Finite Group Databasebeta

← C2×#11727788 #13355804

Subgroups — C2×#11727788 #13355804

Order 1792.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90495C211yesmaximal, characteristic
2C2×#90177C211yesmaximal, characteristic, complemented
3C22×C7×#99C211yesmaximal, characteristic, complemented
4C22×#6408C211yesmaximal, characteristic, complemented
5C22×#6380C211yesmaximal, characteristic, complemented
6C2×#89322C211yesmaximal, characteristic, complemented
7C2×#89321C211yesmaximal, characteristic, complemented
8#11727788C218yesmaximal, direct product factor
9C23×C7×D4C2211yescharacteristic
10C23×C22⋊D7C2211yescharacteristic
11C22×C7×C22⋊C4C2211yescharacteristic
12C22×C7×C22⋊C4C2211yescharacteristic
13C2×#6516C412yescomplemented
14C22×C22⋊Dic7C2211yescharacteristic
15C22×C22⋊Dic7C2211yescharacteristic
16C22×C22⋊Dic7C2211yescharacteristic
17#90495—22no—
18#90495—22no—
19#90495C414yescomplemented
20#90495C2214yes—
21C2×#6502—22no—
22C2×#6500—21no—
23C2×#6498—21no—
24C2×#6492C412yescomplemented
25C2×C4×C22⋊D7—22no—
26#90177—22no—
27#90177—22no—
28#90177—22no—
29#90177C2214yescomplemented
30C2×(C22⋊D7)⋊C4—22no—
31C2×D7×C22⋊C4—21no—
32C2×#6440—21no—
33C2×C7×#99—22no—
34C2×C7×#99—22no—
35C2×C7×#99C2214yescomplemented
36C2×#6408—22no—
37C2×#6408—22no—
38C2×#6408C2214yescomplemented
39C2×#6380—22no—
40C2×#6380—22no—
41C2×#6380C2214yescomplemented
42#89322C2214yescomplemented
43#89321C2214yescomplemented
44C2×#1913—71nomaximal, Sylow
45C25×C7C2×C411yescharacteristic, complemented
46C25×C7C2311yescharacteristic
47C24×D7D411yescharacteristic
48C22×C7×D4—21no—
49C22×C7×D4—21no—
50C22×C7×D4—21no—
51C22×C7×D4—21no—
52C22×C7×D4—21no—
53C22×C7×D4—21no—
54C22×C7×D4—21no—
55C22×C7×D4—21no—
56C22×C7×D4—21no—
57C22×C7×D4—21no—
58C22×C7×D4—21no—
59C22×C7×D4—21no—
60C22×C7×D4C2×C412yescomplemented
61C22×C7×D4C2312yes—
62C23×C4×C7—21no—
63C23×C4×C7—21no—
64C23×C4×C7C2×C411yescharacteristic, complemented
65C22×C22⋊D7—21no—
66C22×C22⋊D7—21no—
67C22×C22⋊D7—21no—
68C22×C22⋊D7—21no—
69C22×C22⋊D7—21no—
70C22×C22⋊D7—21no—
71C22×C22⋊D7—21no—
72C22×C22⋊D7—21no—
73C22×C22⋊D7—22no—
74C22×C22⋊D7C2×C412yes—
75C22×C22⋊D7C2×C412yes—
76C22×C22⋊D7D412yes—
77C22×C22⋊D7D412yes—
78C22×C22⋊D7D412yes—
79C22×C22⋊D7C2312yes—
80C23×Dic7—21no—
81C23×Dic7—21no—
82C23×Dic7—21no—
83C23×Dic7D411yescharacteristic
84C22×C4×D7—22no—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—21no—
87C2×C7×C22⋊C4—21no—
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4—21no—
90C2×C7×C22⋊C4—21no—
91C2×C7×C22⋊C4—21no—
92C2×C7×C22⋊C4—21no—
93C2×C7×C22⋊C4D412yescomplemented
94C2×C7×C22⋊C4D412yescomplemented
