Finite Group Databasebeta

← #17897777

Subgroups — #17897777

Order 4352.

4874 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763645C211yesmaximal, characteristic
2C2×#11763574C211yesmaximal, characteristic, complemented
3C2×#131×D17C211yesmaximal, characteristic, complemented
4#14537234C213yesmaximal, complemented
5#14537233C211yesmaximal, characteristic, complemented
6#14537232C213yesmaximal, complemented
7#14537232C213yesmaximal, complemented
8#14537231C211yesmaximal, characteristic, complemented
9#14537231C211yesmaximal, characteristic, complemented
10#14537230C213yesmaximal, complemented
11#14537227C213yesmaximal, complemented
12#14537226C213yesmaximal, complemented
13C2×#11762774C213yesmaximal, complemented
14D17×#408C213yesmaximal, complemented
15C17×#2880C211yesmaximal, characteristic, complemented
16#11763645—28no—
17#11763645—28no—
18C2×#10587694C411yescharacteristic
19C2×#10587694C411yescharacteristic
20C2×#10587697C411yescharacteristic
21C2×#10587697C413yes—
22C2×#10587696C411yescharacteristic
23C2×#10587696C413yes—
24C2×#10587691C413yes—
25C2×#10587691C413yes—
26C22×#63252C2213yes—
27C22×#63252C2213yes—
28C2×#41×D17C2213yes—
29C2×#41×D17C2211yescharacteristic
30C2×#41×D17C2213yes—
31C2×#41×D17C2211yescharacteristic
32#11763574—28no—
33C2×#10587593C2213yescomplemented
34C2×#10587593C2213yescomplemented
35C2×#10587634C2211yescharacteristic, complemented
36C2×#10587634C2211yescharacteristic, complemented
37C2×#10587587C2213yescomplemented
38C2×#10587587C2213yescomplemented
39#131×D17—28no—
40C22×#63218C2213yescomplemented
41C2×M16×D17C2213yescomplemented
42C2×M16×D17C2213yescomplemented
43C22×C8×D17C2213yescomplemented
44#11762777C2213yescomplemented
45#11762777C2213yescomplemented
46#11762776C2213yescomplemented
47#11762776C2213yescomplemented
48#11762775C2213yescomplemented
49#11762775C2213yescomplemented
50#11762774C2213yescomplemented
51#11762774C2216yescomplemented
52#11762774C2211yescharacteristic, complemented
53#11762774C2213yescomplemented
54#11762774C2213yescomplemented
55#11762774C2213yescomplemented
56#11762774C2213yescomplemented
57#11762774C2213yescomplemented
58#11762774C2213yescomplemented
59#11762774C2216yescomplemented
60#11762774C2216yescomplemented
61#11762773C2213yescomplemented
62#11762772C2213yescomplemented
63#11762772C2213yescomplemented
64#11762771C2216yescomplemented
65#11762771C2216yescomplemented
66C2×C22⋊#3622C2213yescomplemented
67C2×#10587491C2213yescomplemented
68C2×#10587491C2213yescomplemented
69C22⋊C8×D17C2216yescomplemented
70C22⋊C8×D17C2216yescomplemented
71C22×#41×C17C2211yescharacteristic
72C2×C17×#131C2211yescharacteristic, complemented
73C2×C17×#131C2211yescharacteristic, complemented
74C17×#408C2213yescomplemented
