Finite Group Databasebeta

← C2×#14539666 #17905010

Subgroups — C2×#14539666 #17905010

Order 4352.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763387C211yesmaximal, characteristic
2#14539666C2116yesmaximal, direct product factor
3C2×#11763142C211yesmaximal, characteristic, complemented
4C2×#11763150C211yesmaximal, characteristic, complemented
5C2×#11763133C211yesmaximal, characteristic, complemented
6C2×#11763137C211yesmaximal, characteristic, complemented
7C2×#11763065C211yesmaximal, characteristic, complemented
8C2×#11763057C211yesmaximal, characteristic, complemented
9C2×#11763048C211yesmaximal, characteristic, complemented
10C2×#11763040C211yesmaximal, characteristic, complemented
11C2×#11762969C211yesmaximal, characteristic, complemented
12C2×#11762969C211yesmaximal, characteristic, complemented
13C2×#11762965C211yesmaximal, characteristic, complemented
14C2×#11762948C211yesmaximal, characteristic, complemented
15C2×#11762776C211yesmaximal, characteristic, complemented
16C2×C17×#536C211yesmaximal, characteristic, complemented
17C22×#63252C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63231C2211yescharacteristic
20C22×#63230C2211yescharacteristic
21C22×#63230C2211yescharacteristic
22C22×#63223C2211yescharacteristic
23C23×#3622C2211yescharacteristic
24#11763387—24no—
25#11763387C2218yes—
26C2×#10587610C2211yescharacteristic
27C2×#10587610C2211yescharacteristic
28C2×#10587632—21no—
29C2×#10587616C2211yescharacteristic
30C2×#10587616C2211yescharacteristic
31C2×#10587625—21no—
32C2×#10587625—21no—
33C2×#10587624—21no—
34C22×C4⋊Dic17C2211yescharacteristic
35#11763150C2218yescomplemented
36#11763142C2218yescomplemented
37#11763137C2218yescomplemented
38#11763133C2218yescomplemented
39#11763065C2218yescomplemented
40#11763057C2218yescomplemented
41#11763048C2218yescomplemented
42#11763040C2218yescomplemented
43#11762969C2218yescomplemented
44#11762969C2218yescomplemented
45#11762965C2218yescomplemented
46#11762948C2218yescomplemented
47C2×#10587478C2211yescharacteristic
48C2×#10587478C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51C2×#10587506C2211yescharacteristic
52C2×#10587506C2211yescharacteristic
53C2×#10587506C2211yescharacteristic
54C2×#10587506C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587480C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59#11762776C2218yescomplemented
60C2×C22⋊#3622C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×C22⋊#3622C2211yescharacteristic
64C22×#41×C17C2211yescharacteristic
65C23×Q8×C17C2211yescharacteristic
66C17×#536—24no—
67C17×#536C2218yescomplemented
68C2×C17×C4⋊Q8—21no—
69C2×C17×#124—21no—
70C2×C17×#123—21no—
71C2×C17×#123—21no—
72C2×C17×C22⋊Q8C2211yescharacteristic
73C2×C17×C22⋊Q8C2211yescharacteristic
74C2×C17×C22⋊Q8C2211yescharacteristic
75C2×C17×C22⋊Q8C2211yescharacteristic
76C2×C17×#117C2211yescharacteristic
77C2×#41×C17—42no—
78C2×#41×C17—42no—
79C2×#41×C17D414yes—
80C2×#41×C17C2314yes—
81C22×Q8×C17—21no—
82C22×Q8×C17—22no—
83C22×Q8×C17—42no—
84C22×Q8×C17—42no—
