Finite Group Databasebeta

← C2×#11739815 #13521482

Subgroups — C2×#11739815 #13521482

Order 1792.

3330 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic, complemented
2C22×#6461C211yesmaximal, characteristic, complemented
3C2×#89995C211yesmaximal, characteristic
4C2×#89994C211yesmaximal, characteristic, complemented
5C2×#89985C211yesmaximal, characteristic, complemented
6C2×#89985C211yesmaximal, characteristic, complemented
7C2×#89984C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
9#11739815C2116yesmaximal, direct product factor
10C2×#89753C211yesmaximal, characteristic, complemented
11C2×#89721C211yesmaximal, characteristic, complemented
12C2×#89733C211yesmaximal, characteristic, complemented
13C2×#89729C211yesmaximal, characteristic, complemented
14C2×#89716C211yesmaximal, characteristic, complemented
15C2×#89712C211yesmaximal, characteristic, complemented
16C2×#89705C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C24×C4×C7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C22⋊D7C2211yescharacteristic
22C2×C4×C7×D4—28no—
23C2×C4×C7×D4C2218yescomplemented
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C2×#6461—28no—
47C2×#6461C2218yescomplemented
48#89995C2218yes—
49#89994C2218yescomplemented
50#89985C2218yescomplemented
51#89985C2218yescomplemented
52#89984C2218yescomplemented
53C4×C22⋊Dic7C2218yescomplemented
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62#89753C2218yescomplemented
63#89733C2218yescomplemented
64#89729C2218yescomplemented
65#89721C2218yescomplemented
66#89716C2218yescomplemented
67#89712C2218yescomplemented
68#89705C2218yescomplemented
69C2×#2467—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—24no—
76C22×C7×D4C2314yes—
77C23×C4×C7—24no—
78C23×C4×C7—24no—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—42no—
82C23×C4×C7—42no—
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2314yes—
85C23×C4×C7C2314yes—
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C22×C22⋊D7—24no—
91C22×C22⋊D7—24no—
92C22×C22⋊D7—24no—
93C22×C22⋊D7—42no—
94C22×C22⋊D7—42no—
95C22×C22⋊D7—42no—
96C22×C22⋊D7C2314yes—
97C22×C22⋊D7C2314yes—
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C4×C7×D4—232no—
106C2×C7×C4⋊C4D418yescomplemented
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C22⋊C4—24no—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4C2314yes—
111C2×C7×C22⋊C4C2314yes—
112C2×C42×C7—24no—
113C2×C42×C7C2314yes—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7—24no—
116C2×C22⋊Dic7—24no—
117C2×C22⋊Dic7—42no—
118C2×C22⋊Dic7—42no—
119C2×C22⋊Dic7—42no—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×(C2×D7)⋊C4—24no—
127C2×(C2×D7)⋊C4—24no—
128C2×(C2×D7)⋊C4—24no—
129C2×(C2×D7)⋊C4—24no—
130C2×(C2×D7)⋊C4—42no—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×C4⋊Dic7—24no—
137C2×C4⋊Dic7—42no—
138C2×C4⋊Dic7C2314yes—
139C2×C4⋊Dic7C2314yes—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4—42no—
143C2×Dic7⋊C4C2314yes—
144C2×Dic7⋊C4C2314yes—
145C2×Dic7⋊C4C2314yes—
146C2×C4×Dic7—24no—
147C2×C4×Dic7—42no—
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150#6461—232no—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×C4×D4D711yescharacteristic, complemented
161#2467—716no—
162C2×#399—71no—
163C2×#394—71no—
164C2×#394—71no—
165C2×#392—71no—
166C2×#390—71no—
167C2×#388—71no—
168C2×#388—71no—
169C2×#387—71no—
170C2×#387—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×#380—71no—
