Finite Group Databasebeta

← #32860905

Subgroups — #32860905

Order 18176.

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×#17986835C211yesmaximal, characteristic
2C2×#17986764C211yesmaximal, characteristic, complemented
3C2×#131×D71C211yesmaximal, characteristic, complemented
4#22596790C213yesmaximal, complemented
5#22596789C211yesmaximal, characteristic, complemented
6#22596788C213yesmaximal, complemented
7#22596788C213yesmaximal, complemented
8#22596787C211yesmaximal, characteristic, complemented
9#22596787C211yesmaximal, characteristic, complemented
10#22596786C213yesmaximal, complemented
11#22596783C213yesmaximal, complemented
12#22596782C213yesmaximal, complemented
13C2×#17985964C213yesmaximal, complemented
14#408×D71C213yesmaximal, complemented
15C71×#2880C211yesmaximal, characteristic, complemented
16#17986835—28no—
17#17986835—28no—
18C2×#14556176C411yescharacteristic
19C2×#14556176C411yescharacteristic
20C2×#14556175C413yes—
21C2×#14556175C411yescharacteristic
22C2×#14556174C411yescharacteristic
23C2×#14556174C413yes—
24C2×#14556173C413yes—
25C2×#14556173C413yes—
26C22×#11765865C2213yes—
27C22×#11765865C2213yes—
28C2×#41×D71C2213yes—
29C2×#41×D71C2211yescharacteristic
30C2×#41×D71C2213yes—
31C2×#41×D71C2211yescharacteristic
32#17986764—28no—
33C2×#14556136C2213yescomplemented
34C2×#14556136C2213yescomplemented
35C2×#14556135C2211yescharacteristic, complemented
36C2×#14556135C2211yescharacteristic, complemented
37C2×#14556134C2213yescomplemented
38C2×#14556134C2213yescomplemented
39#131×D71—28no—
40C22×#11765848C2213yescomplemented
41C2×M16×D71C2213yescomplemented
42C2×M16×D71C2213yescomplemented
43C22×C8×D71C2213yescomplemented
44#17985967C2213yescomplemented
45#17985967C2213yescomplemented
46#17985966C2213yescomplemented
47#17985966C2213yescomplemented
48#17985965C2213yescomplemented
49#17985965C2213yescomplemented
50#17985964C2213yescomplemented
51#17985964C2216yescomplemented
52#17985964C2211yescharacteristic, complemented
53#17985964C2213yescomplemented
54#17985964C2213yescomplemented
55#17985964C2213yescomplemented
56#17985964C2213yescomplemented
57#17985964C2213yescomplemented
58#17985964C2213yescomplemented
59#17985964C2216yescomplemented
60#17985964C2216yescomplemented
61#17985963C2213yescomplemented
62#17985962C2213yescomplemented
63#17985962C2213yescomplemented
64#17985961C2216yescomplemented
65#17985961C2216yescomplemented
66C2×C22⋊(C71⋊C8)C2213yescomplemented
67C2×(C2×D71)⋊C8C2213yescomplemented
68C2×(C2×D71)⋊C8C2213yescomplemented
69C22⋊C8×D71C2216yescomplemented
70C22⋊C8×D71C2216yescomplemented
71C22×#41×C71C2211yescharacteristic
72C2×#131×C71C2211yescharacteristic, complemented
73C2×#131×C71C2211yescharacteristic, complemented
74#408×C71C2213yescomplemented
75#408×C71C2213yescomplemented
