Finite Group Databasebeta

← #13259243

Subgroups — #13259243

Order 1792.

1498 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90177C211yesmaximal, characteristic
2C22×#6380C211yesmaximal, characteristic
3C22×#6380C211yesmaximal, characteristic
4C2×C7×#342C211yesmaximal, characteristic, complemented
5C2×#89322C211yesmaximal, characteristic, complemented
6C2×#89322C211yesmaximal, characteristic, complemented
7C2×#89321C211yesmaximal, characteristic, complemented
8C23×C22⋊D7C2211yescharacteristic
9C22×C7×C22⋊C4C2211yescharacteristic
10C22×C7×C22⋊C4C2211yescharacteristic
11C22×C7×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic7C2211yescharacteristic
13C22×C22⋊Dic7C2211yescharacteristic
14C22×C22⋊Dic7C2211yescharacteristic
15C2×C4×C22⋊D7—22no—
16#90177—22no—
17#90177—22no—
18#90177—22no—
19#90177—22no—
20C2×(C22⋊D7)⋊C4—22no—
21C2×D7×C22⋊C4C412yescomplemented
22C2×#6440C412yescomplemented
23C2×#6380—22no—
24C2×#6380—22no—
25C2×#6380—22no—
26C2×#6380—22no—
27C2×#6380C414yescomplemented
28C2×#6380C414yescomplemented
29C7×#342—22no—
30#89322—22no—
31#89322—22no—
32#89321—22no—
33#10768—71nomaximal, Sylow
34C25×C7C2311yescharacteristic
35C24×D7C2×C411yescharacteristic
36C23×C4×C7—21no—
37C23×C4×C7—21no—
38C23×C4×C7—21no—
39C22×C22⋊D7—21no—
40C22×C22⋊D7—21no—
41C22×C22⋊D7—21no—
42C22×C22⋊D7—21no—
43C22×C22⋊D7—21no—
44C22×C22⋊D7—21no—
45C22×C22⋊D7—21no—
46C22×C22⋊D7—21no—
47C22×C22⋊D7C2×C412yes—
48C22×C22⋊D7C2×C412yes—
49C22×C22⋊D7D412yes—
50C22×C22⋊D7D412yes—
51C22×C22⋊D7D412yes—
52C22×C22⋊D7Q812yes—
53C23×Dic7—21no—
54C23×Dic7—21no—
55C23×Dic7—21no—
56C23×Dic7C2×C411yescharacteristic
57C22×C4×D7—22no—
58C2×C7×C22⋊C4—21no—
59C2×C7×C22⋊C4—21no—
60C2×C7×C22⋊C4—21no—
61C2×C7×C22⋊C4—21no—
62C2×C7×C22⋊C4—21no—
63C2×C7×C22⋊C4—21no—
64C2×C7×C22⋊C4—21no—
65C2×C7×C22⋊C4—21no—
66C2×C7×C22⋊C4—21no—
67C2×C7×C22⋊C4—21no—
68C2×C7×C22⋊C4—21no—
69C2×C7×C22⋊C4—21no—
70C2×C7×C22⋊C4—21no—
71C2×C7×C22⋊C4C2×C412yes—
72C2×C7×C22⋊C4C2×C412yescomplemented
73C2×C7×C22⋊C4C2×C412yescomplemented
74C2×C7×C22⋊C4D412yes—
75C2×C7×C22⋊C4D412yes—
76C2×C22⋊Dic7—21no—
77C2×C22⋊Dic7—21no—
78C2×C22⋊Dic7—21no—
79C2×C22⋊Dic7—21no—
80C2×C22⋊Dic7—21no—
81C2×C22⋊Dic7—21no—
82C2×C22⋊Dic7—21no—
83C2×C22⋊Dic7—21no—
84C2×C22⋊Dic7—21no—
85C2×C22⋊Dic7—21no—
86C2×C22⋊Dic7—21no—
87C2×C22⋊Dic7—21no—
88C2×C22⋊Dic7—21no—
89C2×C22⋊Dic7C2×C412yes—
90C2×C22⋊Dic7C2×C412yescomplemented
91C2×C22⋊Dic7C2×C412yescomplemented
92C2×C22⋊Dic7D412yes—
93C2×C22⋊Dic7D412yes—
94C4×C22⋊D7—28no—
95C4×C22⋊D7—28no—
96C2×(C2×D7)⋊C4—22no—
97C2×Dic7⋊C4—22no—
98C2×C4×Dic7—22no—
99(C22⋊D7)⋊C4—28no—
100(C22⋊D7)⋊C4—28no—
101D7×C22⋊C4—24no—
102D7×C22⋊C4—24no—
103#6440—24no—
104#6440—24no—
105#6380—28no—