85C22×Q8×C17D411yescharacteristic
86C22×Q8×C17C2311yescharacteristic
87C22×Q8×C17C2311yescharacteristic
88C22×Q8×C17C2314yes—
89C22×D4×C17D411yescharacteristic
90C22×D4×C17D411yescharacteristic
91C22×D4×C17D411yescharacteristic
92C23×C4×C17—21no—
93C23×C4×C17C2311yescharacteristic
94C23×C4×C17C2311yescharacteristic
95C23×C4×C17C2311yescharacteristic
96C22×C22⋊D17—21no—
97C22×C22⋊D17—21no—
98C22×C22⋊D17—21no—
99C23×Dic17—21no—
100C2×#63252—22no—
101C2×#63252—42no—
102C2×#63252—42no—
103C2×#63252C2314yes—
104C22×D68C2311yescharacteristic
105C22×C4×D17—21no—
106C22×Dic34C2311yescharacteristic
107C17×C4⋊Q8—28no—
108C17×#124—28no—
109C17×#123—28no—
110C17×#123—28no—
111C17×C22⋊Q8—22no—
112C17×C22⋊Q8—22no—
113C17×C22⋊Q8—22no—
114C17×C22⋊Q8—22no—
115C17×C22⋊Q8C2314yes—
116C17×C22⋊Q8C2314yes—
117C17×C22⋊Q8C2314yes—
118C17×C22⋊Q8C2314yes—
119C17×#117—22no—
120C17×#117C2314yes—
121C2×C4⋊C4×C17—21no—
122C2×C4⋊C4×C17—21no—
123C2×C4⋊C4×C17—21no—
124C2×C4⋊C4×C17—21no—
125C2×C4⋊C4×C17C2311yescharacteristic
126C2×C4⋊C4×C17C2311yescharacteristic
127C2×C22⋊C4×C17—21no—
128C2×C22⋊C4×C17—21no—
129C2×C22⋊C4×C17—21no—
130C2×C22⋊C4×C17—21no—
131C2×C22⋊C4×C17—21no—
132C2×C42×C17—21no—
133C2×C22⋊Dic17—21no—
134C2×C22⋊Dic17—21no—
135#10587632—28no—
136C2×#63231—42no—
137C2×#63231—42no—
138C2×#63231C2314yes—
139C2×#63231C2314yes—
140C2×#63230—42no—
141C2×#63230—42no—
142C2×#63230C2314yes—
143C2×#63230C2314yes—
144#10587625—28no—
145#10587625—28no—
146#10587624—28no—
147#10587616—22no—
148#10587616—22no—
149#10587616C2314yes—
150#10587616C2314yes—
151C2×#63227—21no—
152C2×#63227—21no—
153C2×C4⋊Dic17—21no—
154C2×C4⋊Dic17—22no—
155C2×C4⋊Dic17C2311yescharacteristic
156C2×C4⋊Dic17C2311yescharacteristic
157C2×C4⋊Dic17C2314yes—
158#10587610—22no—
159#10587610—22no—
160#10587610C2314yes—
161#10587610C2314yes—
162C2×#63225—21no—
163C2×#63225—21no—
164C2×#63223—42no—
165C2×#63223C2314yes—
166C22×#3622—42no—
167C22×#3622C2311yescharacteristic
168C22×#3622C2311yescharacteristic
169C22×#3622C2311yescharacteristic
170C22×#3622C2311yescharacteristic
171C22×#3622C2314yes—
172#10587506C2314yes—
173#10587506C2314yes—
174#10587506C2314yes—
175#10587506C2314yes—
176C22⋊#3622C2314yes—
177C22⋊#3622C2314yes—
178C22⋊#3622C2314yes—
179C22⋊#3622C2314yes—
180#10587481C2314yes—
181#10587481C2314yes—
182#10587480C2314yes—
183#10587480C2314yes—
184#10587479C2314yes—
185#10587479C2314yes—
186#10587478C2314yes—
187#10587478C2314yes—
188C24×C17C2×D411yescharacteristic
189C24×C17C2×D411yescharacteristic
190C24×C17C2×D411yescharacteristic
191C23×D17—21no—
192#41×C17—48no—
193#41×C17—44no—
194#41×C17—44no—
195C2×Q8×C17—21no—
196C2×Q8×C17—21no—
197C2×Q8×C17—24no—
198C2×Q8×C17—22no—
199C2×Q8×C17—22no—
200C2×Q8×C17—22no—
201C2×Q8×C17—22no—
202C2×Q8×C17—42no—
203C2×Q8×C17—44no—
204C2×Q8×C17—44no—
205C2×Q8×C17—44no—
206C2×Q8×C17—48no—
207C2×Q8×C17C2×D414yes—
208C2×Q8×C17C2412yes—
209C2×Q8×C17C2412yes—
210C2×D4×C17—42no—
211C2×D4×C17—42no—
212C2×D4×C17—42no—
213C2×D4×C17C2×D414yes—
214C2×D4×C17C2×D414yes—
215C2×D4×C17C2×D414yes—