76#407×C71C2213yescomplemented
77C2×C22⋊C8×C71C2213yescomplemented
78#14556176—28no—
79#14556176—28no—
80#14556175—224no—
81#14556175—28no—
82#14556174—28no—
83#14556174—224no—
84#14556173—224no—
85#14556173—224no—
86C2×#11765866C2×C413yes—
87C2×#11765866C2×C413yes—
88C2×#11765866C2×C411yescharacteristic
89C2×#11765866C2×C411yescharacteristic
90C2×#11765865—212no—
91C2×#11765865—212no—
92C2×#11765865—212no—
93C2×#11765865—212no—
94C2×#11765865C2×C413yes—
95C2×#11765865C2×C413yes—
96C2×#11765865C2×C413yes—
97C2×#11765865C2×C413yes—
98C2×#11765865C2×C416yes—
99C2×#11765865C2×C413yes—
100C2×#11765865C2×C413yes—
101C2×#11765865C2313yes—
102C2×#11765865C2313yes—
103C2×#11765865C2313yes—
104C2×#11765865C2311yescharacteristic
105C2×#11765865C2313yes—
106C2×#11765865C2313yes—
107C2×#11765864C2×C413yes—
108C2×#11765864C2×C416yes—
109C2×#11765864C2×C416yes—
110C2×#11765864C2×C413yes—
111C2×#11765864C2×C413yes—
112C2×#11765864C2×C413yes—
113#41×D71—212no—
114#41×D71—212no—
115#41×D71—212no—
116#41×D71—212no—
117#41×D71—24no—
118#41×D71—24no—
119#41×D71D418yes—
120#41×D71D418yes—
121C22×Dic142C2×C413yes—
122C22×Dic142C2×C413yes—
123C2×Q8×D71C2×C413yes—
124C2×Q8×D71C2×C413yes—
125C2×Q8×D71C2×C411yescharacteristic
126C2×Q8×D71C2×C411yescharacteristic
127C22×D284C2×C413yes—
128C22×D284C2×C413yes—
129C22×C22⋊D71C2×C413yes—
130C22×C22⋊D71C2×C416yes—
131C22×C22⋊D71C2×C413yes—
132C2×D4×D71C2×C416yes—
133C2×D4×D71C2×C416yes—
134C2×D4×D71C2×C413yes—
135C2×D4×D71C2×C413yes—
136C2×D4×D71C2×C413yes—
137C2×D4×D71C2×C413yes—
138C22×C4×D71C2316yes—
139C22×C4×D71C2313yes—
140C22×C4×D71C2313yes—
141#14556136—212no—
142#14556136—212no—
143#14556135—24no—
144#14556135—24no—
145#14556134—212no—
146#14556134—212no—
147C2×#11765849C2313yes—
148C2×#11765849C2313yes—
149C2×#11765848—212no—
150C2×#11765848C2316yes—
151C2×#11765848C2313yes—
152C2×#11765848C2313yes—
153C2×#11765848C2313yes—
154C2×#11765848C2311yescharacteristic
155M16×D71—212no—
156M16×D71—212no—
157C22×C71⋊C8C2313yes—
158C22×C71⋊C8C2313yes—
159C2×C8×D71—212no—
160C2×C8×D71C2313yes—
161C2×C8×D71C2313yes—
162C2×C8×D71C2316yes—
163C2×C8×D71C2311yescharacteristic
164C2×C8×D71C2313yes—
165C22⋊(C71⋊C8)C2313yes—
166C22⋊(C71⋊C8)C2316yes—
167C22⋊(C71⋊C8)C2311yescharacteristic
168C22⋊(C71⋊C8)C2313yes—
169C22⋊(C71⋊C8)C2313yes—
170(C2×D71)⋊C8C2313yes—
171(C2×D71)⋊C8C2313yes—
172(C2×D71)⋊C8C2316yes—
173(C2×D71)⋊C8C2316yes—
174(C2×D71)⋊C8C2311yescharacteristic
175(C2×D71)⋊C8C2311yescharacteristic
176(C2×D71)⋊C8C2313yes—
177(C2×D71)⋊C8C2313yes—
178(C2×D71)⋊C8C2313yes—
179(C2×D71)⋊C8C2313yes—
180C2×#41×C71—24no—
181C2×#41×C71—24no—
182C2×#41×C71C2×C411yescharacteristic
183C2×#41×C71C2×C413yes—
184C2×#41×C71C2313yes—
185C2×#41×C71C2311yescharacteristic
186C22×Q8×C71C2×C411yescharacteristic
187C22×D4×C71C2×C413yes—