174C2×C4×C22⋊C4—71no—
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#4114yes—
188C24×C7#4114yes—
189C24×C7C2412yes—
190C24×C7C2412yes—
191C24×C7C2411yescharacteristic
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7—22no—
197C23×D7—22no—
198C23×D7—22no—
199C23×D7C2412yes—
200C2×C7×D4—232no—
201C2×C7×D4—28no—
202C2×C7×D4—28no—
203C2×C7×D4—28no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—28no—
216C22×C4×C7—28no—
217C22×C4×C7—28no—
218C22×C4×C7—28no—
219C22×C4×C7—44no—
220C22×C4×C7—44no—
221C22×C4×C7—416no—
222C22×C4×C7—416no—
223C22×C4×C7C2×D414yes—
224C22×C4×C7C2×D414yes—
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—28no—
233C2×C22⋊D7—28no—
234C2×C22⋊D7—28no—
235C2×C22⋊D7—44no—
236C2×C22⋊D7—44no—
237C2×C22⋊D7—44no—
238C2×C22⋊D7—416no—
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—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7#4114yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C7×C4⋊C4C2×D4116yescomplemented
269C7×C22⋊C4—28no—
270C7×C22⋊C4—28no—
271C42×C7—28no—
272C22⋊Dic7—28no—
273C22⋊Dic7—28no—
274C22⋊Dic7—28no—
275C22⋊Dic7—44no—
276C22⋊Dic7—44no—
277C22⋊Dic7—44no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—28no—
280(C2×D7)⋊C4—28no—
281(C2×D7)⋊C4—28no—
282(C2×D7)⋊C4—44no—
283C4⋊Dic7—28no—
284C4⋊Dic7—44no—
285Dic7⋊C4—28no—
286Dic7⋊C4—28no—
287Dic7⋊C4—44no—
288C4×Dic7—28no—
289C4×Dic7—44no—
290C23×D4—71no—
291C23×D4—71no—
292C23×D4C2×D711yescharacteristic
293C24×C4C2×D711yescharacteristic
294C24×C4C2×D711yescharacteristic
295C2×#126—78no—
296C2×#126—148no—
297C2×C4×D4—28no—
298C2×C4×D4C2×D718yescomplemented
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4C2×D711yescharacteristic
305C22×C22⋊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⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320C22×C42C2×D711yescharacteristic
321#399—78no—
322#394—78no—
323#394—78no—
324#392—78no—
325#390—78no—
326#388—78no—
327#388—78no—
328#387—78no—
329#387—78no—
330#386—78no—
331#386—78no—
332#380—78no—
333C4×C22⋊C4—78no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—28no—
346C23×C7—28no—
347C23×C7—28no—
348C23×C7—22no—
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—44no—
361C23×C7—44no—
362C23×C7—44no—
363C23×C7—44no—
364C23×C7—44no—
365C23×C7—44no—
366C23×C7—44no—
367C23×C7—44no—
368C23×C7C22×D412yes—
369C23×C7C2×#4114yes—
370C23×C7C2×#4114yes—
371C23×C7C2×#4112yes—
372C23×C7C2×#4112yes—
373C23×C7C2×#4112yes—
374C23×C7C2×#4112yes—
375C23×C7H(5,𝔽2)12yes—
376C23×C7H(5,𝔽2)12yes—
377C23×C7C2511yescharacteristic
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—44no—
386C22×D7—44no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7—44no—
392C7×D4—232no—
393C2×C4×C7—28no—
394C2×C4×C7—28no—
395C2×C4×C7—28no—
396C2×C4×C7—28no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—416no—
409C2×C4×C7—416no—
410C2×C4×C7—44no—
411C2×C4×C7C22×D414yes—
412C2×C4×C7C22×D414yes—
413C2×C4×C7C22×D414yes—
414C2×C4×C7C2×#4114yes—
415C22⋊D7—416no—
416C22⋊D7—416no—
417C2×Dic7—28no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—44no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7—44no—
444C2×Dic7C2×#4114yes—
445C25—71no—
446C25C22×D711yescharacteristic
447C25C22×D711yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—74no—
452C22×D4—74no—
453C22×D4—144no—
454C22×D4—144no—
455C22×D4—144no—
456C22×D4—282no—
457C22×D4—282no—
458C22×D4—282no—