95C2×C7×C22⋊C4C2312yes—
96C2×C7×C22⋊C4C2312yes—
97#6516—24no—
98#6516C2×C418yescomplemented
99C2×C22⋊Dic7—21no—
100C2×C22⋊Dic7—21no—
101C2×C22⋊Dic7—21no—
102C2×C22⋊Dic7—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—22no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7C2×C412yescomplemented
112C2×C22⋊Dic7C2×C412yescomplemented
113C2×C22⋊Dic7D412yescomplemented
114C2×C22⋊Dic7D412yescomplemented
115C2×C22⋊Dic7C2312yes—
116C2×C22⋊Dic7C2312yes—
117C2×C22⋊Dic7C2312yes—
118#6502—28no—
119#6502—28no—
120#6500—24no—
121#6500—24no—
122#6498—24no—
123#6498—24no—
124#6492—24no—
125#6492C2×C418yescomplemented
126C4×C22⋊D7—28no—
127C4×C22⋊D7—28no—
128C2×(C2×D7)⋊C4—22no—
129C2×(C2×D7)⋊C4—22no—
130C2×Dic7⋊C4—22no—
131C2×Dic7⋊C4—22no—
132C2×C4×Dic7—22no—
133(C22⋊D7)⋊C4—28no—
134(C22⋊D7)⋊C4—28no—
135D7×C22⋊C4—24no—
136D7×C22⋊C4—24no—
137#6440—24no—
138#6440—24no—
139C7×#99—28no—
140#6408—28no—
141#6380—28no—
142C2×#534—71no—
143C2×#518—71no—
144C22×#99—71no—
145C22×#99—71no—
146C22×#99D711yescharacteristic, complemented
147#1913—78no—
148C2×#342—71no—
149C2×#342—71no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—82no—
157C24×C7—82no—
158C24×C7C22×C411yescharacteristic
159C24×C7C22×C411yescharacteristic
160C24×C7C22×C412yescomplemented
161C24×C7C2×D411yescharacteristic
162C24×C7C2×D411yescharacteristic
163C24×C7C2×D411yescharacteristic
164C24×C7C2×D411yescharacteristic
165C24×C7C2×D411yescharacteristic
166C24×C7C2×D411yescharacteristic
167C24×C7C2×D411yescharacteristic
168C24×C7C2×D411yescharacteristic
169C24×C7#4111yescharacteristic
170C24×C7#4111yescharacteristic
171C24×C7#4111yescharacteristic
172C24×C7#4111yescharacteristic
173C24×C7C2411yescharacteristic
174C23×D7—21no—
175C23×D7—21no—
176C23×D7—21no—
177C23×D7—21no—
178C23×D7—82no—
179C23×D7C22⋊C412yes—
180C23×D7C22⋊C412yes—
181C23×D7C2×D412yes—
182C2×C7×D4—22no—
183C2×C7×D4—22no—
184C2×C7×D4—22no—
185C2×C7×D4—22no—
186C2×C7×D4—22no—
187C2×C7×D4—22no—
188C2×C7×D4—22no—
189C2×C7×D4—22no—
190C2×C7×D4—22no—
191C2×C7×D4—22no—
192C2×C7×D4—22no—
193C2×C7×D4—22no—
194C2×C7×D4—41no—
195C2×C7×D4—41no—
196C2×C7×D4—41no—
197C2×C7×D4—41no—
198C2×C7×D4—41no—
199C2×C7×D4—41no—
200C2×C7×D4—41no—
201C2×C7×D4—41no—
202C2×C7×D4—41no—
203C2×C7×D4—41no—
204C2×C7×D4—41no—
205C2×C7×D4—41no—
206C2×C7×D4—41no—
207C2×C7×D4—41no—
208C2×C7×D4—41no—
209C2×C7×D4—41no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—41no—
221C22×C4×C7—41no—
222C22×C4×C7—82no—
223C22×C4×C7—82no—
224C22×C4×C7C22×C412yescomplemented
225C2×C22⋊D7—22no—
226C2×C22⋊D7—22no—
227C2×C22⋊D7—22no—
228C2×C22⋊D7—22no—