75C17×#408C2213yescomplemented
76C17×#407C2213yescomplemented
77C2×C17×C22⋊C8C2213yescomplemented
78C2×#41×C17—24no—
79C2×#41×C17—24no—
80C2×#41×C17C2×C411yescharacteristic
81C2×#41×C17C2×C413yes—
82C2×#41×C17C2313yes—
83C2×#41×C17C2311yescharacteristic
84C22×Q8×C17C2×C411yescharacteristic
85C22×D4×C17C2×C413yes—
86C23×C4×C17C2313yes—
87C22×C22⋊D17C2×C413yes—
88C22×C22⋊D17C2×C416yes—
89C22×C22⋊D17C2×C413yes—
90#10587697—28no—
91#10587697—224no—
92#10587696—28no—
93#10587696—224no—
94#41×D17—24no—
95#41×D17—24no—
96#41×D17—212no—
97#41×D17—212no—
98#41×D17—212no—
99#41×D17—212no—
100#41×D17D418yes—
101#41×D17D418yes—
102#10587694—28no—
103#10587694—28no—
104C2×#63256C2×C411yescharacteristic
105C2×#63256C2×C413yes—
106C2×#63256C2×C413yes—
107C2×#63256C2×C411yescharacteristic
108C2×Q8×D17C2×C411yescharacteristic
109C2×Q8×D17C2×C413yes—
110C2×Q8×D17C2×C413yes—
111C2×Q8×D17C2×C411yescharacteristic
112#10587691—224no—
113#10587691—224no—
114C2×#63254C2×C413yes—
115C2×#63254C2×C416yes—
116C2×#63254C2×C416yes—
117C2×#63254C2×C413yes—
118C2×#63254C2×C413yes—
119C2×#63254C2×C413yes—
120C2×D4×D17C2×C416yes—
121C2×D4×D17C2×C413yes—
122C2×D4×D17C2×C416yes—
123C2×D4×D17C2×C413yes—
124C2×D4×D17C2×C413yes—
125C2×D4×D17C2×C413yes—
126C2×#63252—212no—
127C2×#63252—212no—
128C2×#63252—212no—
129C2×#63252—212no—
130C2×#63252C2×C413yes—
131C2×#63252C2×C413yes—
132C2×#63252C2×C413yes—
133C2×#63252C2×C413yes—
134C2×#63252C2×C416yes—
135C2×#63252C2×C413yes—
136C2×#63252C2×C413yes—
137C2×#63252C2313yes—
138C2×#63252C2313yes—
139C2×#63252C2311yescharacteristic
140C2×#63252C2313yes—
141C2×#63252C2313yes—
142C2×#63252C2313yes—
143C22×D68C2×C413yes—
144C22×D68C2×C413yes—
145C22×C4×D17C2316yes—
146C22×C4×D17C2313yes—
147C22×C4×D17C2313yes—
148C22×Dic34C2×C413yes—
149C22×Dic34C2×C413yes—
150C17×#131—24no—
151C17×#131—24no—
152C2×M16×C17C2313yes—
153C2×M16×C17C2313yes—
154C22×C8×C17C2313yes—
155C22×C8×C17C2313yes—
156#10587634—24no—
157#10587634—24no—
158C2×#63223C2313yes—
159C2×#63223C2313yes—
160C22×#3622C2313yes—
161C22×#3622C2313yes—
162#10587593—212no—
163#10587593—212no—
164M16×D17—212no—
165M16×D17—212no—
166#10587587—212no—
167#10587587—212no—
168C2×#63218—212no—
169C2×#63218C2316yes—
170C2×#63218C2313yes—
171C2×#63218C2313yes—
172C2×#63218C2313yes—
173C2×#63218C2311yescharacteristic
174C2×C8×D17—212no—
175C2×C8×D17C2313yes—
176C2×C8×D17C2313yes—
177C2×C8×D17C2316yes—
178C2×C8×D17C2311yescharacteristic
179C2×C8×D17C2313yes—
180C17×C22⋊C8C2313yes—
181C17×C22⋊C8C2316yes—
182C17×C22⋊C8C2313yes—
183C17×C22⋊C8C2311yescharacteristic
184C17×C22⋊C8C2313yes—
185C22⋊#3622C2313yes—
186C22⋊#3622C2316yes—
187C22⋊#3622C2311yescharacteristic
188C22⋊#3622C2313yes—
189C22⋊#3622C2313yes—
190#10587491C2313yes—