459C22×D4C22×D714yes—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—42no—
465C23×C4—42no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4C22×D711yescharacteristic
474C23×C4C22×D714yes—
475C23×C4C22×D714yes—
476C23×C4C22×D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480#126—1432no—
481C4×D4—232no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—144no—
488C2×C4⋊C4—144no—
489C2×C4⋊C4—144no—
490C2×C4⋊C4—282no—
491C2×C4⋊C4—282no—
492C2×C4⋊C4C22⋊D718yescomplemented
493C2×C4⋊C4C22×D714yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—74no—
497C2×C22⋊C4—74no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—74no—
500C2×C22⋊C4—74no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—74no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—74no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—144no—
513C2×C22⋊C4—144no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4—282no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4—282no—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—24no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42—282no—
525C2×C42C22×D714yes—
526#95—74no—
527#95—74no—
528#95—74no—
529#95—74no—
530#95—74no—
531#95—74no—
532#95—74no—
533#95—74no—
534C22×C7—24no—
535C22×C7—24no—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—24no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—416no—
549C22×C7—416no—
550C22×C7#52514yes—
551C22×C7#52914yes—
552C22×C7#53814yes—
553C22×C7#54614yes—
554C22×C7#55014yes—
555C22×C7#55114yes—
556C22×C7#55314yes—
557C22×C7C23×D411yescharacteristic
558C22×C7C22×#4111yescharacteristic
559C22×C7C22×#4111yescharacteristic
560C22×C7C22×#4111yescharacteristic
561C22×C7C22×#4111yescharacteristic
562C22×C7C2×H(5,𝔽2)11yescharacteristic
563C22×C7C2×H(5,𝔽2)11yescharacteristic
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—88no—
572C4×C7—24no—
573C4×C7—24no—
574C4×C7—24no—
575C4×C7—24no—
576C4×C7—42no—
577Dic7—24no—
578Dic7—42no—
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—72no—
597C24—142no—
598C24—142no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24#115714yes—
605C24#115714yes—
606C24C23×D712yes—
607C24C23×D712yes—
608C24C23×D711yescharacteristic
609C2×D4—232no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—148no—
614C2×D4—148no—
615C2×D4—148no—
616C2×D4—284no—
617C2×D4—284no—
618C2×D4—284no—
619C2×D4—2816no—
620C2×D4—2816no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—416no—
639C22×C4—416no—
640C22×C4—74no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4—142no—
653C22×C4—142no—
654C22×C4—142no—
655C22×C4—142no—
656C22×C4—142no—
657C22×C4—142no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4—142no—
662C22×C4—142no—
663C22×C4—142no—
664C22×C4—142no—
665C22×C4—142no—
666C22×C4—142no—
667C22×C4—142no—
668C22×C4#115914yes—
669C22×C4C2×C22⋊D714yes—
670C22×C4C2×C22⋊D714yes—
671C22×C4C2×C22⋊D714yes—
672C22×C4C23×D712yes—
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D712yes—
677C4⋊C4—148no—
678C4⋊C4—148no—
679C4⋊C4—148no—
680C4⋊C4—284no—
681C4⋊C4—284no—
682C4⋊C4C2×C22⋊D7116yescomplemented
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—284no—
693C22⋊C4—284no—
694C22⋊C4—284no—
695C22⋊C4—284no—
696C42—28no—
697C42—148no—
698C42—284no—
699C2×C7—44no—
700C2×C7—44no—
701C2×C7#246718yescomplemented
702C2×C7C2×#52511yescharacteristic
703C2×C7C2×#52911yescharacteristic
704C2×C7C2×#53811yescharacteristic
705C2×C7C2×#54611yescharacteristic