229C2×C22⋊D7—22no—
230C2×C22⋊D7—22no—
231C2×C22⋊D7—22no—
232C2×C22⋊D7—22no—
233C2×C22⋊D7—22no—
234C2×C22⋊D7—22no—
235C2×C22⋊D7—22no—
236C2×C22⋊D7—22no—
237C2×C22⋊D7—22no—
238C2×C22⋊D7—22no—
239C2×C22⋊D7—22no—
240C2×C22⋊D7—22no—
241C2×C22⋊D7—22no—
242C2×C22⋊D7—22no—
243C2×C22⋊D7—22no—
244C2×C22⋊D7—22no—
245C2×C22⋊D7—22no—
246C2×C22⋊D7—22no—
247C2×C22⋊D7—22no—
248C2×C22⋊D7—22no—
249C2×C22⋊D7—28no—
250C2×C22⋊D7—84no—
251C2×C22⋊D7C22⋊C414yes—
252C2×C22⋊D7C22⋊C414yes—
253C2×C22⋊D7C22×C414yes—
254C2×C22⋊D7C2×D414yes—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7—22no—
264C22×Dic7—22no—
265C22×Dic7—22no—
266C22×Dic7—41no—
267C22×Dic7—41no—
268C22×Dic7—82no—
269C22×Dic7—82no—
270C22×Dic7—82no—
271C22×Dic7C22⋊C412yes—
272C22×Dic7C22⋊C412yes—
273C22×Dic7C2×D412yes—
274C2×C4×D7—28no—
275C2×C4×D7—84no—
276C7×C22⋊C4—22no—
277C7×C22⋊C4—22no—
278C7×C22⋊C4—22no—
279C7×C22⋊C4—22no—
280C7×C22⋊C4—22no—
281C7×C22⋊C4—41no—
282C7×C22⋊C4—41no—
283C7×C22⋊C4C2×D414yescomplemented
284C22⋊Dic7—22no—
285C22⋊Dic7—22no—
286C22⋊Dic7—22no—
287C22⋊Dic7—22no—
288C22⋊Dic7—22no—
289C22⋊Dic7—22no—
290C22⋊Dic7—28no—
291C22⋊Dic7—22no—
292C22⋊Dic7—22no—
293C22⋊Dic7—41no—
294C22⋊Dic7—41no—
295C22⋊Dic7C22×C414yescomplemented
296C22⋊Dic7C2×D414yescomplemented
297(C2×D7)⋊C4—28no—
298(C2×D7)⋊C4—28no—
299Dic7⋊C4—28no—
300Dic7⋊C4—28no—
301C4×Dic7—28no—
302C23×D4—71no—
303C23×D4C2×D711yescharacteristic
304#534—74no—
305#534—74no—
306#534—142no—
307#534—142no—
308C2×#123—72no—
309C2×#123—141no—
310C2×#121—142no—
311C2×#120—72no—
312C2×#120—141no—
313#518—74no—
314#518—142no—
315#518—142no—
316#518—142no—
317C2×C4×D4—142no—
318C2×C4×D4—142no—
319C2×#117—141no—
320C22×C22⋊C4—71no—
321C22×C22⋊C4—71no—
322C22×C22⋊C4—71no—
323C22×C22⋊C4—141no—
324C22×C22⋊C4C2×D711yescharacteristic
325C22×C22⋊C4C2×D711yescharacteristic
326C2×#99—22no—
327C2×#99—22no—
328C2×#99—74no—
329C2×#99—74no—
330C2×#99—142no—
331C2×#99—142no—
332C2×#99—142no—
333C2×#99—142no—
334C2×#99C2×D714yescomplemented
335#342—74no—
336#342—74no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—42no—
341C23×C7—42no—
342C23×C7—42no—
343C23×C7—42no—
344C23×C7—42no—
345C23×C7—42no—
346C23×C7—42no—
347C23×C7—44no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—82no—
353C23×C7—82no—
354C23×C7—81no—
355C23×C7—81no—
356C23×C7—81no—
357C23×C7—81no—
358C23×C7—81no—
359C23×C7—81no—
360C23×C7—81no—
361C23×C7—81no—
362C23×C7—82no—
363C23×C7—82no—
364C23×C7—82no—
365C23×C7—82no—
366C23×C7C2×C22⋊C411yescharacteristic
367C23×C7C2×C22⋊C411yescharacteristic
368C23×C7C2×C22⋊C411yescharacteristic
369C23×C7C2×C22⋊C411yescharacteristic