188C23×C4×C71C2313yes—
189#131×C71—24no—
190#131×C71—24no—
191C2×M16×C71C2313yes—
192C2×M16×C71C2313yes—
193C22×C8×C71C2313yes—
194C22×C8×C71C2313yes—
195C22⋊C8×C71C2311yescharacteristic
196C22⋊C8×C71C2313yes—
197C22⋊C8×C71C2313yes—
198C22⋊C8×C71C2313yes—
199C22⋊C8×C71C2316yes—
200C23×D71C22×C413yes—
201C23×D71C22×C416yes—
202C23×D71C22×C413yes—
203#11765866—24no—
204#11765866—212no—
205#11765866—212no—
206#11765866C22⋊C418yes—
207#11765865—26no—
208#11765865—26no—
209#11765865—224no—
210#11765865—212no—
211#11765865—212no—
212#11765865—212no—
213#11765865—212no—
214#11765865—212no—
215#11765865—26no—
216#11765865—26no—
217#11765865—26no—
218#11765865—26no—
219#11765865—22no—
220#11765865—26no—
221#11765865—26no—
222#11765865—22no—
223#11765865—212no—
224#11765865C2×D4112yes—
225#11765865C2×D4112yes—
226#11765864—212no—
227#11765864—224no—
228#11765864—224no—
229#11765864—212no—
230#11765864—212no—
231#11765864C22⋊C4124yes—
232C2×Dic142—212no—
233C2×Dic142—212no—
234C2×Dic142C22×C413yes—
235C2×Dic142C22×C413yes—
236C2×Dic142C22×C413yes—
237C2×Dic142C22×C411yescharacteristic
238C2×Dic142C22×C413yes—
239C2×Dic142C22×C413yes—
240Q8×D71—24no—
241Q8×D71—212no—
242Q8×D71—212no—
243Q8×D71C22⋊C418yes—
244C2×D284—212no—
245C2×D284—212no—
246C2×D284C22×C413yes—
247C2×D284C22×C413yes—
248C2×D284C22×C413yes—
249C2×D284C22×C413yes—
250C2×D284C22×C411yescharacteristic
251C2×D284C22×C413yes—
252C2×C22⋊D71—212no—
253C2×C22⋊D71—224no—
254C2×C22⋊D71—212no—
255C2×C22⋊D71C22×C416yes—
256C2×C22⋊D71C22×C413yes—
257C2×C22⋊D71C22×C413yes—
258C2×C22⋊D71C22×C413yes—
259C2×C22⋊D71C22×C413yes—
260C2×C22⋊D71C22×C413yes—
261C2×C22⋊D71C22×C411yescharacteristic
262C2×C22⋊D71C22×C411yescharacteristic
263C2×C22⋊D71C22×C413yes—
264C2×C22⋊D71C22×C416yes—
265D4×D71—224no—
266D4×D71—212no—
267D4×D71—224no—
268D4×D71—212no—
269D4×D71—212no—
270D4×D71C22⋊C4124yes—
271C22×Dic71C22×C413yes—
272C22×Dic71C22×C416yes—
273C22×Dic71C22×C413yes—
274C2×C4×D71—26no—
275C2×C4×D71—26no—
276C2×C4×D71—212no—
277C2×C4×D71—212no—
278C2×C4×D71C22×C416yes—
279C2×C4×D71C22×C413yes—
280C2×C4×D71C22×C413yes—
281C2×C4×D71C22×C416yes—
282C2×C4×D71C22×C413yes—
283C2×C4×D71C22×C413yes—
284C2×C4×D71C2×D4112yes—
285C2×C4×D71C2×D4112yes—
286C2×C4×D71C2413yes—
287C2×C4×D71C2411yescharacteristic
288C2×C4×D71C2411yescharacteristic
289C2×C4×D71C2413yes—
290#11765849—26no—
291#11765849—26no—
292#11765848—26no—
293#11765848—212no—
294#11765848—22no—
295#11765848—26no—
296#11765848—26no—
297C2×C71⋊C8—26no—
298C2×C71⋊C8—26no—
299C2×C71⋊C8C2411yescharacteristic
300C2×C71⋊C8C2413yes—
301C2×C71⋊C8C2413yes—
302C2×C71⋊C8C2411yescharacteristic
303C8×D71—22no—
304C8×D71—26no—
305C8×D71—26no—
306C8×D71—26no—
307C8×D71—212no—
308C24×C71C22×C413yes—
309#41×C71—24no—
310#41×C71—212no—
311#41×C71—26no—
312#41×C71—26no—