191#10587491C2313yes—
192#10587491C2316yes—
193#10587491C2316yes—
194#10587491C2311yescharacteristic
195#10587491C2311yescharacteristic
196#10587491C2313yes—
197#10587491C2313yes—
198#10587491C2313yes—
199#10587491C2313yes—
200C24×C17C22×C413yes—
201C23×D17C22×C413yes—
202C23×D17C22×C416yes—
203C23×D17C22×C413yes—
204#41×C17—24no—
205#41×C17—212no—
206#41×C17—26no—
207#41×C17—26no—
208#41×C17C2×D414yes—
209#41×C17C2×D414yes—
210C2×Q8×C17—24no—
211C2×Q8×C17C22×C413yes—
212C2×Q8×C17C22×C411yescharacteristic
213C2×D4×C17—212no—
214C2×D4×C17C22×C416yes—
215C2×D4×C17C22×C413yes—
216C2×D4×C17C22×C413yes—
217C22×C4×C17—26no—
218C22×C4×C17—26no—
219C22×C4×C17C22×C413yes—
220C22×C4×C17C22×C413yes—
221C22×C4×C17C22×C413yes—
222C22×C4×C17C2413yes—
223C22×C4×C17C2411yescharacteristic
224C22×C4×C17C2413yes—
225C2×C22⋊D17—212no—
226C2×C22⋊D17—224no—
227C2×C22⋊D17—212no—
228C2×C22⋊D17C22×C413yes—
229C2×C22⋊D17C22×C411yescharacteristic
230C2×C22⋊D17C22×C411yescharacteristic
231C2×C22⋊D17C22×C413yes—
232C2×C22⋊D17C22×C416yes—
233C2×C22⋊D17C22×C413yes—
234C2×C22⋊D17C22×C413yes—
235C2×C22⋊D17C22×C413yes—
236C2×C22⋊D17C22×C413yes—
237C2×C22⋊D17C22×C416yes—
238C22×Dic17C22×C413yes—
239C22×Dic17C22×C416yes—
240C22×Dic17C22×C413yes—
241#63256—24no—
242#63256—212no—
243#63256—212no—
244#63256C22⋊C418yes—
245Q8×D17—24no—
246Q8×D17—212no—
247Q8×D17—212no—
248Q8×D17C22⋊C418yes—
249#63254—212no—
250#63254—224no—
251#63254—224no—
252#63254—212no—
253#63254—212no—
254#63254C22⋊C4124yes—
255D4×D17—224no—
256D4×D17—212no—
257D4×D17—224no—
258D4×D17—212no—
259D4×D17—212no—
260D4×D17C22⋊C4124yes—
261#63252—26no—
262#63252—26no—
263#63252—224no—
264#63252—212no—
265#63252—212no—
266#63252—212no—
267#63252—212no—
268#63252—212no—
269#63252—26no—
270#63252—26no—
271#63252—22no—
272#63252—22no—
273#63252—26no—
274#63252—26no—
275#63252—26no—
276#63252—26no—
277#63252—212no—
278#63252C2×D4112yes—
279#63252C2×D4112yes—
280C2×D68—212no—
281C2×D68—212no—
282C2×D68C22×C413yes—
283C2×D68C22×C411yescharacteristic
284C2×D68C22×C413yes—
285C2×D68C22×C413yes—
286C2×D68C22×C413yes—
287C2×D68C22×C413yes—
288C2×C4×D17—26no—
289C2×C4×D17—26no—
290C2×C4×D17—212no—
291C2×C4×D17—212no—
292C2×C4×D17C22×C416yes—
293C2×C4×D17C22×C413yes—
294C2×C4×D17C22×C413yes—
295C2×C4×D17C22×C416yes—
296C2×C4×D17C22×C413yes—
297C2×C4×D17C22×C413yes—
298C2×C4×D17C2×D4112yes—
299C2×C4×D17C2×D4112yes—
300C2×C4×D17C2413yes—
301C2×C4×D17C2411yescharacteristic
302C2×C4×D17C2413yes—
303C2×C4×D17C2411yescharacteristic
304C2×Dic34—212no—
305C2×Dic34—212no—
306C2×Dic34C22×C411yescharacteristic
307C2×Dic34C22×C413yes—
308C2×Dic34C22×C413yes—
309C2×Dic34C22×C413yes—
310C2×Dic34C22×C413yes—
311C2×Dic34C22×C413yes—
312M16×C17—26no—
313M16×C17—26no—