216C22×C4×C17—22no—
217C22×C4×C17—22no—
218C22×C4×C17—22no—
219C22×C4×C17—22no—
220C22×C4×C17—22no—
221C22×C4×C17—22no—
222C22×C4×C17—24no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—44no—
228C22×C4×C17C2×D412yes—
229C22×C4×C17C2×D412yes—
230C22×C4×C17C2×D411yescharacteristic
231C22×C4×C17C2×D411yescharacteristic
232C22×C4×C17C2×D411yescharacteristic
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2412yes—
235C22×C4×C17C2412yes—
236C22×C4×C17C2412yes—
237C22×C4×C17C2411yescharacteristic
238C2×C22⋊D17—24no—
239C2×C22⋊D17—24no—
240C2×C22⋊D17—24no—
241C2×C22⋊D17—44no—
242C2×C22⋊D17—82no—
243C2×C22⋊D17—82no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—24no—
248C22×Dic17—82no—
249#63252—44no—
250#63252—44no—
251#63252—48no—
252C2×D68—22no—
253C2×D68—22no—
254C2×D68—21no—
255C2×D68C2412yes—
256C2×C4×D17—24no—
257C2×C4×D17—44no—
258C2×Dic34—22no—
259C2×Dic34—22no—
260C2×Dic34—21no—
261C2×Dic34C2412yes—
262C4⋊C4×C17—21no—
263C4⋊C4×C17—21no—
264C4⋊C4×C17—24no—
265C4⋊C4×C17—24no—
266C4⋊C4×C17—24no—
267C4⋊C4×C17—24no—
268C4⋊C4×C17C2412yes—
269C4⋊C4×C17C2412yes—
270C22⋊C4×C17—24no—
271C22⋊C4×C17—24no—
272C22⋊C4×C17—24no—
273C22⋊C4×C17—24no—
274C22⋊C4×C17—24no—
275C42×C17—24no—
276C22⋊Dic17—24no—
277C22⋊Dic17—24no—
278#63231—44no—
279#63231—44no—
280#63230—44no—
281#63230—44no—
282#63227—24no—
283#63227—24no—
284C4⋊Dic17—21no—
285C4⋊Dic17—21no—
286C4⋊Dic17—24no—
287C4⋊Dic17C2412yes—
288C4⋊Dic17C2412yes—
289#63225—24no—
290#63225—24no—
291#63223—44no—
292C2×#3622—22no—
293C2×#3622—22no—
294C2×#3622—22no—
295C2×#3622—22no—
296C2×#3622—44no—
297C2×#3622C2412yes—
298C2×#3622C2412yes—
299C2×#3622C2412yes—
300C2×#3622C2412yes—
301C2×#3201—171nomaximal, Sylow
302C23×C17—22no—
303C23×C17—22no—
304C23×C17—22no—
305C23×C17—22no—
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—22no—
311C23×C17C22×D412yes—
312C23×C17C22×D412yes—
313C23×C17C22×D412yes—
314C23×C17C22×D411yescharacteristic
315C22×D17—22no—
316C22×D17—42no—
317C22×D17—42no—
318C22×D17—42no—
319Q8×C17—22no—
320Q8×C17—22no—
321Q8×C17—22no—
322Q8×C17—22no—
323Q8×C17—44no—
324Q8×C17—48no—
325Q8×C17—42no—
326Q8×C17—42no—
327D4×C17—44no—
328D4×C17—44no—
329D4×C17—44no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—24no—
334C2×C4×C17—24no—
335C2×C4×C17—24no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—22no—
343C2×C4×C17—22no—
344C2×C4×C17—22no—
345C2×C4×C17—22no—
346C2×C4×C17—48no—
347C2×C4×C17—42no—
348C2×C4×C17—42no—
349C2×C4×C17—42no—
350C2×C4×C17—42no—
351C2×C4×C17C22×D412yes—
352C2×C4×C17C22×D412yes—
353C2×C4×C17C22×D412yes—
354C2×C4×C17C22×D411yescharacteristic
355C2×C4×C17H(5,𝔽2)12yes—
356C2×C4×C17H(5,𝔽2)12yes—
357C2×C4×C17C2511yescharacteristic
358C22⋊D17—48no—
359C22⋊D17—84no—
360C22⋊D17—84no—
361C2×Dic17—22no—
362C2×Dic17—22no—
363C2×Dic17—22no—
364C2×Dic17—42no—
365C2×Dic17—42no—
366C2×Dic17—42no—
367C2×Dic17—84no—
368D68—22no—
369D68—22no—
370D68—42no—
371C4×D17—48no—
372Dic34—22no—
373Dic34—22no—
374Dic34—42no—
375#3622—22no—
376#3622—22no—
377#3622—22no—
378#3622—22no—