106#6380—28no—
107C2×#518—71no—
108C22×#99—71no—
109C22×#99—71no—
110C2×#342—71no—
111C2×#342—71no—
112C2×#342—71no—
113C2×#342D711yescharacteristic, complemented
114C24×C7—82no—
115C24×C7C22×C411yescharacteristic
116C24×C7C22×C411yescharacteristic
117C24×C7C22×C411yescharacteristic
118C24×C7C2×D411yescharacteristic
119C24×C7C2×D411yescharacteristic
120C24×C7C2×D411yescharacteristic
121C24×C7C2×D411yescharacteristic
122C24×C7C2×D411yescharacteristic
123C24×C7C2×D411yescharacteristic
124C24×C7C2×D411yescharacteristic
125C24×C7C2×Q811yescharacteristic
126C24×C7#4111yescharacteristic
127C24×C7#4111yescharacteristic
128C24×C7#4111yescharacteristic
129C24×C7#4111yescharacteristic
130C23×D7—21no—
131C23×D7—21no—
132C23×D7—21no—
133C23×D7—21no—
134C23×D7—82no—
135C23×D7C4212yes—
136C23×D7C22⋊C412yes—
137C23×D7C4⋊C412yes—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—41no—
144C22×C4×C7—41no—
145C22×C4×C7—41no—
146C22×C4×C7—41no—
147C22×C4×C7—82no—
148C22×C4×C7—82no—
149C22×C4×C7—82no—
150C2×C22⋊D7—22no—
151C2×C22⋊D7—22no—
152C2×C22⋊D7—22no—
153C2×C22⋊D7—22no—
154C2×C22⋊D7—22no—
155C2×C22⋊D7—22no—
156C2×C22⋊D7—22no—
157C2×C22⋊D7—22no—
158C2×C22⋊D7—22no—
159C2×C22⋊D7—22no—
160C2×C22⋊D7—22no—
161C2×C22⋊D7—22no—
162C2×C22⋊D7—22no—
163C2×C22⋊D7—22no—
164C2×C22⋊D7—22no—
165C2×C22⋊D7—22no—
166C2×C22⋊D7—22no—
167C2×C22⋊D7—22no—
168C2×C22⋊D7—22no—
169C2×C22⋊D7—22no—
170C2×C22⋊D7—22no—
171C2×C22⋊D7—22no—
172C2×C22⋊D7—22no—
173C2×C22⋊D7—22no—
174C2×C22⋊D7C22⋊C414yes—
175C2×C22⋊D7C22⋊C414yes—
176C2×C22⋊D7C4⋊C414yes—
177C2×C22⋊D7C4⋊C414yes—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—22no—
183C22×Dic7—22no—
184C22×Dic7—22no—
185C22×Dic7—22no—
186C22×Dic7—22no—
187C22×Dic7—41no—
188C22×Dic7—41no—
189C22×Dic7—41no—
190C22×Dic7—41no—
191C22×Dic7—82no—
192C22×Dic7—82no—
193C22×Dic7—82no—
194C22×Dic7C4212yes—
195C22×Dic7C22⋊C412yes—
196C22×Dic7C4⋊C412yes—
197C2×C4×D7—28no—
198C2×C4×D7—84no—
199C7×C22⋊C4—22no—
200C7×C22⋊C4—22no—
201C7×C22⋊C4—22no—
202C7×C22⋊C4—22no—
203C7×C22⋊C4—22no—
204C7×C22⋊C4—22no—
205C7×C22⋊C4—22no—
206C7×C22⋊C4—41no—
207C7×C22⋊C4—41no—
208C7×C22⋊C4—41no—
209C7×C22⋊C4—41no—
210C7×C22⋊C4C22⋊C414yes—
211C22⋊Dic7—22no—
212C22⋊Dic7—22no—
213C22⋊Dic7—22no—
214C22⋊Dic7—22no—
215C22⋊Dic7—22no—
216C22⋊Dic7—22no—
217C22⋊Dic7—22no—
218C22⋊Dic7—41no—
219C22⋊Dic7—41no—
220C22⋊Dic7—41no—
221C22⋊Dic7—41no—
222C22⋊Dic7C22⋊C414yes—
223(C2×D7)⋊C4—28no—
224Dic7⋊C4—28no—
225C4×Dic7—28no—
226C23×D4—71no—
227#518—142no—
228#518—142no—
229#518—142no—
230#518—142no—
231C2×C4×D4—142no—
232C2×C4×D4—142no—
233C2×#117—72no—
234C22×C22⋊C4—71no—
235C22×C22⋊C4—71no—
236C22×C22⋊C4—71no—
237C22×C22⋊C4—72no—
238C22×C22⋊C4C2×D711yescharacteristic