313#41×C71C2×D414yes—
314#41×C71C2×D414yes—
315C2×Q8×C71—24no—
316C2×Q8×C71C22×C413yes—
317C2×Q8×C71C22×C411yescharacteristic
318C2×D4×C71—212no—
319C2×D4×C71C22×C416yes—
320C2×D4×C71C22×C413yes—
321C2×D4×C71C22×C413yes—
322C22×C4×C71—26no—
323C22×C4×C71—26no—
324C22×C4×C71C22×C413yes—
325C22×C4×C71C22×C413yes—
326C22×C4×C71C22×C413yes—
327C22×C4×C71C2413yes—
328C22×C4×C71C2411yescharacteristic
329C22×C4×C71C2413yes—
330M16×C71—26no—
331M16×C71—26no—
332C2×C8×C71—26no—
333C2×C8×C71—26no—
334C2×C8×C71C2411yescharacteristic
335C2×C8×C71C2411yescharacteristic
336C2×C8×C71C2413yes—
337C2×C8×C71C2413yes—
338C23×C71—26no—
339C23×C71—43no—
340C23×C71—43no—
341C23×C71C23×C411yescharacteristic
342C23×C71C23×C413yes—
343C23×C71C23×C413yes—
344C22×D71—26no—
345C22×D71—212no—
346C22×D71—43no—
347C22×D71—43no—
348C22×D71—46no—
349C22×D71—46no—
350C22×D71—43no—
351C22×D71—43no—
352C22×D71C2×C22⋊C4112yes—
353C22×D71C23×C411yescharacteristic
354C22×D71C23×C413yes—
355C22×D71C23×C413yes—
356C22×D71C23×C411yescharacteristic
357Q8×C71—26no—
358Q8×C71C2×C22⋊C414yes—
359D4×C71—212no—
360D4×C71—26no—
361D4×C71C2×C22⋊C4112yes—
362C2×C4×C71—26no—
363C2×C4×C71—26no—
364C2×C4×C71—26no—
365C2×C4×C71—21no—
366C2×C4×C71—21no—
367C2×C4×C71—23no—
368C2×C4×C71—23no—
369C2×C4×C71C23×C411yescharacteristic
370C2×C4×C71C23×C413yes—
371C2×C4×C71C23×C413yes—
372C2×C4×C71C22×D416yes—
373C2×C4×C71C22×D416yes—
374C2×C4×C71C2511yescharacteristic
375C22⋊D71—212no—
376C22⋊D71—26no—
377C22⋊D71—26no—
378C22⋊D71—26no—
379C22⋊D71—22no—
380C22⋊D71—26no—
381C22⋊D71—26no—
382C22⋊D71—22no—
383C22⋊D71—26no—
384C22⋊D71C2×C22⋊C4124yes—
385C2×Dic71—26no—
386C2×Dic71—212no—
387C2×Dic71C2×C22⋊C4112yes—
388C2×Dic71C23×C413yes—
389C2×Dic71C23×C411yescharacteristic
390C2×Dic71C23×C411yescharacteristic
391C2×Dic71C23×C413yes—
392D284—26no—
393D284—26no—
394D284—26no—
395D284—22no—
396D284—26no—
397D284C2×C22⋊C4112yes—
398C4×D71—212no—
399C4×D71—26no—
400C4×D71—26no—
401C4×D71—21no—
402C4×D71—21no—
403C4×D71—23no—
404C4×D71—23no—
405C4×D71—212no—
406C4×D71C2×C22⋊C4112yes—
407C4×D71C2×C22⋊C4112yes—
408C4×D71C22×D412yes—
409C4×D71C22×D416yes—
410C4×D71C22×D416yes—
411C4×D71C22×D412yes—
412Dic142—26no—
413Dic142—26no—
414Dic142—26no—
415Dic142—22no—
416Dic142—26no—
417Dic142C2×C22⋊C4112yes—
418C8×C71—21no—
419C8×C71—21no—
420C8×C71—23no—
421C8×C71—23no—
422C71⋊C8—21no—
423C71⋊C8—23no—
424C71⋊C8—23no—
425C71⋊C8—21no—
426C22×C71—23no—
427C22×C71—23no—
428C22×C71—23no—
429C22×C71—21no—
430C22×C71—23no—
431C22×C71—23no—
432C22×C71—21no—
433C22×C71—21no—
434C22×C71—86no—
435C22×C71C22×C22⋊C416yes—
436C22×C71C24×C411yescharacteristic
437C2×D71—21no—
438C2×D71—23no—
439C2×D71—21no—
440C2×D71—23no—
441C2×D71—21no—
442C2×D71—23no—
443C2×D71—23no—
444C2×D71—21no—
445C2×D71—23no—
446C2×D71—21no—
