288. C2×#466C2×C11semidirect
289. C2×#442C2×C11semidirect
290. C2×#435C2×C11semidirect
291. C2×#428C2×C11semidirect
292. C22×#106C2×C11semidirect
360. C8×C11C2×#41semidirect
366. #553C22×C11semidirect
368. #547C22×C11semidirect
389. #501C22×C11semidirect
390. #482C22×C11semidirect
391. #481C22×C11semidirect
392. #481C22×C11semidirect
393. #480C22×C11semidirect
394. #478C22×C11semidirect
395. #476C22×C11semidirect
396. #469C22×C11semidirect
397. #466C22×C11semidirect
398. #442C22×C11semidirect
399. #435C22×C11semidirect
400. #428C22×C11semidirect
410. C2×#106C22×C11semidirect
561. C2×C11#3345direct (N × H)
625. C2×C8C11×#41semidirect
661. C11C2×#3345direct (N × H)
729. C8C2×C11×#41semidirect
767. C2C11×#3345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
C2×C11×#5472
C11×#33452
C2×C11×#5012
C2×C11×#4812
C2×C11×#4822
C2×C11×#4802
C2×C11×#4782
C2×C11×#4762
C2×C11×#4692
C2×C11×#4662
C2×C11×#4422
C2×C11×#4352
C2×C11×#4282
C22×C11×#1062
C2×#334511