314C2×C8×C17—26no—
315C2×C8×C17—26no—
316C2×C8×C17C2411yescharacteristic
317C2×C8×C17C2411yescharacteristic
318C2×C8×C17C2413yes—
319C2×C8×C17C2413yes—
320#63223—26no—
321#63223—26no—
322C2×#3622—26no—
323C2×#3622—26no—
324C2×#3622C2411yescharacteristic
325C2×#3622C2413yes—
326C2×#3622C2413yes—
327C2×#3622C2411yescharacteristic
328#63218—22no—
329#63218—26no—
330#63218—26no—
331#63218—26no—
332#63218—212no—
333C8×D17—22no—
334C8×D17—26no—
335C8×D17—26no—
336C8×D17—26no—
337C8×D17—212no—
338#60065—171nomaximal, Sylow
339C23×C17—26no—
340C23×C17—43no—
341C23×C17—43no—
342C23×C17C23×C413yes—
343C23×C17C23×C411yescharacteristic
344C23×C17C23×C413yes—
345C22×D17—26no—
346C22×D17—212no—
347C22×D17—43no—
348C22×D17—43no—
349C22×D17—46no—
350C22×D17—46no—
351C22×D17—43no—
352C22×D17—43no—
353C22×D17C2×C22⋊C4112yes—
354C22×D17C23×C411yescharacteristic
355C22×D17C23×C413yes—
356C22×D17C23×C413yes—
357C22×D17C23×C411yescharacteristic
358Q8×C17—26no—
359Q8×C17C2×C22⋊C414yes—
360D4×C17—212no—
361D4×C17—26no—
362D4×C17C2×C22⋊C4112yes—
363C2×C4×C17—26no—
364C2×C4×C17—26no—
365C2×C4×C17—26no—
366C2×C4×C17—23no—
367C2×C4×C17—23no—
368C2×C4×C17—21no—
369C2×C4×C17—21no—
370C2×C4×C17C23×C411yescharacteristic
371C2×C4×C17C23×C413yes—
372C2×C4×C17C23×C413yes—
373C2×C4×C17C22×D416yes—
374C2×C4×C17C22×D416yes—
375C2×C4×C17C2511yescharacteristic
376C22⋊D17—212no—
377C22⋊D17—26no—
378C22⋊D17—22no—
379C22⋊D17—26no—
380C22⋊D17—26no—
381C22⋊D17—22no—
382C22⋊D17—26no—
383C22⋊D17—26no—
384C22⋊D17—26no—
385C22⋊D17C2×C22⋊C4124yes—
386C2×Dic17—26no—
387C2×Dic17—212no—
388C2×Dic17C2×C22⋊C4112yes—
389C2×Dic17C23×C413yes—
390C2×Dic17C23×C411yescharacteristic
391C2×Dic17C23×C411yescharacteristic
392C2×Dic17C23×C413yes—
393D68—26no—
394D68—22no—
395D68—26no—
396D68—26no—
397D68—26no—
398D68C2×C22⋊C4112yes—
399C4×D17—212no—
400C4×D17—26no—
401C4×D17—26no—
402C4×D17—21no—
403C4×D17—21no—
404C4×D17—23no—
405C4×D17—23no—
406C4×D17—212no—
407C4×D17C2×C22⋊C4112yes—
408C4×D17C2×C22⋊C4112yes—
409C4×D17C22×D416yes—
410C4×D17C22×D416yes—
411C4×D17C22×D412yes—
412C4×D17C22×D412yes—
413Dic34—26no—
414Dic34—22no—
415Dic34—26no—
416Dic34—26no—
417Dic34—26no—
418Dic34C2×C22⋊C4112yes—
419C8×C17—21no—
420C8×C17—21no—
421C8×C17—23no—
422C8×C17—23no—
423#3622—21no—
424#3622—23no—
425#3622—23no—
426#3622—21no—
427C2×#585—171no—
428C2×#568—171no—
429C22×#131—171no—
430#2880—173no—
431#2880—173no—
432#2880—173no—
433#2880—173no—
434#2880—171no—
435#2880—171no—
436#2880—171no—
437#2880D1711yescharacteristic, complemented
438#2879—173no—
439#2879—173no—
440C2×#408—173no—
441C2×#408—173no—
442C22×C17—23no—
443C22×C17—23no—
444C22×C17—23no—
445C22×C17—21no—
446C22×C17—23no—
447C22×C17—23no—
448C22×C17—21no—
449C22×C17—21no—