370C23×C7C4×D411yescharacteristic
371C23×C7C4×D411yescharacteristic
372C23×C7C4×D411yescharacteristic
373C23×C7C4×D411yescharacteristic
374C23×C7C4×D411yescharacteristic
375C23×C7C4×D411yescharacteristic
376C23×C7C4×D411yescharacteristic
377C23×C7C4×D411yescharacteristic
378C23×C7#12011yescharacteristic
379C23×C7#12011yescharacteristic
380C23×C7#12011yescharacteristic
381C23×C7#12011yescharacteristic
382C23×C7#12111yescharacteristic
383C23×C7#12111yescharacteristic
384C23×C7#12111yescharacteristic
385C23×C7#12111yescharacteristic
386C23×C7#12111yescharacteristic
387C23×C7#12111yescharacteristic
388C23×C7#12111yescharacteristic
389C23×C7#12111yescharacteristic
390C23×C7#12311yescharacteristic
391C23×C7#12311yescharacteristic
392C23×C7#12311yescharacteristic
393C23×C7#12311yescharacteristic
394C23×C7C23×C411yescharacteristic
395C23×C7C22×D411yescharacteristic
396C23×C7C22×D411yescharacteristic
397C23×C7C22×D411yescharacteristic
398C23×C7C22×D411yescharacteristic
399C23×C7C2×#4111yescharacteristic
400C23×C7C2×#4111yescharacteristic
401C22×D7—22no—
402C22×D7—22no—
403C22×D7—22no—
404C22×D7—22no—
405C22×D7—22no—
406C22×D7—22no—
407C22×D7—44no—
408C22×D7—44no—
409C22×D7—82no—
410C22×D7—82no—
411C22×D7—82no—
412C22×D7—82no—
413C22×D7—82no—
414C22×D7C2×C22⋊C414yes—
415C7×D4—42no—
416C7×D4—42no—
417C7×D4—42no—
418C7×D4—42no—
419C7×D4—42no—
420C7×D4—42no—
421C7×D4—42no—
422C7×D4—42no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—24no—
427C2×C4×C7—44no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—42no—
433C2×C4×C7—82no—
434C2×C4×C7—82no—
435C2×C4×C7—82no—
436C2×C4×C7—82no—
437C2×C4×C7—82no—
438C22⋊D7—24no—
439C22⋊D7—24no—
440C22⋊D7—24no—
441C22⋊D7—24no—
442C22⋊D7—24no—
443C22⋊D7—24no—
444C22⋊D7—24no—
445C22⋊D7—24no—
446C22⋊D7—88no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—24no—
454C2×Dic7—24no—
455C2×Dic7—44no—
456C2×Dic7—44no—
457C2×Dic7—42no—
458C2×Dic7—82no—
459C2×Dic7—82no—
460C2×Dic7—82no—
461C2×Dic7—82no—
462C2×Dic7—82no—
463C2×Dic7—82no—
464C2×Dic7—82no—
465C2×Dic7C2×C22⋊C414yes—
466C4×D7—88no—
467C25—71no—
468C25C4×D711yescharacteristic, complemented
469C25C22×D711yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—72no—
483C22×D4—72no—
484C22×D4—72no—
485C22×D4—72no—
486C22×D4—72no—
487C22×D4—72no—
488C22×D4—141no—
489C22×D4—141no—
490C22×D4—141no—
491C22×D4—141no—
492C22×D4—141no—
493C22×D4—141no—
494C22×D4—141no—
495C22×D4—141no—
496C22×D4—142no—
497C22×D4C4×D712yescomplemented
498C22×D4C22×D712yes—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—71no—
502C23×C4—142no—
503C23×C4—141no—