447C2×D71—412no—
448C2×D71—812no—
449C2×D71—86no—
450C2×D71C22×C22⋊C416yes—
451C2×D71C22×C22⋊C412yes—
452C4×C71—21no—
453C4×C71—23no—
454C4×C71C22×C22⋊C416yes—
455C4×C71C23×D411yescharacteristic
456C4×C71C23×D411yescharacteristic
457Dic71—23no—
458Dic71—21no—
459Dic71C22×C22⋊C412yes—
460Dic71C22×C22⋊C416yes—
461#60065—711nomaximal, Sylow
462C2×C71—26no—
463C2×C71—43no—
464C2×C71—41no—
465C2×C71C23×C22⋊C411yescharacteristic
466C2×C71#357311yescharacteristic
467C2×C71#357311yescharacteristic
468D71—22no—
469D71—26no—
470D71—43no—
471D71—41no—
472C2×#585—711no—
473C2×#568—711no—
474C22×#131—711no—
475#2880—713no—
476#2880—713no—
477#2880—713no—
478#2880—713no—
479#2880—711no—
480#2880—711no—
481#2880—711no—
482#2880D7111yescharacteristic, complemented
483#2879—713no—
484#2879—713no—
485C2×#408—713no—
486C2×#408—713no—
487C71#6006511yescharacteristic, complemented, Sylow
488#585—1428no—
489#585—1428no—
490C2×2−1+4—711no—
491C2×2−1+4—713no—
492C2×2−1+4—711no—
493C2×2−1+4—711no—
494C2×H(5,𝔽2)—713no—
495C2×H(5,𝔽2)—711no—
496C2×H(5,𝔽2)—713no—
497C2×H(5,𝔽2)—713no—
498C22×#41—711no—
499C22×#41—713no—
500C22×#41—713no—
501C22×#41—711no—
502C22×#41—713no—
503C22×#41—713no—
504C22×#41C2×D7111yescharacteristic
505#568—1428no—
506C2×#131—711no—
507C2×#131—711no—
508C2×#131—713no—
509C2×#131—713no—
510C2×#131—713no—
511C2×#131—713no—
512C2×#131—1428no—
513C2×#131C2×D7111yescharacteristic, complemented
514C2×#131C2×D7111yescharacteristic, complemented
515C22×M16—713no—
516C22×M16—713no—
517C22×M16—713no—
518C23×C8—713no—
519#408—713no—
520#408—713no—
521#408—713no—
522#408—713no—
523#408—713no—
524#408—713no—
525#408—713no—
526#408—711no—
527#408—716no—
528#408—713no—
529#408—713no—
530#408—713no—
531#408—713no—
532#408—713no—
533#408—713no—
534#408—716no—
535#408—716no—
536#408C2×D7113yescomplemented
537#408C2×D7113yescomplemented
538#407—713no—
539#407—713no—
540#407—713no—
541#407—716no—
542#407—716no—
543#407C2×D7113yescomplemented
544C2×C22⋊C8—713no—
545C2×C22⋊C8—713no—
546C2×C22⋊C8—713no—
547C2×C22⋊C8—716no—
548C2×C22⋊C8—716no—
549C2×C22⋊C8C2×D7113yescomplemented
5502−1+4—1428no—
5512−1+4—1428no—
5522−1+4—1428no—
5532−1+4—14224no—
554H(5,𝔽2)—14224no—
555H(5,𝔽2)—14224no—
556H(5,𝔽2)—14224no—
557H(5,𝔽2)—1428no—
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—718no—
561C2×#41—718no—
562C2×#41—711no—
563C2×#41—713no—
564C2×#41—713no—
565C2×#41—711no—
566C2×#41—713no—
567C2×#41—716no—
568C2×#41—713no—
569C2×#41—716no—
570C2×#41—713no—
571C2×#41—713no—
572C2×#41—713no—
573C2×#41—713no—
574C2×#41—713no—
575C2×#41—713no—
576C2×#41—716no—
577C2×#41—713no—
578C2×#41—713no—
579C2×#41—713no—
580C2×#41—713no—
581C2×#41—713no—
582C2×#41—711no—
583C2×#41—713no—
584C2×#41—713no—
585C2×#41—14212no—
586C2×#41—14212no—
587C2×#41—14212no—