450C22×C17—86no—
451C22×C17C22×C22⋊C416yes—
452C22×C17C24×C411yescharacteristic
453C2×D17—21no—
454C2×D17—23no—
455C2×D17—21no—
456C2×D17—23no—
457C2×D17—21no—
458C2×D17—23no—
459C2×D17—23no—
460C2×D17—21no—
461C2×D17—23no—
462C2×D17—21no—
463C2×D17—412no—
464C2×D17—812no—
465C2×D17—86no—
466C2×D17C22×C22⋊C416yes—
467C2×D17C22×C22⋊C412yes—
468C4×C17—21no—
469C4×C17—23no—
470C4×C17C22×C22⋊C416yes—
471C4×C17C23×D411yescharacteristic
472C4×C17C23×D411yescharacteristic
473Dic17—23no—
474Dic17—21no—
475Dic17C22×C22⋊C412yes—
476Dic17C22×C22⋊C416yes—
477#585—348no—
478#585—348no—
479C2×2−1+4—171no—
480C2×2−1+4—173no—
481C2×2−1+4—171no—
482C2×2−1+4—171no—
483C2×H(5,𝔽2)—173no—
484C2×H(5,𝔽2)—171no—
485C2×H(5,𝔽2)—173no—
486C2×H(5,𝔽2)—173no—
487C22×#41—171no—
488C22×#41—173no—
489C22×#41—173no—
490C22×#41—171no—
491C22×#41—173no—
492C22×#41—173no—
493C22×#41C2×D1711yescharacteristic
494#568—348no—
495C2×#131—171no—
496C2×#131—171no—
497C2×#131—173no—
498C2×#131—173no—
499C2×#131—173no—
500C2×#131—173no—
501C2×#131—348no—
502C2×#131C2×D1711yescharacteristic, complemented
503C2×#131C2×D1711yescharacteristic, complemented
504C22×M16—173no—
505C22×M16—173no—
506C22×M16—173no—
507C23×C8—173no—
508#408—173no—
509#408—173no—
510#408—173no—
511#408—173no—
512#408—173no—
513#408—173no—
514#408—173no—
515#408—171no—
516#408—176no—
517#408—173no—
518#408—173no—
519#408—173no—
520#408—173no—
521#408—173no—
522#408—173no—
523#408—176no—
524#408—176no—
525#408C2×D1713yescomplemented
526#408C2×D1713yescomplemented
527#407—173no—
528#407—173no—
529#407—173no—
530#407—176no—
531#407—176no—
532#407C2×D1713yescomplemented
533C2×C22⋊C8—173no—
534C2×C22⋊C8—173no—
535C2×C22⋊C8—173no—
536C2×C22⋊C8—176no—
537C2×C22⋊C8—176no—
538C2×C22⋊C8C2×D1713yescomplemented
539C2×C17—26no—
540C2×C17—43no—
541C2×C17—41no—
542C2×C17C23×C22⋊C411yescharacteristic
543C2×C17#357311yescharacteristic
544C2×C17#357311yescharacteristic
545D17—22no—
546D17—26no—
547D17—43no—
548D17—41no—
5492−1+4—348no—
5502−1+4—348no—
5512−1+4—348no—
5522−1+4—3424no—
553H(5,𝔽2)—3424no—
554H(5,𝔽2)—3424no—
555H(5,𝔽2)—3424no—
556H(5,𝔽2)—348no—
557C2×#41—24no—
558C2×#41—24no—
559C2×#41—178no—
560C2×#41—178no—
561C2×#41—171no—
562C2×#41—173no—
563C2×#41—173no—
564C2×#41—171no—
565C2×#41—173no—
566C2×#41—176no—
567C2×#41—173no—
568C2×#41—176no—
569C2×#41—173no—
570C2×#41—173no—
571C2×#41—173no—
572C2×#41—173no—
573C2×#41—173no—
574C2×#41—173no—
575C2×#41—176no—
576C2×#41—173no—
577C2×#41—173no—
578C2×#41—173no—
579C2×#41—173no—
580C2×#41—173no—
581C2×#41—171no—
582C2×#41—173no—
583C2×#41—173no—
584C2×#41—3412no—
585C2×#41—3412no—
586C2×#41—3412no—
587C2×#41—3412no—
588C2×#41—3412no—
589C2×#41—3412no—
590C2×#41—3412no—
591C2×#41—3412no—
592C2×#41—344no—
