Finite Group Databasebeta

← C2×#11734192 #13560106

Subgroups — C2×#11734192 #13560106

Order 1792.

2930 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#392C211yesmaximal, characteristic, complemented
2C2×#89995C211yesmaximal, characteristic, complemented
3C2×#89995C211yesmaximal, characteristic, complemented
4C2×#89995C211yesmaximal, characteristic, complemented
5C2×#89994C211yesmaximal, characteristic, complemented
6C2×#89992C211yesmaximal, characteristic, complemented
7C2×#89992C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic, complemented
9C2×#89725C211yesmaximal, characteristic, complemented
10C2×#89724C211yesmaximal, characteristic, complemented
11C2×#89720C211yesmaximal, characteristic, complemented
12C2×#89733C211yesmaximal, characteristic, complemented
13C2×#89730C211yesmaximal, characteristic, complemented
14#11734192C2116yesmaximal, direct product factor
15C2×#89447C211yesmaximal, characteristic, complemented
16C2×C7⋊#401C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C22⋊D7C2211yescharacteristic
22C23×C22⋊D7C2211yescharacteristic
23C24×Dic7C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C7×#392C2218yescomplemented
43C2×C7×#95C2211yescharacteristic
44#89995C2218yescomplemented
45#89995C2218yescomplemented
46#89995C2218yescomplemented
47#89994C2218yescomplemented
48#89992C2218yescomplemented
49#89992C2218yescomplemented
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59#89733C2218yescomplemented
60#89731C2218yescomplemented
61#89730C2218yescomplemented
62#89725C2218yescomplemented
63#89724C2218yescomplemented
64#89720C2218yescomplemented
65#89447C2218yescomplemented
66C7⋊#401C2218yescomplemented
67C2×#2825—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C25×C7C2311yescharacteristic
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C22×C7×D4—24no—
73C22×C7×D4—24no—
74C22×C7×D4—42no—
75C22×C7×D4—42no—
76C22×C7×D4—42no—
77C22×C7×D4—42no—
78C22×C7×D4—42no—
79C22×C7×D4—42no—
80C22×C7×D4—42no—
81C22×C7×D4C2314yes—
82C22×C7×D4C2314yes—
83C22×C7×D4C2314yes—
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—24no—
89C22×C22⋊D7—42no—
90C22×C22⋊D7—42no—
91C22×C22⋊D7—42no—
92C22×C22⋊D7—42no—
93C22×C22⋊D7—42no—
94C22×C22⋊D7—42no—
95C22×C22⋊D7—42no—
96C22×C22⋊D7—42no—
97C22×C22⋊D7C2314yes—
98C22×C22⋊D7C2314yes—
99C22×C22⋊D7C2314yes—
100C23×Dic7—42no—
101C23×Dic7—42no—
102C23×Dic7—42no—
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C23×Dic7C2311yescharacteristic
108C23×Dic7C2311yescharacteristic
109C23×Dic7C2311yescharacteristic
110C23×Dic7C2314yes—
111C2×C7×C22⋊C4—42no—
112C2×C7×C22⋊C4—42no—
113C2×C7×C22⋊C4—42no—
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C7×C22⋊C4C2314yes—
117C2×C22⋊Dic7—42no—
118C2×C22⋊Dic7—42no—
119C2×C22⋊Dic7—42no—
120C2×C22⋊Dic7—42no—
121C2×C22⋊Dic7—42no—
122C2×C22⋊Dic7—42no—
123C2×C22⋊Dic7—42no—