588C2×#41—14212no—
589C2×#41—14212no—
590C2×#41—14212no—
591C2×#41—14212no—
592C2×#41—14212no—
593C2×#41—1424no—
594C2×#41—1424no—
595C2×#41C4×D7111yescharacteristic
596C2×#41C4×D7113yes—
597C2×#41C22×D7113yes—
598C2×#41C22×D7111yescharacteristic
599C22×Q8—711no—
600C22×Q8—713no—
601C22×Q8—713no—
602C22×Q8—711no—
603C22×Q8—713no—
604C22×Q8—713no—
605C22×Q8C4×D7111yescharacteristic
606C22×D4—713no—
607C22×D4—713no—
608C22×D4—716no—
609C22×D4—713no—
610C22×D4—713no—
611C22×D4—716no—
612C22×D4—713no—
613C22×D4—716no—
614C22×D4—713no—
615C22×D4—713no—
616C22×D4—713no—
617C22×D4C4×D7113yes—
618C23×C4—713no—
619C23×C4—716no—
620C23×C4—713no—
621C23×C4C22×D7113yes—
622#131—24no—
623#131—24no—
624#131—14212no—
625#131—14212no—
626#131—14212no—
627#131—14212no—
628#131—1424no—
629#131—1424no—
630C2×M16—713no—
631C2×M16—713no—
632C2×M16—713no—
633C2×M16—711no—
634C2×M16—716no—
635C2×M16—713no—
636C2×M16—713no—
637C2×M16—14212no—
638C2×M16—14212no—
639C2×M16—14212no—
640C2×M16C22×D7113yes—
641C2×M16C22×D7113yes—
642C22×C8—713no—
643C22×C8—713no—
644C22×C8—711no—
645C22×C8—713no—
646C22×C8—713no—
647C22×C8—713no—
648C22×C8—716no—
649C22×C8—14212no—
650C22×C8C22×D7113yes—
651C22×C8C22×D7113yes—
652C22⋊C8—713no—
653C22⋊C8—711no—
654C22⋊C8—716no—
655C22⋊C8—713no—
656C22⋊C8—713no—
657C22⋊C8—713no—
658C22⋊C8—711no—
659C22⋊C8—713no—
660C22⋊C8—711no—
661C22⋊C8—716no—
662C22⋊C8—716no—
663C22⋊C8—713no—
664C22⋊C8—713no—
665C22⋊C8—713no—
666C22⋊C8—713no—
667C22⋊C8C22×D7113yes—
668C22⋊C8C22×D7116yes—
669C22⋊C8C22×D7111yescharacteristic
670C22⋊C8C22×D7113yes—
671C22⋊C8C22×D7113yes—
672C24—713no—
673C24—716no—
674C24—713no—
675C24C2×C4×D7113yes—
676#41—24no—
677#41—212no—
678#41—26no—
679#41—26no—
680#41—718no—
681#41—7124no—
682#41—7112no—
683#41—7112no—
684#41—1422no—
685#41—1426no—
686#41—1426no—
687#41—1422no—
688#41—1426no—
689#41—1426no—
690#41—1426no—
691#41—1426no—
692#41—14212no—
693#41—14212no—
694#41—14212no—
695#41—14212no—
696#41—14224no—
697#41—14212no—
698#41—14212no—
699#41—14224no—
700#41—14212no—
701#41—14212no—
702#41—14224no—
703#41—14212no—
704#41—14212no—
705#41—1424no—
706#41—14212no—
707#41—1426no—
708#41—1426no—
709#41D4×D7114yes—
710#41D4×D7114yes—
711C2×Q8—24no—
712C2×Q8—718no—
713C2×Q8—713no—
714C2×Q8—713no—
715C2×Q8—713no—
716C2×Q8—711no—
717C2×Q8—713no—
718C2×Q8—713no—
719C2×Q8—14212no—
720C2×Q8—14212no—
721C2×Q8—14212no—
722C2×Q8—14212no—
723C2×Q8—1424no—
724C2×Q8C2×C4×D7113yes—
725C2×Q8C2×C4×D7111yescharacteristic
726C2×D4—212no—
727C2×D4—716no—
728C2×D4—7124no—
729C2×D4—713no—
730C2×D4—713no—
731C2×D4—711no—
732C2×D4—713no—
733C2×D4—713no—
734C2×D4—713no—
735C2×D4—711no—
736C2×D4—713no—
737C2×D4—716no—
738C2×D4—713no—
739C2×D4—713no—
740C2×D4—713no—
741C2×D4—711no—
742C2×D4—713no—
743C2×D4—713no—
744C2×D4—14212no—
745C2×D4—14212no—
