Finite Group Databasebeta

← C2×#11740444 #13523911

Subgroups — C2×#11740444 #13523911

Order 1792.

3330 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#124C211yesmaximal, characteristic, complemented
2C22×#6446C211yesmaximal, characteristic, complemented
3C2×#90003C211yesmaximal, characteristic, complemented
4C2×#90002C211yesmaximal, characteristic, complemented
5C2×#89995C211yesmaximal, characteristic
6C2×#89992C211yesmaximal, characteristic, complemented
7#11740444C2116yesmaximal, direct product factor
8C2×#89728C211yesmaximal, characteristic, complemented
9C2×#89725C211yesmaximal, characteristic, complemented
10C2×#89724C211yesmaximal, characteristic, complemented
11C2×#89729C211yesmaximal, characteristic, complemented
12C2×#89717C211yesmaximal, characteristic, complemented
13C2×#89730C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
15C2×#89705C211yesmaximal, characteristic, complemented
16C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C24×Dic7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C2×C7×#124—28no—
24C2×C7×#124C2218yescomplemented
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C42×C7C2211yescharacteristic
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
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6446—28no—
45C2×#6446C2218yescomplemented
46#90003C2218yescomplemented
47#90002C2218yescomplemented
48#89995C2218yes—
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
59C2×C7⋊#95C2211yescharacteristic
60#89730C2218yescomplemented
61#89729C2218yescomplemented
62#89728C2218yescomplemented
63#89725C2218yescomplemented
64#89724C2218yescomplemented
65#89717C2218yescomplemented
66C22⋊C4×Dic7C2218yescomplemented
67C4×(C2×D7)⋊C4C2218yescomplemented
68#89705C2218yescomplemented
69C2×#2557—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C22×C7×Q8—24no—
74C22×C7×Q8—24no—
75C22×C7×Q8—42no—
76C22×C7×Q8C2314yes—
77C22×C7×D4—24no—
78C22×C7×D4—24no—
79C22×C7×D4—42no—
80C22×C7×D4C2314yes—
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C22×C22⋊D7—24no—
87C22×C22⋊D7—24no—
88C22×C22⋊D7—24no—
89C22×C22⋊D7—24no—
90C22×C22⋊D7—42no—
91C22×C22⋊D7—42no—
92C22×C22⋊D7C2314yes—
93C22×C22⋊D7C2314yes—
94C23×Dic7—24no—
95C23×Dic7—42no—
96C23×Dic7—42no—
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2314yes—
105C22×C4×D7—24no—
106C22×C4×D7—24no—
107C22×C4×D7—42no—
108C22×C4×D7C2314yes—
109C7×#124—232no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4D418yescomplemented
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2314yes—
118C2×C42×C7—24no—
119C2×C42×C7C2314yes—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—42no—
124C2×C22⋊Dic7—42no—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×(C2×D7)⋊C4—24no—
131C2×(C2×D7)⋊C4—24no—
132C2×(C2×D7)⋊C4—24no—
133C2×(C2×D7)⋊C4—42no—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×C4⋊Dic7—24no—
139C2×C4⋊Dic7C2314yes—
140C2×Dic7⋊C4—24no—
141C2×Dic7⋊C4—24no—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×C4×Dic7—42no—
145C2×C4×Dic7—42no—
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148#6446—232no—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#124D711yescharacteristic, complemented
160C22×#123—71no—
161#2557—716no—
162C2×#397—71no—
163C2×#397—71no—
164C2×#393—71no—
165C2×#392—71no—
166C2×#391—71no—
167C2×#390—71no—
168C2×#388—71no—
169C2×#387—71no—
170C2×#386—71no—
171C2×#386—71no—
172C2×#386—71no—
173C2×C4×C22⋊C4—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—22no—
188C24×C7C2×D414yes—
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#4114yes—
199C23×D7C2412yes—
200C2×C7×Q8—28no—
201C2×C7×Q8—28no—
202C2×C7×Q8—44no—
203C2×C7×Q8—416no—
