Finite Group Databasebeta

← C2×#11734353 #13521294

Subgroups — C2×#11734353 #13521294

Order 1792.

3894 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic7C211yesmaximal, characteristic, complemented
2C22×#6446C211yesmaximal, characteristic, complemented
3C22×#6449C211yesmaximal, characteristic, complemented
4C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic, complemented
5C2×C7×#394C211yesmaximal, characteristic, complemented
6C2×#89995C211yesmaximal, characteristic
7C2×#89757C211yesmaximal, characteristic, complemented
8C2×#89762C211yesmaximal, characteristic, complemented
9C2×#89731C211yesmaximal, characteristic, complemented
10C2×#89721C211yesmaximal, characteristic, complemented
11C2×#89716C211yesmaximal, characteristic, complemented
12C2×#89722C211yesmaximal, characteristic, complemented
13C2×#89718C211yesmaximal, characteristic, complemented
14#11734353C2116yesmaximal, direct product factor
15C2×#89440C211yesmaximal, characteristic, complemented
16C2×#89419C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C2×D4×Dic7—28no—
33C2×D4×Dic7C2218yescomplemented
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C22×C4⋊Dic7C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C2×#6449—28no—
49C2×#6449C2218yescomplemented
50C2×#6446—28no—
51C2×#6446C2218yescomplemented
52C2×(C22⋊D7)⋊C4—28no—
53C2×(C22⋊D7)⋊C4C2218yescomplemented
54C7×#394C2218yescomplemented
55C2×C7×#95C2211yescharacteristic
56#89995C2218yes—
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62#89762C2218yescomplemented
63#89757C2218yescomplemented
64#89731C2218yescomplemented
65#89722C2218yescomplemented
66#89721C2218yescomplemented
67#89718C2218yescomplemented
68#89716C2218yescomplemented
69#89440C2218yescomplemented
70#89419C2218yescomplemented
71C2×#2455—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—24no—
78C22×C7×D4C2314yes—
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—24no—
87C22×C22⋊D7—24no—
88C22×C22⋊D7—24no—
89C22×C22⋊D7—42no—
90C22×C22⋊D7C2314yes—
91C22×C22⋊D7C2314yes—
92C23×Dic7—24no—
93C23×Dic7—24no—
94C23×Dic7—24no—
95C23×Dic7—24no—
96C23×Dic7—42no—
97C23×Dic7—42no—
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2314yes—
102C23×Dic7C2314yes—
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C22×C4×D7—24no—
108C22×C4×D7—24no—
109C22×C4×D7—42no—
110C22×C4×D7C2314yes—
111C2×C7×C4⋊C4—24no—
112C2×C7×C4⋊C4C2314yes—
113C2×C7×C22⋊C4—24no—
114C2×C7×C22⋊C4—24no—
115C2×C7×C22⋊C4—24no—
116C2×C7×C22⋊C4—24no—
117C2×C7×C22⋊C4C2314yes—
118C2×C7×C22⋊C4C2314yes—
119C2×C7×C22⋊C4C2314yes—
120C2×C7×C22⋊C4C2314yes—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—42no—
124C2×C22⋊Dic7D418yescomplemented
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129D4×Dic7—232no—
130C2×(C2×D7)⋊C4—24no—
131C2×(C2×D7)⋊C4—24no—
132C2×(C2×D7)⋊C4—24no—
133C2×(C2×D7)⋊C4D418yescomplemented
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×C4⋊Dic7—24no—
139C2×C4⋊Dic7—24no—
140C2×C4⋊Dic7—24no—
141C2×C4⋊Dic7—24no—
142C2×C4⋊Dic7C2314yes—
143C2×C4⋊Dic7C2314yes—
144C2×C4⋊Dic7C2314yes—
145C2×C4⋊Dic7C2314yes—
146C2×Dic7⋊C4—24no—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4—24no—
149C2×Dic7⋊C4—42no—
150C2×Dic7⋊C4C2314yes—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×C4×Dic7—24no—
155C2×C4×Dic7—24no—
156C2×C4×Dic7C2314yes—
157C2×C4×Dic7C2314yes—
158#6449—232no—
159#6446—232no—
160(C22⋊D7)⋊C4—232no—
161C7×#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×#123—71no—
168C22×#123—71no—
169C22×C4×D4—71no—
170C22×C4×D4—71no—
171#2455—716no—
172C2×#399—71no—
173C2×#394—71no—
174C2×#394D711yescharacteristic, complemented
175C2×#392—71no—
176C2×#389—71no—
177C2×#389—71no—
178C2×#388—71no—
179C2×#388—71no—
180C2×#385—71no—
181C2×#385—71no—
182C2×#385—71no—