593C2×#41—344no—
594C2×#41C4×D1711yescharacteristic
595C2×#41C4×D1713yes—
596C2×#41C22×D1713yes—
597C2×#41C22×D1711yescharacteristic
598C22×Q8—171no—
599C22×Q8—173no—
600C22×Q8—173no—
601C22×Q8—171no—
602C22×Q8—173no—
603C22×Q8—173no—
604C22×Q8C4×D1711yescharacteristic
605C22×D4—173no—
606C22×D4—173no—
607C22×D4—176no—
608C22×D4—173no—
609C22×D4—173no—
610C22×D4—176no—
611C22×D4—173no—
612C22×D4—176no—
613C22×D4—173no—
614C22×D4—173no—
615C22×D4—173no—
616C22×D4C4×D1713yes—
617C23×C4—173no—
618C23×C4—176no—
619C23×C4—173no—
620C23×C4C22×D1713yes—
621#131—24no—
622#131—24no—
623#131—3412no—
624#131—3412no—
625#131—3412no—
626#131—3412no—
627#131—344no—
628#131—344no—
629C2×M16—173no—
630C2×M16—173no—
631C2×M16—173no—
632C2×M16—171no—
633C2×M16—176no—
634C2×M16—173no—
635C2×M16—173no—
636C2×M16—3412no—
637C2×M16—3412no—
638C2×M16—3412no—
639C2×M16C22×D1713yes—
640C2×M16C22×D1713yes—
641C22×C8—173no—
642C22×C8—173no—
643C22×C8—171no—
644C22×C8—173no—
645C22×C8—173no—
646C22×C8—173no—
647C22×C8—176no—
648C22×C8—3412no—
649C22×C8C22×D1713yes—
650C22×C8C22×D1713yes—
651C22⋊C8—173no—
652C22⋊C8—171no—
653C22⋊C8—176no—
654C22⋊C8—173no—
655C22⋊C8—173no—
656C22⋊C8—173no—
657C22⋊C8—171no—
658C22⋊C8—173no—
659C22⋊C8—171no—
660C22⋊C8—176no—
661C22⋊C8—176no—
662C22⋊C8—173no—
663C22⋊C8—173no—
664C22⋊C8—173no—
665C22⋊C8—173no—
666C22⋊C8C22×D1713yes—
667C22⋊C8C22×D1716yes—
668C22⋊C8C22×D1711yescharacteristic
669C22⋊C8C22×D1713yes—
670C22⋊C8C22×D1713yes—
671C17#6006511yescharacteristic, complemented, Sylow
672C24—173no—
673C24—176no—
674C24—173no—
675C24C2×C4×D1713yes—
676#41—24no—
677#41—212no—
678#41—26no—
679#41—26no—
680#41—178no—
681#41—1724no—
682#41—1712no—
683#41—1712no—
684#41—342no—
685#41—346no—
686#41—346no—
687#41—342no—
688#41—346no—
689#41—346no—
690#41—346no—
691#41—346no—
692#41—3412no—
693#41—3412no—
694#41—3412no—
695#41—3412no—
696#41—3424no—
697#41—3412no—
698#41—3412no—
699#41—3424no—
700#41—3412no—
701#41—3412no—
702#41—3424no—
703#41—3412no—
704#41—3412no—
705#41—344no—
706#41—3412no—
707#41—346no—
708#41—346no—
709#41D4×D1714yes—
710#41D4×D1714yes—
711C2×Q8—24no—
712C2×Q8—178no—
713C2×Q8—173no—
714C2×Q8—173no—
715C2×Q8—173no—
716C2×Q8—171no—
717C2×Q8—173no—
718C2×Q8—173no—
719C2×Q8—3412no—
720C2×Q8—3412no—
721C2×Q8—3412no—
722C2×Q8—3412no—
723C2×Q8—344no—
724C2×Q8C2×C4×D1713yes—
725C2×Q8C2×C4×D1711yescharacteristic
726C2×D4—212no—
727C2×D4—176no—
728C2×D4—1724no—
729C2×D4—173no—
730C2×D4—173no—
731C2×D4—171no—
732C2×D4—173no—
733C2×D4—173no—
734C2×D4—173no—
735C2×D4—171no—
736C2×D4—173no—
737C2×D4—176no—
738C2×D4—173no—
739C2×D4—173no—
740C2×D4—173no—
741C2×D4—171no—
742C2×D4—173no—
743C2×D4—173no—
744C2×D4—3412no—
745C2×D4—3412no—
746C2×D4—3412no—
747C2×D4—3412no—