239C22×C22⋊C4C2×D711yescharacteristic
240C22×C22⋊C4C2×D711yescharacteristic
241C2×#99—74no—
242C2×#99—74no—
243C2×#99—142no—
244C2×#99—142no—
245C2×#99—142no—
246C2×#99—142no—
247#342—22no—
248#342—142no—
249#342—142no—
250#342—142no—
251C23×C7—42no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7—42no—
255C23×C7—42no—
256C23×C7—42no—
257C23×C7—42no—
258C23×C7—81no—
259C23×C7—81no—
260C23×C7—81no—
261C23×C7—81no—
262C23×C7—81no—
263C23×C7—81no—
264C23×C7—81no—
265C23×C7—81no—
266C23×C7C2×C4211yescharacteristic
267C23×C7C2×C22⋊C411yescharacteristic
268C23×C7C2×C22⋊C411yescharacteristic
269C23×C7C2×C22⋊C411yescharacteristic
270C23×C7C2×C22⋊C411yescharacteristic
271C23×C7C2×C22⋊C411yescharacteristic
272C23×C7C2×C4⋊C411yescharacteristic
273C23×C7C2×C4⋊C411yescharacteristic
274C23×C7C2×C4⋊C411yescharacteristic
275C23×C7#11711yescharacteristic
276C23×C7#11711yescharacteristic
277C23×C7C4×D411yescharacteristic
278C23×C7C4×D411yescharacteristic
279C23×C7C4×D411yescharacteristic
280C23×C7C4×D411yescharacteristic
281C23×C7C4×D411yescharacteristic
282C23×C7C4×D411yescharacteristic
283C23×C7C4×D411yescharacteristic
284C23×C7C4×D411yescharacteristic
285C23×C7#12011yescharacteristic
286C23×C7#12011yescharacteristic
287C23×C7#12011yescharacteristic
288C23×C7#12011yescharacteristic
289C23×C7#12111yescharacteristic
290C23×C7#12111yescharacteristic
291C23×C7#12111yescharacteristic
292C23×C7#12111yescharacteristic
293C23×C7C22⋊Q811yescharacteristic
294C23×C7C22⋊Q811yescharacteristic
295C23×C7C22⋊Q811yescharacteristic
296C23×C7C22⋊Q811yescharacteristic
297C23×C7#12311yescharacteristic
298C23×C7#12311yescharacteristic
299C23×C7#12311yescharacteristic
300C23×C7#12311yescharacteristic
301C22×D7—22no—
302C22×D7—22no—
303C22×D7—22no—
304C22×D7—22no—
305C22×D7—22no—
306C22×D7—22no—
307C22×D7—44no—
308C22×D7—82no—
309C22×D7—82no—
310C22×D7—82no—
311C22×D7—82no—
312C22×D7—82no—
313C22×D7—82no—
314C22×D7#9514yes—
315C2×C4×C7—24no—
316C2×C4×C7—44no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—82no—
320C2×C4×C7—82no—
321C2×C4×C7—82no—
322C2×C4×C7—82no—
323C2×C4×C7—82no—
324C2×C4×C7—82no—
325C2×C4×C7—82no—
326C2×C4×C7—82no—
327C22⋊D7—24no—
328C22⋊D7—24no—
329C22⋊D7—24no—
330C22⋊D7—24no—
331C22⋊D7—24no—
332C22⋊D7—24no—
333C22⋊D7—24no—
334C22⋊D7—24no—
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—22no—
339C2×Dic7—22no—
340C2×Dic7—22no—
341C2×Dic7—24no—
342C2×Dic7—44no—
343C2×Dic7—42no—
344C2×Dic7—42no—
345C2×Dic7—82no—
346C2×Dic7—82no—
347C2×Dic7—82no—
348C2×Dic7—82no—
349C2×Dic7—82no—
350C2×Dic7—82no—
351C2×Dic7—82no—
352C2×Dic7—82no—
353C2×Dic7#9514yes—
354C4×D7—88no—
355C25—71no—
356C25C22×D711yescharacteristic
357C22×D4—72no—
358C22×D4—72no—