204C2×C7×D4—28no—
205C2×C7×D4—28no—
206C2×C7×D4—44no—
207C2×C7×D4—416no—
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—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7C2×D414yes—
221C22×C4×C7C2×D414yes—
222C22×C4×C7#4114yes—
223C22×C4×C7C2412yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C2×C22⋊D7—28no—
229C2×C22⋊D7—28no—
230C2×C22⋊D7—28no—
231C2×C22⋊D7—28no—
232C2×C22⋊D7—44no—
233C2×C22⋊D7—44no—
234C2×C22⋊D7—416no—
235C2×C22⋊D7—416no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
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—28no—
256C22×Dic7—44no—
257C22×Dic7—44no—
258C22×Dic7—416no—
259C22×Dic7#4114yes—
260C22×Dic7#4114yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C22×Dic7C2412yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C2×C4×D7—28no—
269C2×C4×D7—28no—
270C2×C4×D7—44no—
271C2×C4×D7—416no—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—28no—
274C7×C22⋊C4—28no—
275C7×C22⋊C4C2×D4116yescomplemented
276C42×C7—28no—
277C22⋊Dic7—28no—
278C22⋊Dic7—28no—
279C22⋊Dic7—28no—
280C22⋊Dic7—44no—
281C22⋊Dic7—44no—
282(C2×D7)⋊C4—28no—
283(C2×D7)⋊C4—28no—
284(C2×D7)⋊C4—28no—
285(C2×D7)⋊C4—44no—
286C4⋊Dic7—28no—
287Dic7⋊C4—28no—
288Dic7⋊C4—28no—
289C4×Dic7—44no—
290C4×Dic7—44no—
291C23×Q8C2×D711yescharacteristic
292C23×D4—71no—
293C23×D4—71no—
294C23×D4C2×D711yescharacteristic
295C24×C4—71no—
296C24×C4—71no—
297C2×#124—28no—
298C2×#124C2×D718yescomplemented
299C2×#123—78no—
300C2×#123—148no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C22⋊C4—71no—
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⋊C4C2×D711yescharacteristic
314C22×C22⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C42—71no—
318C22×C42—71no—
319C22×C42C2×D711yescharacteristic
320#397—78no—
321#397—78no—
322#393—78no—
323#392—78no—
324#391—78no—
325#390—78no—
326#388—78no—
327#387—78no—
328#386—78no—
329#386—78no—
330#386—78no—
331C4×C22⋊C4—78no—
332C4×C22⋊C4—78no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C23×C7—28no—
344C23×C7—28no—
345C23×C7—28no—
346C23×C7—22no—
347C23×C7—22no—
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—44no—
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×C7—44no—
369C23×C7—44no—
370C23×C7C22×D414yes—
371C23×C7C22×D412yes—
372C23×C7C2×#4112yes—
373C23×C7C2×#4112yes—
374C23×C7C2×#4112yes—
375C23×C7C2×#4112yes—
376C23×C7H(5,𝔽2)12yes—
377C23×C7H(5,𝔽2)12yes—
378C23×C7C2511yescharacteristic
379C22×D7—28no—
380C22×D7—28no—
381C22×D7—28no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7—44no—
392C22×D7C2×#4114yes—
393C7×Q8—416no—
394C7×D4—416no—
395C2×C4×C7—28no—
396C2×C4×C7—28no—
397C2×C4×C7—28no—
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—22no—
409C2×C4×C7—22no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7C22×D414yes—
413C2×C4×C7C22×D414yes—
414C2×C4×C7C2×#4114yes—
415C22⋊D7—416no—
416C22⋊D7—416no—
417C2×Dic7—28no—
418C2×Dic7—28no—
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—416no—
439C2×Dic7—44no—
440C2×Dic7—44no—
441C2×Dic7—44no—
442C2×Dic7—44no—
443C2×Dic7—44no—
444C2×Dic7C2×#4114yes—
445C2×Dic7C2×#4114yes—
446C4×D7—416no—
447C25—71no—
448C25C22×D711yescharacteristic
449C25C22×D711yescharacteristic
450C22×Q8—24no—
451C22×Q8—24no—
452C22×Q8—42no—
453C22×Q8C22×D714yes—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—42no—
457C22×D4—74no—
458C22×D4—74no—
459C22×D4—144no—
460C22×D4—144no—
461C22×D4—144no—
462C22×D4—144no—
463C22×D4—282no—
464C22×D4—282no—
465C22×D4C22×D714yes—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—74no—
474C23×C4—74no—
475C23×C4—144no—
476C23×C4—144no—
477C23×C4—144no—
478C23×C4—282no—
479C23×C4—282no—
480C23×C4—282no—