504C23×C4—141no—
505C23×C4—141no—
506C23×C4C4×D711yescharacteristic, complemented
507#123—78no—
508#123—144no—
509#123—144no—
510#123—144no—
511#121—148no—
512#121—148no—
513#120—78no—
514#120—144no—
515#120—144no—
516#120—144no—
517C4×D4—148no—
518C4×D4—148no—
519C4×D4—148no—
520C4×D4—148no—
521#117—144no—
522#117—144no—
523C2×C4⋊C4—142no—
524C2×C4⋊C4—142no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
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—72no—
534C2×C22⋊C4—72no—
535C2×C22⋊C4—72no—
536C2×C22⋊C4—72no—
537C2×C22⋊C4—72no—
538C2×C22⋊C4—72no—
539C2×C22⋊C4—72no—
540C2×C22⋊C4—144no—
541C2×C22⋊C4—144no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—142no—
544C2×C22⋊C4—142no—
545C2×C22⋊C4—141no—
546C2×C22⋊C4—141no—
547C2×C22⋊C4—141no—
548C2×C22⋊C4—141no—
549C2×C22⋊C4—141no—
550C2×C22⋊C4—141no—
551C2×C22⋊C4—141no—
552C2×C22⋊C4—141no—
553C2×C22⋊C4—141no—
554C2×C22⋊C4—141no—
555C2×C22⋊C4—141no—
556C2×C22⋊C4C22⋊D712yescomplemented
557C2×C22⋊C4C22⋊D712yescomplemented
558C2×C22⋊C4C22×D712yes—
559C2×C22⋊C4C22×D712yes—
560C2×C42—142no—
561#99—28no—
562#99—148no—
563#99—148no—
564C22×C7—22no—
565C22×C7—22no—
566C22×C7—22no—
567C22×C7—22no—
568C22×C7—22no—
569C22×C7—22no—
570C22×C7—22no—
571C22×C7—41no—
572C22×C7—41no—
573C22×C7—41no—
574C22×C7—41no—
575C22×C7—41no—
576C22×C7—41no—
577C22×C7—41no—
578C22×C7—41no—
579C22×C7—41no—
580C22×C7—41no—
581C22×C7—41no—
582C22×C7—41no—
583C22×C7—41no—
584C22×C7—41no—
585C22×C7—41no—
586C22×C7—41no—
587C22×C7—41no—
588C22×C7—41no—
589C22×C7—41no—
590C22×C7—41no—
591C22×C7—41no—
592C22×C7—41no—
593C22×C7—41no—
594C22×C7—41no—
595C22×C7—41no—
596C22×C7—41no—
597C22×C7—41no—
598C22×C7—41no—
599C22×C7—44no—
600C22×C7—42no—
601C22×C7—82no—
602C22×C7—82no—
603C22×C7—82no—
604C22×C7—82no—
605C22×C7—82no—
606C22×C7—82no—
607C22×C7#38611yescharacteristic
608C22×C7#38611yescharacteristic
609C22×C7#38611yescharacteristic
610C22×C7#38611yescharacteristic
611C22×C7#38611yescharacteristic
612C22×C7#38611yescharacteristic
613C22×C7#38611yescharacteristic
614C22×C7#38611yescharacteristic
615C22×C7C22×C22⋊C411yescharacteristic
616C22×C7C2×C4×D411yescharacteristic
617C22×C7C2×C4×D411yescharacteristic
618C22×C7C2×#12011yescharacteristic
619C22×C7C2×#12111yescharacteristic
620C22×C7C2×#12111yescharacteristic
621C22×C7C2×#12311yescharacteristic
622C2×D7—24no—
623C2×D7—44no—
624C2×D7—44no—
625C2×D7—44no—
626C2×D7—44no—
627C2×D7—82no—
628C2×D7—82no—
629C2×D7—82no—
630C4×C7—44no—
631C4×C7—42no—
632C4×C7—82no—
633Dic7—24no—
634Dic7—44no—
635Dic7—44no—
636Dic7—82no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—72no—