746C2×D4—14212no—
747C2×D4—14212no—
748C2×D4—14224no—
749C2×D4—14212no—
750C2×D4—14224no—
751C2×D4—14224no—
752C2×D4—14212no—
753C2×D4—14212no—
754C2×D4C2×C4×D7116yes—
755C2×D4C2×C4×D7113yes—
756C2×D4C2×C4×D7113yes—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—713no—
760C22×C4—713no—
761C22×C4—713no—
762C22×C4—7112no—
763C22×C4—7112no—
764C22×C4—711no—
765C22×C4—713no—
766C22×C4—716no—
767C22×C4—713no—
768C22×C4—716no—
769C22×C4—716no—
770C22×C4—713no—
771C22×C4—713no—
772C22×C4—713no—
773C22×C4—711no—
774C22×C4—14212no—
775C22×C4—14212no—
776C22×C4—1426no—
777C22×C4—1426no—
778C22×C4C2×C4×D7113yes—
779C22×C4C2×C4×D7113yes—
780C22×C4C2×C4×D7113yes—
781C22×C4C23×D7113yes—
782C22×C4C23×D7111yescharacteristic
783C22×C4C23×D7113yes—
784M16—26no—
785M16—26no—
786M16—1422no—
787M16—1426no—
788M16—1426no—
789M16—14212no—
790M16—1426no—
791M16—1426no—
792M16—1426no—
793C2×C8—26no—
794C2×C8—26no—
795C2×C8—711no—
796C2×C8—713no—
797C2×C8—713no—
798C2×C8—711no—
799C2×C8—1422no—
800C2×C8—1426no—
801C2×C8—1426no—
802C2×C8—1426no—
803C2×C8—14212no—
804C2×C8—1426no—
805C2×C8—1426no—
806C2×C8C23×D7111yescharacteristic
807C2×C8C23×D7113yes—
808C2×C8C23×D7113yes—
809C2×C8C23×D7111yescharacteristic
810C23—26no—
811C23—43no—
812C23—43no—
813C23—2843no—
814C23—2843no—
815C23—2843no—
816C23—2843no—
817C23—2846no—
818C23—2846no—
819C23—7112no—
820C23—711no—
821C23—713no—
822C23—713no—
823C23—711no—
824C23—14212no—
825C23—1426no—
826C23C22×C4×D7113yes—
827C23C22×C4×D7111yescharacteristic
828C23C22×C4×D7113yes—
829Q8—26no—
830Q8—7112no—
831Q8—1422no—
832Q8—1426no—
833Q8—1426no—
834Q8—1426no—
835Q8—1426no—
836Q8C22⋊C4×D7114yes—
837D4—212no—
838D4—26no—
839D4—7124no—
840D4—7112no—
841D4—1422no—
842D4—1426no—
843D4—1426no—
844D4—1426no—
845D4—1422no—
846D4—1426no—
847D4—1426no—
848D4—1426no—
849D4—1422no—
850D4—1426no—
851D4—1426no—
852D4—1426no—
853D4—14212no—
854D4—1426no—
855D4C22⋊C4×D71112yes—
856C2×C4—26no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—23no—
860C2×C4—23no—
861C2×C4—26no—
862C2×C4—26no—
863C2×C4—711no—
864C2×C4—713no—
865C2×C4—7112no—
866C2×C4—712no—
867C2×C4—716no—
868C2×C4—716no—
869C2×C4—712no—
870C2×C4—7112no—
871C2×C4—7112no—
872C2×C4—713no—
873C2×C4—711no—
874C2×C4—14212no—
875C2×C4—14212no—
876C2×C4—14212no—
877C2×C4—1426no—
878C2×C4—1423no—
879C2×C4—1423no—
880C2×C4—1421no—
881C2×C4—1421no—
882C2×C4—1426no—
883C2×C4—1426no—
884C2×C4C22×C4×D7113yes—
885C2×C4C22×C4×D7111yescharacteristic
886C2×C4C22×C4×D7113yes—
887C2×C4C2×D4×D7116yes—
888C2×C4C2×D4×D7116yes—
889C2×C4C24×D7111yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—1421no—
895C8—1423no—
896C8—1423no—
897C8—1421no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—28412no—
908C22—5686no—
909C22—56812no—
910C22—712no—
911C22—716no—
912C22—1423no—