124C2×C22⋊Dic7—42no—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132C2×C22⋊Dic7C2314yes—
133C2×(C2×D7)⋊C4—42no—
134C2×(C2×D7)⋊C4—42no—
135C2×(C2×D7)⋊C4—42no—
136C2×(C2×D7)⋊C4—42no—
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×(C2×D7)⋊C4C2314yes—
141C2×C4⋊Dic7—42no—
142C2×C4⋊Dic7C2314yes—
143C2×Dic7⋊C4—42no—
144C2×Dic7⋊C4—42no—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C7×#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157#2825—716no—
158C2×#401—71no—
159C2×#397—71no—
160C2×#397—71no—
161C2×#397—71no—
162C2×#396—71no—
163C2×#394—71no—
164C2×#394—71no—
165C2×#394—71no—
166C2×#392—71no—
167C2×#392—71no—
168C2×#392—71no—
169C2×#392D711yescharacteristic, complemented
170C2×#386—71no—
171C2×#386—71no—
172C2×#386—71no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7#4114yes—
194C24×C7C2412yes—
195C24×C7C2412yes—
196C24×C7C2412yes—
197C24×C7C2411yescharacteristic
198C23×D7—22no—
199C23×D7—22no—
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7—22no—
205C23×D7C2412yes—
206C2×C7×D4—28no—
207C2×C7×D4—28no—
208C2×C7×D4—44no—
209C2×C7×D4—44no—
210C2×C7×D4—44no—
211C2×C7×D4—44no—
212C2×C7×D4—44no—
213C2×C7×D4—44no—
214C2×C7×D4—44no—
215C2×C7×D4—416no—
216C2×C7×D4—416no—
217C2×C7×D4—416no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C2×C22⋊D7—28no—
235C2×C22⋊D7—44no—
236C2×C22⋊D7—44no—
237C2×C22⋊D7—44no—
238C2×C22⋊D7—44no—
239C2×C22⋊D7—44no—
240C2×C22⋊D7—44no—
241C2×C22⋊D7—44no—
242C2×C22⋊D7—44no—
243C2×C22⋊D7—416no—
244C2×C22⋊D7—416no—
245C2×C22⋊D7—416no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7—22no—
264C22×Dic7—22no—
265C22×Dic7—22no—
266C22×Dic7—22no—
267C22×Dic7—44no—
268C22×Dic7—44no—
269C22×Dic7—44no—
270C22×Dic7—416no—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C22×Dic7C2412yes—
275C22×Dic7C2412yes—
276C22×Dic7C2412yes—
277C22×Dic7C2412yes—
278C7×C22⋊C4—44no—
279C7×C22⋊C4—44no—
280C7×C22⋊C4—44no—
281C22⋊Dic7—44no—
282C22⋊Dic7—44no—
283C22⋊Dic7—44no—
284C22⋊Dic7—44no—
285C22⋊Dic7—44no—
286C22⋊Dic7—44no—
287C22⋊Dic7—44no—
288C22⋊Dic7—44no—
289(C2×D7)⋊C4—44no—
290(C2×D7)⋊C4—44no—
291(C2×D7)⋊C4—44no—
292(C2×D7)⋊C4—44no—
293C4⋊Dic7—44no—
294Dic7⋊C4—44no—
295Dic7⋊C4—44no—
296C23×D4—71no—
297C23×D4—71no—
298C23×D4—71no—
299C23×D4C2×D711yescharacteristic
300C23×D4C2×D711yescharacteristic
301C23×D4C2×D711yescharacteristic
302C24×C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C22⋊C4C2×D711yescharacteristic
319C22×C22⋊C4C2×D711yescharacteristic
320C22×C22⋊C4C2×D711yescharacteristic
321#401—78no—
322#397—78no—
323#397—78no—
324#397—78no—
325#396—78no—
326#394—78no—
327#394—78no—
328#394—78no—
329#392—78no—
330#392—78no—
331#392—78no—
332#392C2×D718yescomplemented
333#386—78no—
334#386—78no—
335#386—78no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95C2×D711yescharacteristic
346C23×C7—28no—
347C23×C7—28no—
348C23×C7—28no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—44no—