644C24—72no—
645C24—72no—
646C24—82no—
647C24—82no—
648C24—141no—
649C24—141no—
650C24—141no—
651C24—141no—
652C24—562no—
653C24C2×C4×D711yescharacteristic
654C24C2×C4×D711yescharacteristic
655C24C2×C4×D712yescomplemented
656C24#115711yescharacteristic
657C24#115711yescharacteristic
658C24D4×D711yescharacteristic
659C24D4×D711yescharacteristic
660C24D4×D711yescharacteristic
661C24D4×D711yescharacteristic
662C24D4×D711yescharacteristic
663C24D4×D711yescharacteristic
664C24#115911yescharacteristic
665C24#115911yescharacteristic
666C24C2×C22⋊D711yescharacteristic
667C24C2×C22⋊D711yescharacteristic
668C24C23×D711yescharacteristic
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—41no—
682C2×D4—41no—
683C2×D4—41no—
684C2×D4—41no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—41no—
690C2×D4—41no—
691C2×D4—41no—
692C2×D4—41no—
693C2×D4—41no—
694C2×D4—41no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4—74no—
698C2×D4—74no—
699C2×D4—74no—
700C2×D4—74no—
701C2×D4—142no—
702C2×D4—142no—
703C2×D4—142no—
704C2×D4—142no—
705C2×D4—142no—
706C2×D4—142no—
707C2×D4—142no—
708C2×D4—142no—
709C2×D4—142no—
710C2×D4—142no—
711C2×D4—142no—
712C2×D4—142no—
713C2×D4—142no—
714C2×D4—142no—
715C2×D4—142no—
716C2×D4—142no—
717C2×D4—142no—
718C2×D4—142no—
719C2×D4—142no—
720C2×D4—142no—
721C2×D4—142no—
722C2×D4—142no—
723C2×D4—142no—
724C2×D4—142no—
725C2×D4—148no—
726C2×D4—564no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—72no—
740C22×C4—72no—
741C22×C4—72no—
742C22×C4—82no—
743C22×C4—82no—
744C22×C4—148no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—141no—
749C22×C4—142no—
750C22×C4—142no—
751C22×C4—142no—
752C22×C4—142no—
753C22×C4—142no—
754C22×C4—142no—
755C22×C4—142no—
756C22×C4—281no—
757C22×C4—281no—
758C22×C4—564no—
759C22×C4—562no—
760C22×C4—562no—
761C22×C4—562no—
762C22×C4C2×C4×D712yescomplemented
763C4⋊C4—148no—
764C4⋊C4—148no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—41no—
771C22⋊C4—41no—
772C22⋊C4—74no—
773C22⋊C4—74no—
774C22⋊C4—148no—
775C22⋊C4—148no—
776C22⋊C4—148no—
777C22⋊C4—142no—
778C22⋊C4—142no—
779C22⋊C4—142no—
780C22⋊C4—142no—
781C22⋊C4—142no—
782C22⋊C4—142no—
783C22⋊C4—142no—
784C22⋊C4—142no—
785C22⋊C4—281no—
786C22⋊C4—281no—
787C22⋊C4C2×C22⋊D714yescomplemented
788C42—148no—
789C2×C7—21no—
790C2×C7—21no—
791C2×C7—21no—
792C2×C7—21no—
793C2×C7—21no—
794C2×C7—21no—
795C2×C7—21no—
796C2×C7—21no—
797C2×C7—21no—
798C2×C7—21no—
799C2×C7—21no—
800C2×C7—21no—
801C2×C7—21no—
802C2×C7—21no—
803C2×C7—82no—
804C2×C7#191312yescomplemented
805C2×C7C2×#38611yescharacteristic