379C2×#537—171no—
380C2×#536D1711yescharacteristic, complemented
381#3201—1716no—
382C2×#484—171no—
383C2×#485—171no—
384C2×#482—171no—
385C2×#483—171no—
386C2×#470—171no—
387C2×#468—171no—
388C2×#467—171no—
389C2×#465—171no—
390C2×#452—171no—
391C2×#452—171no—
392C2×#451—171no—
393C2×#448—171no—
394C2×#408—171no—
395C22×C17—22no—
396C22×C17—22no—
397C22×C17—22no—
398C22×C17—22no—
399C22×C17—22no—
400C22×C17—22no—
401C22×C17—22no—
402C22×C17—22no—
403C22×C17—22no—
404C22×C17—44no—
405C22×C17—44no—
406C22×C17—44no—
407C22×C17#53412yes—
408C22×C17#57712yes—
409C22×C17#57812yes—
410C22×C17C23×D411yescharacteristic
411C2×D17—42no—
412C2×D17—42no—
413C2×D17—42no—
414C2×D17—84no—
415C4×C17—22no—
416C4×C17—22no—
417C4×C17—22no—
418C4×C17—42no—
419C4×C17—42no—
420C4×C17—42no—
421C4×C17—42no—
422C4×C17#53412yes—
423C4×C17C2×H(5,𝔽2)11yescharacteristic
424C4×C17C2×H(5,𝔽2)11yescharacteristic
425Dic17—42no—
426Dic17—42no—
427Dic17—42no—
428C22×#41—171no—
429C22×#41C2×D1711yescharacteristic
430C23×Q8C2×D1711yescharacteristic
431C22×Q16—171no—
432C22×Q16—171no—
433C22×SD16—171no—
434C22×SD16—171no—
435C22×M16—171no—
436C23×C8—171no—
437#537—178no—
438#537—344no—
439#536—24no—
440#536C2×D1718yescomplemented
441C2×C4⋊Q8—21no—
442C2×#124—21no—
443C2×#123—21no—
444C2×#123—21no—
445C2×C22⋊Q8—171no—
446C2×C22⋊Q8—171no—
447C2×C22⋊Q8—341no—
448C2×C22⋊Q8C2×D1711yescharacteristic
449C2×C22⋊Q8C2×D1711yescharacteristic
450C2×C22⋊Q8C2×D1711yescharacteristic
451C2×C22⋊Q8C2×D1711yescharacteristic
452C2×#121—171no—
453C2×#121—171no—
454C2×#121—341no—
455C2×#121—341no—
456C2×#121—341no—
457C2×#117C2×D1711yescharacteristic
458C22×C4⋊C4—171no—
459#485—178no—
460#484—178no—
461#483—178no—
462#482—178no—
463#470—178no—
464#468—178no—
465#467—178no—
466#465—178no—
467#452—178no—
468#452—178no—
469#451—178no—
470#448—178no—
471C2×#107—171no—
472C2×#107—171no—
473C2×#106—171no—
474C2×#106—171no—
475C2×#103—171no—
476C2×#103—171no—
477C2×#103—171no—
478C2×#103—171no—
479C2×#103—171no—
480C2×#103—171no—
481C2×#102—171no—
482C2×#102—171no—
483#408—178no—
484C2×C22⋊C8—171no—
485C2×C22⋊C8—171no—
486C2×C22⋊C8—171no—
487C2×C22⋊C8—171no—
488C2×C17—42no—
489C2×C17—42no—
490C2×C17—42no—
491C2×C17#320114yescomplemented
492C2×C17C2×#53411yescharacteristic
493C2×C17C2×#57711yescharacteristic
494C2×C17C2×#57811yescharacteristic
495D17—82no—
496C2×#41—42no—
497C2×#41—42no—
498C2×#41—174no—
499C2×#41—342no—
500C2×#41—682no—
501C2×#41—682no—
502C2×#41C22⋊D1714yes—
503C2×#41C22×D1714yes—
504C22×Q8—21no—
505C22×Q8—22no—
506C22×Q8—42no—
507C22×Q8—42no—
508C22×Q8—171no—
509C22×Q8C22⋊D1711yescharacteristic
510C22×Q8C22×D1711yescharacteristic
511C22×Q8C22×D1711yescharacteristic
512C22×Q8C22×D1714yes—
513C22×D4—171no—
514C22×D4—341no—
515C22×D4—341no—
516C22×D4—341no—
517C22×D4C22⋊D1711yescharacteristic
518C22×D4C22⋊D1711yescharacteristic
519C22×D4C22⋊D1711yescharacteristic
520C23×C4—21no—
521C23×C4—341no—
522C23×C4—341no—
523C23×C4C22×D1711yescharacteristic
524C23×C4C22×D1711yescharacteristic
525C23×C4C22×D1711yescharacteristic