370C23×C7—44no—
371C23×C7—44no—
372C23×C7—44no—
373C23×C7—44no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7—44no—
384C23×C7—44no—
385C23×C7—44no—
386C23×C7—44no—
387C23×C7C2×#4114yes—
388C23×C7C2×#4112yes—
389C23×C7H(5,𝔽2)12yes—
390C23×C7H(5,𝔽2)12yes—
391C23×C7H(5,𝔽2)12yes—
392C23×C7H(5,𝔽2)12yes—
393C23×C7H(5,𝔽2)12yes—
394C23×C7H(5,𝔽2)12yes—
395C23×C7C2511yescharacteristic
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—22no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7—44no—
406C22×D7—44no—
407C22×D7—44no—
408C22×D7—44no—
409C22×D7—44no—
410C7×D4—416no—
411C7×D4—416no—
412C7×D4—416no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—44no—
426C2×C4×C7—44no—
427C2×C4×C7—44no—
428C2×C4×C7—44no—
429C22⋊D7—416no—
430C22⋊D7—416no—
431C22⋊D7—416no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—416no—
454C2×Dic7—44no—
455C2×Dic7—44no—
456C2×Dic7—44no—
457C2×Dic7—44no—
458C2×Dic7—44no—
459C2×Dic7—44no—
460C2×Dic7—44no—
461C25—71no—
462C25C22×D711yescharacteristic
463C25C22×D711yescharacteristic
464C25C22×D711yescharacteristic
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—42no—
468C22×D4—42no—
469C22×D4—42no—
470C22×D4—42no—
471C22×D4—42no—
472C22×D4—42no—
473C22×D4—42no—
474C22×D4—74no—
475C22×D4—74no—
476C22×D4—74no—
477C22×D4—144no—
478C22×D4—282no—
479C22×D4—282no—
480C22×D4—282no—
481C22×D4—282no—
482C22×D4—282no—
483C22×D4—282no—
484C22×D4—282no—
485C22×D4—282no—
486C22×D4C22×D714yes—
487C22×D4C22×D714yes—
488C22×D4C22×D714yes—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—71no—
495C23×C4—71no—
496C23×C4—74no—
497C23×C4—282no—
498C23×C4—282no—
499C23×C4—282no—
500C23×C4C22×D711yescharacteristic
501C23×C4C22×D711yescharacteristic
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D711yescharacteristic
504C2×C4⋊C4—74no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—282no—
508C2×C4⋊C4—282no—
509C2×C4⋊C4—282no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—74no—
515C2×C22⋊C4—74no—
516C2×C22⋊C4—74no—
517C2×C22⋊C4—74no—
518C2×C22⋊C4—74no—
519C2×C22⋊C4—74no—
520C2×C22⋊C4—74no—
521C2×C22⋊C4—74no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—282no—
526C2×C22⋊C4—282no—
527C2×C22⋊C4—282no—
528C2×C22⋊C4—282no—
529C2×C22⋊C4—282no—
530C2×C22⋊C4—282no—
531C2×C22⋊C4—282no—
532C2×C22⋊C4—282no—
533C2×C22⋊C4—282no—
534C2×C22⋊C4—282no—
535C2×C22⋊C4—282no—
536C2×C22⋊C4—282no—
537C2×C22⋊C4C22×D714yes—
538C2×C22⋊C4C22×D714yes—
539C2×C22⋊C4C22×D714yes—
540#95—74no—
541#95—74no—
542#95—74no—
543#95—74no—
544#95—74no—
545#95—74no—
546#95—74no—
547#95—74no—
548#95—74no—
549#95C22×D714yes—
550C22×C7—24no—
551C22×C7—24no—
552C22×C7—24no—
553C22×C7—416no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—88no—
573C22×C7—88no—
574C22×C7#53814yes—
575C22×C7#53814yes—
576C22×C7#53814yes—
577C22×C7#56014yes—
578C22×C7#56014yes—