806D7—44no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—44no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—74no—
823C23—82no—
824C23—82no—
825C23—81no—
826C23—81no—
827C23—81no—
828C23—81no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—81no—
833C23—82no—
834C23—82no—
835C23—82no—
836C23—82no—
837C23—142no—
838C23—142no—
839C23—142no—
840C23—142no—
841C23—142no—
842C23—142no—
843C23—284no—
844C23—284no—
845C23—562no—
846C23—562no—
847C23—562no—
848C23—562no—
849C23—562no—
850C23D7×C22⋊C411yescharacteristic
851C23D7×C22⋊C411yescharacteristic
852C23D7×C22⋊C411yescharacteristic
853C23D7×C22⋊C411yescharacteristic
854C23(C22⋊D7)⋊C411yescharacteristic
855C23(C22⋊D7)⋊C411yescharacteristic
856C23(C22⋊D7)⋊C411yescharacteristic
857C23(C22⋊D7)⋊C411yescharacteristic
858C23#644611yescharacteristic
859C23#644611yescharacteristic
860C23#644611yescharacteristic
861C23#644611yescharacteristic
862C23#644711yescharacteristic
863C23#644711yescharacteristic
864C23#644711yescharacteristic
865C23#644711yescharacteristic
866C23C4×C22⋊D711yescharacteristic
867C23C4×C22⋊D711yescharacteristic
868C23C4×C22⋊D711yescharacteristic
869C23C4×C22⋊D711yescharacteristic
870C23#650011yescharacteristic
871C23#650011yescharacteristic
872C23#650011yescharacteristic
873C23#650011yescharacteristic
874C23#650111yescharacteristic
875C23#650111yescharacteristic
876C23#650111yescharacteristic
877C23#650111yescharacteristic
878C23C22×C4×D711yescharacteristic
879C23C2×#115711yescharacteristic
880C23C2×D4×D711yescharacteristic
881C23C2×D4×D711yescharacteristic
882C23C2×D4×D711yescharacteristic
883C23C2×#115911yescharacteristic
884C23C22×C22⋊D711yescharacteristic
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—144no—
894D4—144no—
895D4—144no—
896D4—144no—
897D4—144no—
898D4—144no—
899D4—144no—
900D4—144no—
901D4—568no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—24no—
906C2×C4—44no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—42no—
912C2×C4—74no—
913C2×C4—82no—
914C2×C4—82no—
915C2×C4—82no—
916C2×C4—82no—
917C2×C4—82no—
918C2×C4—142no—
919C2×C4—142no—
920C2×C4—142no—
921C2×C4—142no—
922C2×C4—142no—
923C2×C4—142no—
924C2×C4—144no—
925C2×C4—144no—
926C2×C4—284no—
927C2×C4—284no—
928C2×C4—282no—
929C2×C4—568no—
930C2×C4—562no—
931C2×C4—562no—
932C2×C4—562no—
933C2×C4—562no—
934C2×C4—562no—
935C2×C4—562no—
936C2×C4—562no—
937C7C2×#191311yescharacteristic, complemented, Sylow
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—44no—
974C22—42no—
975C22—82no—
976C22—82no—
977C22—82no—
978C22—82no—
979C22—82no—
980C22—82no—
981C22—144no—
982C22—284no—
983C22—284no—