748C2×D4—3424no—
749C2×D4—3412no—
750C2×D4—3424no—
751C2×D4—3424no—
752C2×D4—3412no—
753C2×D4—3412no—
754C2×D4C2×C4×D1716yes—
755C2×D4C2×C4×D1713yes—
756C2×D4C2×C4×D1713yes—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—173no—
760C22×C4—173no—
761C22×C4—173no—
762C22×C4—1712no—
763C22×C4—1712no—
764C22×C4—171no—
765C22×C4—173no—
766C22×C4—176no—
767C22×C4—173no—
768C22×C4—176no—
769C22×C4—176no—
770C22×C4—173no—
771C22×C4—173no—
772C22×C4—173no—
773C22×C4—171no—
774C22×C4—3412no—
775C22×C4—3412no—
776C22×C4—346no—
777C22×C4—346no—
778C22×C4C2×C4×D1713yes—
779C22×C4C2×C4×D1713yes—
780C22×C4C2×C4×D1713yes—
781C22×C4C23×D1713yes—
782C22×C4C23×D1711yescharacteristic
783C22×C4C23×D1713yes—
784M16—26no—
785M16—26no—
786M16—342no—
787M16—346no—
788M16—346no—
789M16—346no—
790M16—3412no—
791M16—346no—
792M16—346no—
793C2×C8—26no—
794C2×C8—26no—
795C2×C8—171no—
796C2×C8—171no—
797C2×C8—173no—
798C2×C8—173no—
799C2×C8—342no—
800C2×C8—346no—
801C2×C8—346no—
802C2×C8—346no—
803C2×C8—3412no—
804C2×C8—346no—
805C2×C8—346no—
806C2×C8C23×D1711yescharacteristic
807C2×C8C23×D1713yes—
808C2×C8C23×D1713yes—
809C2×C8C23×D1711yescharacteristic
810C23—26no—
811C23—43no—
812C23—43no—
813C23—171no—
814C23—173no—
815C23—1712no—
816C23—173no—
817C23—171no—
818C23—3412no—
819C23—346no—
820C23—683no—
821C23—683no—
822C23—683no—
823C23—683no—
824C23—686no—
825C23—686no—
826C23C22×C4×D1713yes—
827C23C22×C4×D1711yescharacteristic
828C23C22×C4×D1713yes—
829Q8—26no—
830Q8—1712no—
831Q8—342no—
832Q8—346no—
833Q8—346no—
834Q8—346no—
835Q8—346no—
836Q8C22⋊C4×D1714yes—
837D4—212no—
838D4—26no—
839D4—1724no—
840D4—1712no—
841D4—342no—
842D4—346no—
843D4—346no—
844D4—346no—
845D4—342no—
846D4—346no—
847D4—346no—
848D4—346no—
849D4—342no—
850D4—346no—
851D4—346no—
852D4—346no—
853D4—3412no—
854D4—346no—
855D4C22⋊C4×D17112yes—
856C2×C4—26no—
857C2×C4—26no—
858C2×C4—26no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—23no—
862C2×C4—23no—
863C2×C4—1712no—
864C2×C4—171no—
865C2×C4—173no—
866C2×C4—1712no—
867C2×C4—1712no—
868C2×C4—172no—
869C2×C4—176no—
870C2×C4—176no—
871C2×C4—172no—
872C2×C4—173no—
873C2×C4—171no—
874C2×C4—3412no—
875C2×C4—3412no—
876C2×C4—3412no—
877C2×C4—346no—
878C2×C4—346no—
879C2×C4—346no—
880C2×C4—343no—
881C2×C4—343no—
882C2×C4—341no—
883C2×C4—341no—
884C2×C4C22×C4×D1713yes—
885C2×C4C22×C4×D1711yescharacteristic
886C2×C4C22×C4×D1713yes—
887C2×C4C2×D4×D1716yes—
888C2×C4C2×D4×D1716yes—
889C2×C4C24×D1711yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—341no—
895C8—343no—
896C8—343no—
897C8—341no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—172no—
908C22—176no—
909C22—341no—
910C22—343no—
911C22—341no—
912C22—343no—
913C22—343no—
914C22—341no—
915C22—341no—
916C22—343no—