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—22no—
194C24×C7—22no—
195C24×C7C2×D414yes—
196C24×C7#4114yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7—22no—
205C23×D7—22no—
206C23×D7C2×D414yes—
207C23×D7C2412yes—
208C2×C7×D4—232no—
209C2×C7×D4—28no—
210C2×C7×D4—28no—
211C2×C7×D4—28no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
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×C7C2×D414yes—
226C22×C4×C7#4114yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C2×C22⋊D7—232no—
233C2×C22⋊D7—28no—
234C2×C22⋊D7—28no—
235C2×C22⋊D7—28no—
236C2×C22⋊D7—28no—
237C2×C22⋊D7—28no—
238C2×C22⋊D7—44no—
239C2×C22⋊D7—416no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—28no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—28no—
259C22×Dic7—28no—
260C22×Dic7—28no—
261C22×Dic7—44no—
262C22×Dic7—44no—
263C22×Dic7—416no—
264C22×Dic7—416no—
265C22×Dic7C2×D414yes—
266C22×Dic7C2×D414yes—
267C22×Dic7C2×D414yes—
268C22×Dic7#4114yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C22×Dic7C2412yes—
275C22×Dic7C2412yes—
276C2×C4×D7—28no—
277C2×C4×D7—28no—
278C2×C4×D7—44no—
279C2×C4×D7—416no—
280C7×C4⋊C4—28no—
281C7×C22⋊C4—28no—
282C7×C22⋊C4—28no—
283C7×C22⋊C4—28no—
284C7×C22⋊C4—28no—
285C22⋊Dic7—28no—
286C22⋊Dic7—28no—
287C22⋊Dic7—44no—
288C22⋊Dic7C2×D4116yescomplemented
289(C2×D7)⋊C4—28no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4C2×D4116yescomplemented
293C4⋊Dic7—28no—
294C4⋊Dic7—28no—
295C4⋊Dic7—28no—
296C4⋊Dic7—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4—28no—
299Dic7⋊C4—28no—
300Dic7⋊C4—44no—
301C4×Dic7—28no—
302C4×Dic7—28no—
303C23×D4—71no—
304C23×D4—71no—
305C23×D4C2×D711yescharacteristic
306C24×C4—71no—
307C24×C4—71no—
308C24×C4—71no—
309C2×#123—78no—
310C2×#123—78no—
311C2×#123—148no—
312C2×#123—148no—
313C2×C4×D4—78no—
314C2×C4×D4—78no—
315C2×C4×D4—148no—
316C2×C4×D4—148no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4C2×D711yescharacteristic
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C22⋊C4C2×D711yescharacteristic
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C22⋊C4C2×D711yescharacteristic
337C22×C22⋊C4C2×D711yescharacteristic
338C22×C42—71no—
339C22×C42—71no—
340#399—78no—
341#394—78no—
342#394C2×D718yescomplemented
343#392—78no—
344#389—78no—
345#389—78no—
346#388—78no—
347#388—78no—
348#385—78no—
349#385—78no—
350#385—78no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95C2×D711yescharacteristic
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—28no—
361C23×C7—28no—
362C23×C7—28no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
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×C7C22×D414yes—
384C23×C7C22×D412yes—
385C23×C7C22×D412yes—
386C23×C7C2×#4114yes—
387C23×C7C2×#4112yes—
388C23×C7C2×#4112yes—
389C23×C7C2×#4112yes—
390C23×C7H(5,𝔽2)12yes—
391C23×C72−1+412yes—
392C23×C7C2511yescharacteristic
393C22×D7—28no—
394C22×D7—28no—
395C22×D7—28no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—44no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7—44no—
406C22×D7C22×D414yes—
407C7×D4—232no—
408C2×C4×C7—28no—
409C2×C4×C7—28no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
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—44no—
424C2×C4×C7—44no—
425C2×C4×C7—44no—
426C2×C4×C7C22×D414yes—
427C2×C4×C7C2×#4114yes—
428C22⋊D7—232no—
429C22⋊D7—416no—
430C2×Dic7—28no—
431C2×Dic7—28no—
432C2×Dic7—28no—
433C2×Dic7—28no—
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—416no—
452C2×Dic7—416no—
453C2×Dic7—44no—
454C2×Dic7—44no—
455C2×Dic7—44no—
456C2×Dic7C22×D414yes—
457C2×Dic7C22×D414yes—
458C2×Dic7C22×D414yes—
459C2×Dic7C2×#4114yes—
460C4×D7—416no—
461C25—71no—
462C25C22×D711yescharacteristic
463C25C22×D711yescharacteristic
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—74no—