913C22—1421no—
914C22—1421no—
915C22—1423no—
916C22—1421no—
917C22—1423no—
918C22—1421no—
919C22—1423no—
920C22—1421no—
921C22—1423no—
922C22C2×C22⋊C4×D7116yes—
923C22C23×C4×D7111yescharacteristic
924C4—21no—
925C4—23no—
926C4—712no—
927C4—716no—
928C4—1423no—
929C4—1421no—
930C4C2×C22⋊C4×D7116yes—
931C4C22×D4×D7111yescharacteristic
932C4C22×D4×D7111yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—2841no—
937C2—2843no—
938C2—1422no—
939C2—1426no—
940C2C22×C22⋊C4×D7111yescharacteristic
941C2#2260305111yescharacteristic
942C2#2260305311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D71
commutator, socleC22×C71C24×C4
FittingC71×#2880C2
prime radicalC2×#17986835C2
cosocleC2×C4×C71C25
hypercenter#2880D71
hypocenterC71#60065
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#17986764C2semidirect
3. C2×#131×D71C2semidirect
4. #22596790C2semidirect
5. #22596789C2semidirect
6. #22596788C2semidirect
7. #22596788C2semidirect
8. #22596787C2semidirect
9. #22596787C2semidirect
10. #22596786C2semidirect
11. #22596783C2semidirect
12. #22596782C2semidirect
13. C2×#17985964C2semidirect
14. #408×D71C2semidirect
15. C71×#2880C2semidirect
33. C2×#14556136C22semidirect
34. C2×#14556136C22semidirect
35. C2×#14556135C22semidirect
36. C2×#14556135C22semidirect
37. C2×#14556134C22semidirect
38. C2×#14556134C22semidirect
40. C22×#11765848C22semidirect
41. C2×M16×D71C22semidirect
42. C2×M16×D71C22semidirect
43. C22×C8×D71C22semidirect
44. #17985967C22semidirect
45. #17985967C22semidirect
46. #17985966C22semidirect
47. #17985966C22semidirect
48. #17985965C22semidirect
49. #17985965C22semidirect
50. #17985964C22semidirect
51. #17985964C22semidirect
52. #17985964C22semidirect
53. #17985964C22semidirect
54. #17985964C22semidirect
55. #17985964C22semidirect
56. #17985964C22semidirect
57. #17985964C22semidirect
58. #17985964C22semidirect
59. #17985964C22semidirect
60. #17985964C22semidirect
61. #17985963C22semidirect
62. #17985962C22semidirect
63. #17985962C22semidirect
64. #17985961C22semidirect
65. #17985961C22semidirect
66. C2×C22⋊(C71⋊C8)C22semidirect
67. C2×(C2×D71)⋊C8C22semidirect
68. C2×(C2×D71)⋊C8C22semidirect
69. C22⋊C8×D71C22semidirect
70. C22⋊C8×D71C22semidirect
72. C2×#131×C71C22semidirect
73. C2×#131×C71C22semidirect
74. #408×C71C22semidirect
75. #408×C71C22semidirect
76. #407×C71C22semidirect
77. C2×C22⋊C8×C71C22semidirect
482. #2880D71semidirect
487. C71#60065semidirect
513. C2×#131C2×D71semidirect
514. C2×#131C2×D71semidirect
536. #408C2×D71semidirect
537. #408C2×D71semidirect
543. #407C2×D71semidirect
549. C2×C22⋊C8C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179868352
C2×#179867642
C2×#131×D712
#225967902
#225967892
#225967882
#225967872
#225967862
#225967832
#225967822
C2×#179859642
#408×D712
C71×#28802
#6006571