359C22×D4—72no—
360C22×D4—72no—
361C22×D4—72no—
362C22×D4—72no—
363C22×D4—141no—
364C22×D4—141no—
365C22×D4—141no—
366C22×D4—141no—
367C22×D4—141no—
368C22×D4—141no—
369C22×D4—141no—
370C22×D4—141no—
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—71no—
375C23×C4—142no—
376C23×C4—141no—
377C23×C4—141no—
378C23×C4—141no—
379C4×D4—148no—
380C4×D4—148no—
381C4×D4—148no—
382C4×D4—148no—
383#117—144no—
384#117—144no—
385C2×C4⋊C4—142no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—72no—
400C2×C22⋊C4—72no—
401C2×C22⋊C4—72no—
402C2×C22⋊C4—72no—
403C2×C22⋊C4—72no—
404C2×C22⋊C4—144no—
405C2×C22⋊C4—142no—
406C2×C22⋊C4—141no—
407C2×C22⋊C4—141no—
408C2×C22⋊C4—141no—
409C2×C22⋊C4—144no—
410C2×C22⋊C4—141no—
411C2×C22⋊C4—141no—
412C2×C22⋊C4—141no—
413C2×C22⋊C4—141no—
414C2×C22⋊C4—141no—
415C2×C22⋊C4—141no—
416C2×C22⋊C4—141no—
417C2×C22⋊C4—141no—
418C2×C22⋊C4—141no—
419C2×C22⋊C4—141no—
420C2×C22⋊C4C4×D712yes—
421C2×C22⋊C4C4×D712yescomplemented
422C2×C22⋊C4C4×D712yescomplemented
423C2×C22⋊C4D2812yes—
424C2×C22⋊C4C22⋊D712yes—
425C2×C42—142no—
426#99—148no—
427#99—148no—
428C22×C7—22no—
429C22×C7—22no—
430C22×C7—22no—
431C22×C7—22no—
432C22×C7—22no—
433C22×C7—22no—
434C22×C7—22no—
435C22×C7—41no—
436C22×C7—41no—
437C22×C7—41no—
438C22×C7—41no—
439C22×C7—41no—
440C22×C7—41no—
441C22×C7—41no—
442C22×C7—41no—
443C22×C7—41no—
444C22×C7—41no—
445C22×C7—41no—
446C22×C7—41no—
447C22×C7—41no—
448C22×C7—41no—
449C22×C7—41no—
450C22×C7—41no—
451C22×C7—41no—
452C22×C7—41no—
453C22×C7—41no—
454C22×C7—41no—
455C22×C7—41no—
456C22×C7—41no—
457C22×C7—41no—
458C22×C7—41no—
459C22×C7—41no—
460C22×C7—41no—
461C22×C7—41no—
462C22×C7—41no—
463C22×C7C2×#9511yescharacteristic
464C22×C7C4×C22⋊C411yescharacteristic
465C22×C7C4×C22⋊C411yescharacteristic
466C22×C7#37911yescharacteristic
467C22×C7#38011yescharacteristic
468C22×C7#38011yescharacteristic
469C22×C7#38111yescharacteristic
470C22×C7#38511yescharacteristic
471C22×C7#38511yescharacteristic
472C22×C7#38511yescharacteristic
473C22×C7#38511yescharacteristic
474C22×C7#38611yescharacteristic
475C22×C7#38611yescharacteristic
476C22×C7#38611yescharacteristic
477C22×C7#38611yescharacteristic
478C2×D7—24no—
479C2×D7—44no—
480C2×D7—44no—
481C2×D7—44no—
482C2×D7—82no—
483C2×D7—82no—
484C2×D7—82no—
485C2×D7—82no—
486C4×C7—44no—
487C4×C7—82no—
488C4×C7—82no—
489Dic7—24no—
490Dic7—44no—
491Dic7—82no—
492Dic7—82no—
493C24—72no—
494C24—72no—
495C24—72no—
496C24—82no—
497C24—141no—
498C24—141no—
499C24—141no—
500C24—141no—
501C24—562no—
502C24C2×C4×D711yescharacteristic
503C24C2×C4×D711yescharacteristic
504C24C2×C4×D711yescharacteristic
505C24C2×D2811yescharacteristic
506C24#115711yescharacteristic
507C24#115711yescharacteristic