468C22×D4—74no—
469C22×D4—144no—
470C22×D4—144no—
471C22×D4—144no—
472C22×D4—144no—
473C22×D4—144no—
474C22×D4—282no—
475C22×D4C22×D714yes—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—74no—
484C23×C4—74no—
485C23×C4—74no—
486C23×C4—144no—
487C23×C4—144no—
488C23×C4—144no—
489C23×C4—144no—
490C23×C4—144no—
491C23×C4—144no—
492C23×C4—282no—
493C23×C4—282no—
494C23×C4—282no—
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500#123—1432no—
501#123—1432no—
502C4×D4—1432no—
503C4×D4—1432no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—74no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—74no—
511C2×C4⋊C4—74no—
512C2×C4⋊C4—74no—
513C2×C4⋊C4—144no—
514C2×C4⋊C4—144no—
515C2×C4⋊C4—144no—
516C2×C4⋊C4—144no—
517C2×C4⋊C4—144no—
518C2×C4⋊C4—144no—
519C2×C4⋊C4—144no—
520C2×C4⋊C4—282no—
521C2×C4⋊C4C22×D714yes—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—78no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—78no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—74no—
532C2×C22⋊C4—74no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4—74no—
535C2×C22⋊C4—74no—
536C2×C22⋊C4—144no—
537C2×C22⋊C4—144no—
538C2×C22⋊C4—144no—
539C2×C22⋊C4—144no—
540C2×C22⋊C4—144no—
541C2×C22⋊C4—282no—
542C2×C22⋊C4C22×D714yes—
543C2×C22⋊C4C22×D714yes—
544C2×C22⋊C4C22×D714yes—
545C2×C22⋊C4C22×D714yes—
546C2×C42—74no—
547C2×C42—74no—
548C2×C42—144no—
549C2×C42—144no—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95—74no—
555#95C22×D714yes—
556C22×C7—24no—
557C22×C7—24no—
558C22×C7—24no—
559C22×C7—24no—
560C22×C7—24no—
561C22×C7—24no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—416no—
569C22×C7—416no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7#52514yes—
573C22×C7#52514yes—
574C22×C7#53914yes—
575C22×C7D4214yes—
576C22×C7#54714yes—
577C22×C7#54714yes—
578C22×C7#55914yes—
579C22×C7C23×D411yescharacteristic
580C22×C7C23×D411yescharacteristic
581C22×C7C22×#4111yescharacteristic
582C22×C7C22×#4111yescharacteristic
583C22×C7C22×#4111yescharacteristic
584C22×C7C2×H(5,𝔽2)11yescharacteristic
585C22×C7C2×2−1+411yescharacteristic
586C2×D7—24no—
587C2×D7—24no—
588C2×D7—24no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—416no—
593C2×D7—42no—
594C4×C7—24no—
595C4×C7—24no—
596C4×C7—42no—
597C4×C7—42no—
598C4×C7—42no—
599Dic7—24no—
600Dic7—24no—
601Dic7—24no—
602Dic7—24no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—74no—
619C24—72no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24—142no—
626C24D4×D714yes—
627C24#115914yes—
628C24C23×D712yes—
629C24C23×D712yes—
630C24C23×D711yescharacteristic
631C2×D4—232no—
632C2×D4—28no—
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—148no—
636C2×D4—148no—
637C2×D4—1432no—
638C2×D4—148no—
639C2×D4—148no—
640C2×D4—148no—
641C2×D4—284no—
642C2×D4—2816no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—74no—
657C22×C4—74no—
658C22×C4—74no—
659C22×C4—74no—
660C22×C4—72no—
661C22×C4—72no—
662C22×C4—72no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—148no—
668C22×C4—148no—
669C22×C4—148no—
670C22×C4—148no—
671C22×C4—148no—
672C22×C4—142no—
673C22×C4—142no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—148no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—284no—
691C22×C4—2816no—
692C22×C4—284no—
693C22×C4—284no—
694C22×C4—2816no—
695C22×C4—2816no—
696C22×C4D4×D714yes—
697C22×C4#115914yes—
698C22×C4C23×D712yes—
699C22×C4C23×D712yes—
700C22×C4C23×D712yes—
701C22×C4C23×D712yes—
702C22×C4C23×D712yes—
703C4⋊C4—28no—
704C4⋊C4—148no—
705C4⋊C4—148no—
706C4⋊C4—148no—
707C4⋊C4—148no—
708C4⋊C4—148no—
709C4⋊C4—148no—
710C4⋊C4—148no—
711C4⋊C4—284no—
712C22⋊C4—28no—
713C22⋊C4—28no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—716no—
717C22⋊C4—716no—
718C22⋊C4—148no—