526C2×Q16—174no—
527C2×Q16—174no—
528C2×Q16—682no—
529C2×Q16—682no—
530C2×SD16—174no—
531C2×SD16—174no—
532C2×SD16—682no—
533C2×SD16—682no—
534C2×M16—174no—
535C2×M16—682no—
536C22×C8—171no—
537C22×C8—171no—
538C22×C8—171no—
539C22×C8—171no—
540C22×C8—174no—
541C22×C8—682no—
542C4⋊Q8—28no—
543#124—28no—
544#123—28no—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—174no—
551C22⋊Q8—174no—
552C22⋊Q8—348no—
553C22⋊Q8—342no—
554C22⋊Q8—342no—
555C22⋊Q8C22×D1714yes—
556C22⋊Q8C22×D1714yes—
557C22⋊Q8C22×D1714yes—
558C22⋊Q8C22×D1714yes—
559#121—174no—
560#121—174no—
561#121—348no—
562#121—348no—
563#121—348no—
564#121—342no—
565#121—342no—
566#117—22no—
567#117C22×D1714yes—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—171no—
573C2×C4⋊C4—171no—
574C2×C4⋊C4—174no—
575C2×C4⋊C4—341no—
576C2×C4⋊C4—342no—
577C2×C4⋊C4—341no—
578C2×C4⋊C4—341no—
579C2×C4⋊C4C22×D1711yescharacteristic
580C2×C4⋊C4C22×D1711yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—341no—
587C2×C22⋊C4—341no—
588C2×C22⋊C4—341no—
589C2×C22⋊C4—341no—
590C2×C42—21no—
591#107—174no—
592#107—174no—
593#106—174no—
594#106—174no—
595#103—174no—
596#103—174no—
597#103—174no—
598#103—174no—
599#103—174no—
600#103—174no—
601#102—174no—
602#102—174no—
603C22⋊C8—174no—
604C22⋊C8—174no—
605C22⋊C8—174no—
606C22⋊C8—174no—
607C17C2×#320111yescharacteristic, complemented, Sylow
608C24—341no—
609C24C2×C22⋊D1711yescharacteristic
610C24C2×C22⋊D1711yescharacteristic
611C24C2×C22⋊D1711yescharacteristic
612#41—48no—
613#41—44no—
614#41—44no—
615#41—684no—
616#41—684no—
617#41—688no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—24no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—42no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—48no—
630C2×Q8—172no—
631C2×Q8—341no—
632C2×Q8—342no—
633C2×Q8—342no—
634C2×Q8C2×C22⋊D1714yes—
635C2×Q8C23×D1712yes—
636C2×Q8C23×D1712yes—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—172no—
641C2×D4—344no—
642C2×D4—344no—
643C2×D4—344no—
644C2×D4—342no—
645C2×D4—342no—
646C2×D4—341no—
647C2×D4—684no—
648C2×D4—1362no—
649C2×D4—1362no—
650C2×D4C2×C22⋊D1714yes—
651C2×D4C2×C22⋊D1714yes—
652C2×D4C2×C22⋊D1714yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—44no—
665C22×C4—341no—
666C22×C4—341no—
667C22×C4—341no—
668C22×C4—344no—
669C22×C4—344no—
670C22×C4—684no—
671C22×C4—1362no—
672C22×C4C2×C22⋊D1712yes—
673C22×C4C2×C22⋊D1712yes—
674C22×C4C2×C22⋊D1712yes—
675C22×C4C2×C22⋊D1711yescharacteristic
676C22×C4C2×C22⋊D1711yescharacteristic
677C22×C4C2×C22⋊D1711yescharacteristic
678C22×C4C23×D1712yes—
679C22×C4C23×D1712yes—
680C22×C4C23×D1712yes—
681C22×C4C23×D1711yescharacteristic
682Q16—684no—
683Q16—684no—
684SD16—684no—
685SD16—684no—
686M16—684no—
687C2×C8—172no—
688C2×C8—172no—
689C2×C8—172no—
690C2×C8—172no—
691C2×C8—342no—
692C2×C8—342no—
693C2×C8—342no—
694C2×C8—342no—
695C2×C8—684no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—172no—
703C4⋊C4—172no—
704C4⋊C4—344no—
705C4⋊C4—341no—
706C4⋊C4—341no—
707C4⋊C4—344no—
708C4⋊C4—344no—