508C24D4×D711yescharacteristic
509C24D4×D711yescharacteristic
510C24D4×D711yescharacteristic
511C24D4×D711yescharacteristic
512C24D4×D711yescharacteristic
513C24#115911yescharacteristic
514C24Q8×D711yescharacteristic
515C24#116111yescharacteristic
516C24C2×C22⋊D711yescharacteristic
517C2×D4—74no—
518C2×D4—74no—
519C2×D4—74no—
520C2×D4—74no—
521C2×D4—142no—
522C2×D4—142no—
523C2×D4—142no—
524C2×D4—142no—
525C2×D4—142no—
526C2×D4—142no—
527C2×D4—142no—
528C2×D4—142no—
529C2×D4—142no—
530C2×D4—142no—
531C2×D4—142no—
532C2×D4—142no—
533C2×D4—142no—
534C2×D4—142no—
535C2×D4—142no—
536C2×D4—142no—
537C2×D4—142no—
538C2×D4—142no—
539C2×D4—142no—
540C2×D4—142no—
541C2×D4—142no—
542C2×D4—142no—
543C2×D4—142no—
544C2×D4—142no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—72no—
555C22×C4—72no—
556C22×C4—72no—
557C22×C4—82no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—148no—
561C22×C4—141no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4—141no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—281no—
571C22×C4—281no—
572C22×C4—281no—
573C22×C4—281no—
574C22×C4—564no—
575C22×C4—562no—
576C22×C4—562no—
577C22×C4—562no—
578C4⋊C4—148no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—74no—
591C22⋊C4—148no—
592C22⋊C4—142no—
593C22⋊C4—142no—
594C22⋊C4—142no—
595C22⋊C4—142no—
596C22⋊C4—142no—
597C22⋊C4—142no—
598C22⋊C4—142no—
599C22⋊C4—281no—
600C22⋊C4—281no—
601C22⋊C4—281no—
602C22⋊C4—281no—
603C22⋊C4(C2×D7)⋊C414yes—
604C42—148no—
605C2×C7—21no—
606C2×C7—21no—
607C2×C7—21no—
608C2×C7—21no—
609C2×C7—21no—
610C2×C7—21no—
611C2×C7—21no—
612C2×C7—21no—
613C2×C7—21no—
614C2×C7—21no—
615C2×C7—21no—
616C2×C7—21no—
617C2×C7—21no—
618C2×C7—21no—
619C2×C7C22⋊#9511yescharacteristic
620C2×C7#182812yes—
621D7—44no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—74no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—142no—
639C23—142no—
640C23—142no—
641C23—142no—
642C23—142no—
643C23—142no—
644C23—284no—
645C23—562no—
646C23—562no—
647C23—562no—
648C23—562no—
649C23—562no—
650C23—562no—
651C23C42×D711yescharacteristic
652C23#643511yescharacteristic
653C23C4×D2811yescharacteristic
654C23C4×D2811yescharacteristic
655C23D7×C22⋊C411yescharacteristic
656C23D7×C22⋊C411yescharacteristic
657C23D7×C22⋊C411yescharacteristic
658C23D7×C22⋊C411yescharacteristic
659C23(C22⋊D7)⋊C411yescharacteristic
660C23(C22⋊D7)⋊C411yescharacteristic
661C23#644511yescharacteristic
662C23#644511yescharacteristic
663C23#644611yescharacteristic
664C23#644611yescharacteristic
665C23#644711yescharacteristic
666C23#644711yescharacteristic
667C23D7×C4⋊C411yescharacteristic
668C23D7×C4⋊C411yescharacteristic
669C23D7×C4⋊C411yescharacteristic