719C22⋊C4—148no—
720C22⋊C4—148no—
721C22⋊C4—148no—
722C22⋊C4—148no—
723C22⋊C4—284no—
724C42—148no—
725C42—148no—
726C2×C7—44no—
727C2×C7—44no—
728C2×C7#245518yescomplemented
729C2×C7C2×#52511yescharacteristic
730C2×C7C2×#52511yescharacteristic
731C2×C7C2×#53911yescharacteristic
732C2×C7C2×D4211yescharacteristic
733C2×C7C2×#54711yescharacteristic
734C2×C7C2×#54711yescharacteristic
735C2×C7C2×#55911yescharacteristic
736D7—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—28no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—74no—
764C23—148no—
765C23—148no—
766C23—148no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—142no—
772C23—142no—
773C23—284no—
774C23—284no—
775C23—284no—
776C23—284no—
777C23C2×D4×D714yes—
778C23C2×D4×D712yes—
779C23C2×D4×D712yes—
780C23C2×#115914yes—
781C23C2×#115912yes—
782C23C2×#115912yes—
783C23D7×#4112yes—
784C23#655312yes—
785C23#655412yes—
786C23C24×D711yescharacteristic
787D4—232no—
788D4—1432no—
789D4—2816no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—74no—
809C2×C4—74no—
810C2×C4—74no—
811C2×C4—74no—
812C2×C4—148no—
813C2×C4—148no—
814C2×C4—148no—
815C2×C4—148no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—142no—
833C2×C4—2816no—
834C2×C4—2816no—
835C2×C4—2816no—
836C2×C4—284no—
837C2×C4—284no—
838C2×C4—284no—
839C2×C4C2×D4×D714yes—
840C2×C4C2×#115914yes—
841C7C2×#245511yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—416no—
853C22—416no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—144no—
859C22—144no—
860C22—144no—
861C22—282no—
862C22—2816no—
863C22—282no—
864C22—282no—
865C22—282no—
866C22#9027714yes—
867C22#9029714yes—
868C22#9030014yes—
869C22#9030214yes—
870C22#9034614yes—
871C22#9035614yes—
872C22#9037214yes—
873C22C22×D4×D711yescharacteristic
874C22C22×D4×D711yescharacteristic
875C22C22×#115911yescharacteristic
876C22C22×#115911yescharacteristic
877C22C2×D7×#4111yescharacteristic
878C22C2×#655311yescharacteristic
879C22C2×#655411yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—144no—
886C4—144no—
887C4—144no—
888C4—144no—
889C4—282no—
890C4—282no—
891C4—282no—
892C2—44no—
893C2—44no—
894C2—284no—
895C2#1173435318yesdirect product factor
896C2C2×#9027711yescharacteristic
897C2C2×#9029711yescharacteristic
898C2C2×#9030211yescharacteristic
899C2C2×#9030011yescharacteristic
900C2C2×#9035611yescharacteristic
901C2C2×#9034611yescharacteristic
902C2C2×#9037211yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#394D7
hypocenterC7C2×#2455
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic7C2semidirect
2. C22×#6446C2semidirect
3. C22×#6449C2semidirect
4. C22×(C22⋊D7)⋊C4C2semidirect
5. C2×C7×#394C2semidirect
7. C2×#89757C2semidirect
8. C2×#89762C2semidirect
9. C2×#89731C2semidirect
10. C2×#89721C2semidirect
11. C2×#89716C2semidirect
12. C2×#89722C2semidirect
13. C2×#89718C2semidirect
14. #11734353C2direct (N × H)
15. C2×#89440C2semidirect
16. C2×#89419C2semidirect
33. C2×D4×Dic7C22semidirect
49. C2×#6449C22semidirect
51. C2×#6446C22semidirect
53. C2×(C22⋊D7)⋊C4C22semidirect
54. C7×#394C22semidirect
62. #89762C22semidirect
63. #89757C22semidirect
64. #89731C22semidirect
65. #89722C22semidirect
66. #89721C22semidirect
67. #89718C22semidirect
68. #89716C22semidirect
69. #89440C22semidirect
70. #89419C22semidirect
124. C2×C22⋊Dic7D4semidirect
133. C2×(C2×D7)⋊C4D4semidirect
174. C2×#394D7semidirect
288. C22⋊Dic7C2×D4semidirect
292. (C2×D7)⋊C4C2×D4semidirect
342. #394C2×D7semidirect
728. C2×C7#2455semidirect
841. C7C2×#2455semidirect
895. C2#11734353direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic72
C22×#64462
C22×#64492
C22×(C22⋊D7)⋊C42
C2×C7×#3942
C2×#899952
C2×#897572
C2×#897622
C2×#897312
C2×#897212
C2×#897162
C2×#897222
C2×#897182
#117343532
C2×#894402
C2×#894192
C2×#24557