579C22×C7#56014yes—
580C22×C7#56014yes—
581C22×C7C22×#4111yescharacteristic
582C22×C7C2×H(5,𝔽2)11yescharacteristic
583C22×C7C2×H(5,𝔽2)11yescharacteristic
584C22×C7C2×H(5,𝔽2)11yescharacteristic
585C22×C7C2×H(5,𝔽2)11yescharacteristic
586C22×C7C2×H(5,𝔽2)11yescharacteristic
587C22×C7C2×H(5,𝔽2)11yescharacteristic
588C2×D7—42no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—42no—
594C2×D7—42no—
595C2×D7—88no—
596C4×C7—42no—
597C4×C7—42no—
598C4×C7—42no—
599C4×C7—42no—
600Dic7—42no—
601Dic7—42no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606Dic7—42no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—72no—
628C24—142no—
629C24—142no—
630C24—142no—
631C24—142no—
632C24—142no—
633C24—142no—
634C24—142no—
635C24#115914yes—
636C24C23×D712yes—
637C24C23×D712yes—
638C24C23×D712yes—
639C24C23×D711yescharacteristic
640C2×D4—28no—
641C2×D4—28no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—416no—
650C2×D4—416no—
651C2×D4—416no—
652C2×D4—148no—
653C2×D4—284no—
654C2×D4—284no—
655C2×D4—284no—
656C2×D4—284no—
657C2×D4—284no—
658C2×D4—284no—
659C2×D4—284no—
660C2×D4—284no—
661C2×D4—2816no—
662C2×D4—2816no—
663C2×D4—2816no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—72no—
677C22×C4—72no—
678C22×C4—72no—
679C22×C4—72no—
680C22×C4—72no—
681C22×C4—72no—
682C22×C4—72no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4—142no—
693C22×C4—142no—
694C22×C4—142no—
695C22×C4—142no—
696C22×C4—142no—
697C22×C4—142no—
698C22×C4—142no—
699C22×C4—142no—
700C22×C4—142no—
701C22×C4—142no—
702C22×C4—142no—
703C22×C4—142no—
704C22×C4—284no—
705C22×C4—284no—
706C22×C4—284no—
707C22×C4—2816no—
708C22×C4C23×D712yes—
709C22×C4C23×D712yes—
710C22×C4C23×D712yes—
711C22×C4C23×D712yes—
712C4⋊C4—284no—
713C4⋊C4—284no—
714C4⋊C4—284no—
715C22⋊C4—44no—
716C22⋊C4—44no—
717C22⋊C4—44no—
718C22⋊C4—284no—
719C22⋊C4—284no—
720C22⋊C4—284no—
721C22⋊C4—284no—
722C22⋊C4—284no—
723C22⋊C4—284no—
724C22⋊C4—284no—
725C22⋊C4—284no—
726C22⋊C4—284no—
727C22⋊C4—284no—
728C22⋊C4—284no—
729C22⋊C4—284no—
730C2×C7—44no—
731C2×C7—82no—
732C2×C7—82no—
733C2×C7#282518yescomplemented
734C2×C7C2×#53811yescharacteristic
735C2×C7C2×#53811yescharacteristic
736C2×C7C2×#53811yescharacteristic
737C2×C7C2×#56011yescharacteristic
738C2×C7C2×#56011yescharacteristic
739C2×C7C2×#56011yescharacteristic
740C2×C7C2×#56011yescharacteristic
741D7—82no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—142no—
784C23—142no—
785C23—142no—
786C23—142no—
787C23—142no—
788C23—142no—
789C23—142no—
790C23—284no—
791C23—284no—
792C23—284no—
793C23—284no—
794C23—284no—
795C23—284no—
796C23—284no—
797C23C2×#115914yes—
798C23C2×#115912yes—
799C23#654812yes—
800C23#654812yes—
801C23#654812yes—
802C23#654812yes—
803C23#654812yes—
804C23#655312yes—
805C23C24×D711yescharacteristic
806D4—416no—
807D4—416no—
808D4—416no—
809D4—2816no—
810D4—2816no—