670C23#645511yescharacteristic
671C23#645611yescharacteristic
672C23#645611yescharacteristic
673C23#645711yescharacteristic
674C23#645711yescharacteristic
675C23#645811yescharacteristic
676C23#645911yescharacteristic
677C23#645911yescharacteristic
678C23#646011yescharacteristic
679C23C2×(C2×D7)⋊C411yescharacteristic
680C23C4×C22⋊D711yescharacteristic
681C23C4×C22⋊D711yescharacteristic
682C23#650011yescharacteristic
683C23#650011yescharacteristic
684C23#650111yescharacteristic
685C23#650911yescharacteristic
686D4—144no—
687D4—144no—
688D4—144no—
689D4—144no—
690D4—144no—
691D4—144no—
692D4—144no—
693D4—144no—
694C2×C4—24no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—74no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—144no—
714C2×C4—284no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—568no—
718C2×C4—562no—
719C2×C4—562no—
720C2×C4—562no—
721C2×C4—562no—
722C2×C4—562no—
723C2×C4—562no—
724C2×C4—562no—
725C2×C4—562no—
726C7#1076811yescharacteristic, complemented, Sylow
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—144no—
763C22—284no—
764C22—284no—
765C22—284no—
766C22—562no—
767C22—562no—
768C22—562no—
769C22—562no—
770C22D7×#9511yescharacteristic
771C22#8943611yescharacteristic
772C22#8943711yescharacteristic
773C22#8943711yescharacteristic
774C22#8943811yescharacteristic
775C22#8943911yescharacteristic
776C22#8944011yescharacteristic
777C22#8944011yescharacteristic
778C22C4×(C2×D7)⋊C411yescharacteristic
779C22#8972711yescharacteristic
780C22#8972811yescharacteristic
781C22#8972811yescharacteristic
782C22#8975911yescharacteristic
783C22#8976111yescharacteristic
784C22#8976111yescharacteristic
785C4—44no—
786C4—82no—
787C4—82no—
788C4—144no—
789C4—284no—
790C4—562no—
791C4—562no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—284no—
807C2#1172671412yes—
808C2(C2×D7)⋊#9511yescharacteristic
subgroupG/H
centerC22#89436
commutatorC23×C7C2×C42
FrattiniC25C22×D7
FittingC2×C7×#342C2
socleC22×C7#381
prime radicalC23×C22⋊D7C22
cosocleC25×C7C23
hypercenterC2×#342D7
hypocenterC7#10768
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. C2×C7×#342C2semidirect
5. C2×#89322C2semidirect
6. C2×#89322C2semidirect
7. C2×#89321C2semidirect
21. C2×D7×C22⋊C4C4semidirect
22. C2×#6440C4semidirect
27. C2×#6380C4semidirect
28. C2×#6380C4semidirect
72. C2×C7×C22⋊C4C2×C4semidirect
73. C2×C7×C22⋊C4C2×C4semidirect
90. C2×C22⋊Dic7C2×C4semidirect
91. C2×C22⋊Dic7C2×C4semidirect
113. C2×#342D7semidirect
421. C2×C22⋊C4C4×D7semidirect
422. C2×C22⋊C4C4×D7semidirect
726. C7#10768semidirect

Maximal subgroups

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

subgroupindex
C2×#901772
C22×#63802
C2×C7×#3422
C2×#893222
C2×#893212
#107687