709C4⋊C4C23×D1712yes—
710C4⋊C4C23×D1712yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—344no—
717C22⋊C4—344no—
718C22⋊C4—344no—
719C22⋊C4—344no—
720C42—24no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—342no—
731C23—682no—
732C23—682no—
733C23—682no—
734C23C22×C22⋊D1712yes—
735C23C22×C22⋊D1712yes—
736C23C22×C22⋊D1712yes—
737C23C22×C22⋊D1711yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—44no—
743Q8—48no—
744Q8—42no—
745Q8—42no—
746Q8—342no—
747Q8—342no—
748Q8—682no—
749D4—44no—
750D4—44no—
751D4—44no—
752D4—342no—
753D4—342no—
754D4—688no—
755D4—682no—
756D4—1364no—
757D4—1364no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—48no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—342no—
780C2×C4—342no—
781C2×C4—342no—
782C2×C4—688no—
783C2×C4—682no—
784C2×C4—682no—
785C2×C4—682no—
786C2×C4—1364no—
787C2×C4#1058769112yes—
788C2×C4#1058769112yes—
789C2×C4C22×C22⋊D1712yes—
790C2×C4C22×C22⋊D1712yes—
791C2×C4C22×C22⋊D1712yes—
792C2×C4C22×C22⋊D1711yescharacteristic
793C2×C4C24×D1711yescharacteristic
794C8—342no—
795C8—342no—
796C8—342no—
797C8—342no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—682no—
811C22—682no—
812C22—682no—
813C22—1364no—
814C22#1176336812yes—
815C22#1176361712yes—
816C22#1176362412yes—
817C22C23×C22⋊D1711yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—682no—
826C4—682no—
827C4—682no—
828C4#1176336812yes—
829C4C2×#1058769111yescharacteristic
830C4C2×#1058769111yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—1362no—
835C2#1453966614yesdirect product factor
836C2C2×#1176336811yescharacteristic
837C2C2×#1176361711yescharacteristic
838C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#536C2
socleC23×C17C22×D4
prime radicalC2×#11763387C2
hypercenterC2×#536D17
hypocenterC17C2×#3201
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. #14539666C2direct (N × H)
3. C2×#11763142C2semidirect
4. C2×#11763150C2semidirect
5. C2×#11763133C2semidirect
6. C2×#11763137C2semidirect
7. C2×#11763065C2semidirect
8. C2×#11763057C2semidirect
9. C2×#11763048C2semidirect
10. C2×#11763040C2semidirect
11. C2×#11762969C2semidirect
12. C2×#11762969C2semidirect
13. C2×#11762965C2semidirect
14. C2×#11762948C2semidirect
15. C2×#11762776C2semidirect
16. C2×C17×#536C2semidirect
35. #11763150C22semidirect
36. #11763142C22semidirect
37. #11763137C22semidirect
38. #11763133C22semidirect
39. #11763065C22semidirect
40. #11763057C22semidirect
41. #11763048C22semidirect
42. #11763040C22semidirect
43. #11762969C22semidirect
44. #11762969C22semidirect
45. #11762965C22semidirect
46. #11762948C22semidirect
59. #11762776C22semidirect
67. C17×#536C22semidirect
380. C2×#536D17semidirect
440. #536C2×D17semidirect
491. C2×C17#3201semidirect
607. C17C2×#3201semidirect
835. C2#14539666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633872
#145396662
C2×#117631422
C2×#117631502
C2×#117631332
C2×#117631372
C2×#117630652
C2×#117630572
C2×#117630482
C2×#117630402
C2×#117629692
C2×#117629652
C2×#117629482
C2×#117627762
C2×C17×#5362
C2×#320117