984C22—284no—
985C22—284no—
986C22—562no—
987C22—562no—
988C22—562no—
989C22#8972811yescharacteristic
990C22#8972811yescharacteristic
991C22#8972811yescharacteristic
992C22#8972811yescharacteristic
993C22#8972811yescharacteristic
994C22#8972811yescharacteristic
995C22#8972811yescharacteristic
996C22#8972811yescharacteristic
997C22C2×D7×C22⋊C411yescharacteristic
998C22C2×(C22⋊D7)⋊C411yescharacteristic
999C22C2×#644611yescharacteristic
1000C22C2×#644711yescharacteristic
1001C22C2×C4×C22⋊D711yescharacteristic
1002C22C2×#650011yescharacteristic
1003C22C2×#650111yescharacteristic
1004C4—44no—
1005C4—42no—
1006C4—82no—
1007C4—144no—
1008C4—284no—
1009C4—284no—
1010C4—562no—
1011C2—21no—
1012C2—21no—
1013C2—21no—
1014C2—21no—
1015C2—21no—
1016C2—21no—
1017C2—21no—
1018C2—21no—
1019C2—21no—
1020C2—21no—
1021C2—21no—
1022C2—21no—
1023C2—21no—
1024C2—21no—
1025C2—82no—
1026C2—284no—
1027C2#1172778812yesdirect product factor
1028C2C2×#8972811yescharacteristic
subgroupG/H
centerC22#89728
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC22×C7×#99C2
socleC22×C7#386
prime radicalC2×#90495C2
cosocleC24×C7C24
hypercenterC22×#99D7
hypocenterC7C2×#1913
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
2. C2×#90177C2semidirect
3. C22×C7×#99C2semidirect
4. C22×#6408C2semidirect
5. C22×#6380C2semidirect
6. C2×#89322C2semidirect
7. C2×#89321C2semidirect
8. #11727788C2direct (N × H)
13. C2×#6516C4semidirect
19. #90495C4semidirect
24. C2×#6492C4semidirect
29. #90177C22semidirect
35. C2×C7×#99C22semidirect
38. C2×#6408C22semidirect
41. C2×#6380C22semidirect
42. #89322C22semidirect
43. #89321C22semidirect
45. C25×C7C2×C4semidirect
60. C22×C7×D4C2×C4semidirect
64. C23×C4×C7C2×C4semidirect
93. C2×C7×C22⋊C4D4semidirect
94. C2×C7×C22⋊C4D4semidirect
98. #6516C2×C4semidirect
111. C2×C22⋊Dic7C2×C4semidirect
112. C2×C22⋊Dic7C2×C4semidirect
113. C2×C22⋊Dic7D4semidirect
114. C2×C22⋊Dic7D4semidirect
125. #6492C2×C4semidirect
146. C22×#99D7semidirect
160. C24×C7C22×C4semidirect
224. C22×C4×C7C22×C4semidirect
283. C7×C22⋊C4C2×D4semidirect
295. C22⋊Dic7C22×C4semidirect
296. C22⋊Dic7C2×D4semidirect
334. C2×#99C2×D7semidirect
468. C25C4×D7semidirect
497. C22×D4C4×D7semidirect
506. C23×C4C4×D7semidirect
556. C2×C22⋊C4C22⋊D7semidirect
557. C2×C22⋊C4C22⋊D7semidirect
655. C24C2×C4×D7semidirect
762. C22×C4C2×C4×D7semidirect
787. C22⋊C4C2×C22⋊D7semidirect
804. C2×C7#1913semidirect
937. C7C2×#1913semidirect
1027. C2#11727788direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904952
C2×#901772
C22×C7×#992
C22×#64082
C22×#63802
C2×#893222
C2×#893212
#117277882
C2×#19137