917C22—341no—
918C22—343no—
919C22—6812no—
920C22—1366no—
921C22—13612no—
922C22C2×C22⋊C4×D1716yes—
923C22C23×C4×D1711yescharacteristic
924C4—21no—
925C4—23no—
926C4—172no—
927C4—176no—
928C4—343no—
929C4—341no—
930C4C2×C22⋊C4×D1716yes—
931C4C22×D4×D1711yescharacteristic
932C4C22×D4×D1711yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—342no—
937C2—346no—
938C2—681no—
939C2—683no—
940C2C22×C22⋊C4×D1711yescharacteristic
941C2#1454349511yescharacteristic
942C2#1454349711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
FittingC17×#2880C2
prime radicalC2×#11763645C2
cosocleC2×C4×C17C25
hypercenter#2880D17
hypocenterC17#60065
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#11763574C2semidirect
3. C2×#131×D17C2semidirect
4. #14537234C2semidirect
5. #14537233C2semidirect
6. #14537232C2semidirect
7. #14537232C2semidirect
8. #14537231C2semidirect
9. #14537231C2semidirect
10. #14537230C2semidirect
11. #14537227C2semidirect
12. #14537226C2semidirect
13. C2×#11762774C2semidirect
14. D17×#408C2semidirect
15. C17×#2880C2semidirect
33. C2×#10587593C22semidirect
34. C2×#10587593C22semidirect
35. C2×#10587634C22semidirect
36. C2×#10587634C22semidirect
37. C2×#10587587C22semidirect
38. C2×#10587587C22semidirect
40. C22×#63218C22semidirect
41. C2×M16×D17C22semidirect
42. C2×M16×D17C22semidirect
43. C22×C8×D17C22semidirect
44. #11762777C22semidirect
45. #11762777C22semidirect
46. #11762776C22semidirect
47. #11762776C22semidirect
48. #11762775C22semidirect
49. #11762775C22semidirect
50. #11762774C22semidirect
51. #11762774C22semidirect
52. #11762774C22semidirect
53. #11762774C22semidirect
54. #11762774C22semidirect
55. #11762774C22semidirect
56. #11762774C22semidirect
57. #11762774C22semidirect
58. #11762774C22semidirect
59. #11762774C22semidirect
60. #11762774C22semidirect
61. #11762773C22semidirect
62. #11762772C22semidirect
63. #11762772C22semidirect
64. #11762771C22semidirect
65. #11762771C22semidirect
66. C2×C22⋊#3622C22semidirect
67. C2×#10587491C22semidirect
68. C2×#10587491C22semidirect
69. C22⋊C8×D17C22semidirect
70. C22⋊C8×D17C22semidirect
72. C2×C17×#131C22semidirect
73. C2×C17×#131C22semidirect
74. C17×#408C22semidirect
75. C17×#408C22semidirect
76. C17×#407C22semidirect
77. C2×C17×C22⋊C8C22semidirect
437. #2880D17semidirect
502. C2×#131C2×D17semidirect
503. C2×#131C2×D17semidirect
525. #408C2×D17semidirect
526. #408C2×D17semidirect
532. #407C2×D17semidirect
538. C2×C22⋊C8C2×D17semidirect
671. C17#60065semidirect

Maximal subgroups

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

subgroupindex
C2×#117636452
C2×#117635742
C2×#131×D172
#145372342
#145372332
#145372322
#145372312
#145372302
#145372272
#145372262
C2×#117627742
D17×#4082
C17×#28802
#6006517