706C2×C7C2×#55011yescharacteristic
707C2×C7C2×#55111yescharacteristic
708C2×C7C2×#55311yescharacteristic
709D7—82no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—142no—
737C23—142no—
738C23—142no—
739C23—142no—
740C23—142no—
741C23—142no—
742C23—142no—
743C23—284no—
744C23—284no—
745C23—284no—
746C23—284no—
747C23—284no—
748C23—284no—
749C23—284no—
750C23C2×#115714yes—
751C23C2×#115714yes—
752C23C2×#115712yes—
753C23C2×#115712yes—
754C23C2×#115912yes—
755C23#654812yes—
756C23D7×#4112yes—
757C23#655312yes—
758C23C22×C22⋊D712yes—
759C23C24×D711yescharacteristic
760D4—232no—
761D4—2816no—
762D4—2816no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—416no—
779C2×C4—416no—
780C2×C4—44no—
781C2×C4—74no—
782C2×C4—148no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—142no—
803C2×C4—284no—
804C2×C4—284no—
805C2×C4—284no—
806C2×C4—284no—
807C2×C4—284no—
808C2×C4—284no—
809C2×C4C2×#115914yes—
810C2×C4C22×C22⋊D714yes—
811C2×C4C22×C22⋊D714yes—
812C2×C4C22×C22⋊D714yes—
813C7C2×#246711yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—416no—
829C22—416no—
830C22—282no—
831C22—282no—
832C22—282no—
833C22—282no—
834C22—282no—
835C22—282no—
836C22—282no—
837C22—568no—
838C22#9022914yes—
839C22#9024714yes—
840C22#9025114yes—
841C22#9025614yes—
842C22#9048214yes—
843C22#9049714yes—
844C22#9052514yes—
845C22C22×#115711yescharacteristic
846C22C22×#115711yescharacteristic
847C22C22×#115911yescharacteristic
848C22C2×#654811yescharacteristic
849C22C2×D7×#4111yescharacteristic
850C22C2×#655311yescharacteristic
851C22C23×C22⋊D711yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—144no—
858C4—282no—
859C4—282no—
860C4—282no—
861C4—282no—
862C4—282no—
863C4—282no—
864C2—44no—
865C2—44no—
866C2—562no—
867C2#1173981518yesdirect product factor
868C2C2×#9022911yescharacteristic
869C2C2×#9025611yescharacteristic
870C2C2×#9025111yescharacteristic
871C2C2×#9024711yescharacteristic
872C2C2×#9048211yescharacteristic
873C2C2×#9049711yescharacteristic
874C2C2×#9052511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C4×C7×D4C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC22×C4×D4D7
hypocenterC7C2×#2467
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C7×D4C2semidirect
2. C22×#6461C2semidirect
4. C2×#89994C2semidirect
5. C2×#89985C2semidirect
6. C2×#89985C2semidirect
7. C2×#89984C2semidirect
8. C2×C4×C22⋊Dic7C2semidirect
9. #11739815C2direct (N × H)
10. C2×#89753C2semidirect
11. C2×#89721C2semidirect
12. C2×#89733C2semidirect
13. C2×#89729C2semidirect
14. C2×#89716C2semidirect
15. C2×#89712C2semidirect
16. C2×#89705C2semidirect
23. C2×C4×C7×D4C22semidirect
47. C2×#6461C22semidirect
49. #89994C22semidirect
50. #89985C22semidirect
51. #89985C22semidirect
52. #89984C22semidirect
53. C4×C22⋊Dic7C22semidirect
62. #89753C22semidirect
63. #89733C22semidirect
64. #89729C22semidirect
65. #89721C22semidirect
66. #89716C22semidirect
67. #89712C22semidirect
68. #89705C22semidirect
106. C2×C7×C4⋊C4D4semidirect
160. C22×C4×D4D7semidirect
268. C7×C4⋊C4C2×D4semidirect
298. C2×C4×D4C2×D7semidirect
492. C2×C4⋊C4C22⋊D7semidirect
682. C4⋊C4C2×C22⋊D7semidirect
701. C2×C7#2467semidirect
813. C7C2×#2467semidirect
867. C2#11739815direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C22×#64612
C2×#899952
C2×#899942
C2×#899852
C2×#899842
C2×C4×C22⋊Dic72
#117398152
C2×#897532
C2×#897212
C2×#897332
C2×#897292
C2×#897162
C2×#897122
C2×#897052
C2×#24677