811D4—2816no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—142no—
833C2×C4—142no—
834C2×C4—142no—
835C2×C4—142no—
836C2×C4—142no—
837C2×C4—142no—
838C2×C4—142no—
839C2×C4—142no—
840C2×C4—142no—
841C2×C4—142no—
842C2×C4—142no—
843C2×C4—142no—
844C2×C4—142no—
845C2×C4—142no—
846C2×C4—142no—
847C2×C4—142no—
848C2×C4—142no—
849C2×C4—2816no—
850C2×C4—284no—
851C2×C4—284no—
852C2×C4—284no—
853C2×C4—284no—
854C2×C4—284no—
855C2×C4—284no—
856C2×C4—284no—
857C7C2×#282511yescharacteristic, complemented, Sylow
858C22—24no—
859C22—24no—
860C22—24no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—416no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—88no—
881C22—88no—
882C22—282no—
883C22—282no—
884C22—282no—
885C22—282no—
886C22—282no—
887C22—282no—
888C22—282no—
889C22—568no—
890C22#9028414yes—
891C22#9028414yes—
892C22#9028614yes—
893C22#9030814yes—
894C22#9031114yes—
895C22#9031114yes—
896C22#9041114yes—
897C22C22×#115911yescharacteristic
898C22C2×#654811yescharacteristic
899C22C2×#654811yescharacteristic
900C22C2×#654811yescharacteristic
901C22C2×#654811yescharacteristic
902C22C2×#654811yescharacteristic
903C22C2×#655311yescharacteristic
904C4—42no—
905C4—42no—
906C4—42no—
907C4—42no—
908C4—282no—
909C4—282no—
910C4—282no—
911C4—282no—
912C4—282no—
913C4—282no—
914C4—282no—
915C2—44no—
916C2—82no—
917C2—82no—
918C2—562no—
919C2#1173419218yesdirect product factor
920C2C2×#9028411yescharacteristic
921C2C2×#9028411yescharacteristic
922C2C2×#9028611yescharacteristic
923C2C2×#9030811yescharacteristic
924C2C2×#9031111yescharacteristic
925C2C2×#9031111yescharacteristic
926C2C2×#9041111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#392C2
socleC24×C7C24
hypercenterC2×#392D7
hypocenterC7C2×#2825
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×C7×#392C2semidirect
2. C2×#89995C2semidirect
3. C2×#89995C2semidirect
4. C2×#89995C2semidirect
5. C2×#89994C2semidirect
6. C2×#89992C2semidirect
7. C2×#89992C2semidirect
8. C2×#89731C2semidirect
9. C2×#89725C2semidirect
10. C2×#89724C2semidirect
11. C2×#89720C2semidirect
12. C2×#89733C2semidirect
13. C2×#89730C2semidirect
14. #11734192C2direct (N × H)
15. C2×#89447C2semidirect
16. C2×C7⋊#401C2semidirect
42. C7×#392C22semidirect
44. #89995C22semidirect
45. #89995C22semidirect
46. #89995C22semidirect
47. #89994C22semidirect
48. #89992C22semidirect
49. #89992C22semidirect
59. #89733C22semidirect
60. #89731C22semidirect
61. #89730C22semidirect
62. #89725C22semidirect
63. #89724C22semidirect
64. #89720C22semidirect
65. #89447C22semidirect
66. C7⋊#401C22semidirect
169. C2×#392D7semidirect
332. #392C2×D7semidirect
733. C2×C7#2825semidirect
857. C7C2×#2825semidirect
919. C2#11734192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3922
C2×#899952
C2×#899942
C2×#899922
C2×#897312
C2×#897252
C2×#897242
C2×#897202
C2×#897332
C2×#897302
#117341922
C2×#894472
C2×C7⋊#4012
C2×#28257