481C23×C4C22×D711yescharacteristic
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486#124—232no—
487#123—1432no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—144no—
492C2×C4⋊C4—144no—
493C2×C4⋊C4—144no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
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—144no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—282no—
513C2×C22⋊C4—282no—
514C2×C22⋊C4—282no—
515C2×C22⋊C4C22⋊D718yescomplemented
516C2×C22⋊C4C22×D714yes—
517C2×C22⋊C4C22×D714yes—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—24no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—282no—
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—
534#95—74no—
535#95—74no—
536C22×C7—24no—
537C22×C7—24no—
538C22×C7—24no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—416no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—88no—
552C22×C7#52914yes—
553C22×C7#53214yes—
554C22×C7#53814yes—
555C22×C7#54614yes—
556C22×C7#54614yes—
557C22×C7#55114yes—
558C22×C7#55914yes—
559C22×C7C23×D411yescharacteristic
560C22×C7C22×#4111yescharacteristic
561C22×C7C22×#4111yescharacteristic
562C22×C7C22×#4111yescharacteristic
563C22×C7C22×#4111yescharacteristic
564C22×C7C2×H(5,𝔽2)11yescharacteristic
565C22×C7C2×H(5,𝔽2)11yescharacteristic
566C2×D7—24no—
567C2×D7—24no—
568C2×D7—24no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—42no—
572C2×D7—42no—
573C2×D7—416no—
574C4×C7—24no—
575C4×C7—24no—
576C4×C7—24no—
577C4×C7—42no—
578C4×C7—42no—
579Dic7—24no—
580Dic7—24no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584Dic7—42no—
585Dic7—42no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—74no—
600C24—72no—
601C24—142no—
602C24—142no—
603C24—142no—
604C24—142no—
605C24—142no—
606C24—142no—
607C24C2×C22⋊D714yes—
608C24C23×D712yes—
609C24C23×D712yes—
610C24C23×D711yescharacteristic
611C2×Q8—28no—
612C2×Q8—28no—
613C2×Q8—44no—
614C2×Q8—416no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—44no—
618C2×D4—416no—
619C2×D4—148no—
620C2×D4—148no—
621C2×D4—148no—
622C2×D4—148no—
623C2×D4—284no—
624C2×D4—284no—
625C2×D4—2816no—
626C2×D4—2816no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—74no—
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—148no—
649C22×C4—148no—
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—142no—
669C22×C4—148no—
670C22×C4—284no—
671C22×C4—2816no—
672C22×C4—284no—
673C22×C4—284no—
674C22×C4—2816no—
675C22×C4#115914yes—
676C22×C4C2×C22⋊D714yes—
677C22×C4C2×C22⋊D714yes—
678C22×C4C23×D712yes—
679C22×C4C23×D712yes—
680C22×C4C23×D712yes—
681C22×C4C23×D712yes—
682C22×C4C23×D712yes—
683C4⋊C4—148no—
684C4⋊C4—148no—
685C4⋊C4—148no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—28no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—148no—
695C22⋊C4—284no—
696C22⋊C4—284no—
697C22⋊C4—284no—
698C22⋊C4C2×C22⋊D7116yescomplemented
699C42—28no—
700C42—284no—
701C42—284no—
702C2×C7—44no—
703C2×C7—82no—
704C2×C7#255718yescomplemented
705C2×C7C2×#52911yescharacteristic
706C2×C7C2×#53211yescharacteristic
707C2×C7C2×#53811yescharacteristic
708C2×C7C2×#54611yescharacteristic
709C2×C7C2×#54611yescharacteristic
710C2×C7C2×#55111yescharacteristic
711C2×C7C2×#55911yescharacteristic
712D7—44no—
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—22no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—74no—
741C23—148no—
742C23—148no—
743C23—148no—
744C23—142no—
745C23—142no—
746C23—142no—
747C23—142no—
748C23—142no—
749C23—142no—
750C23—284no—
751C23—284no—
752C23—284no—
753C23—284no—
754C23C2×#115912yes—
755C23#654812yes—
756C23D7×#4112yes—
757C23D7×#4112yes—
758C23D7×#4112yes—
759C23#655312yes—
760C23C22×C22⋊D714yes—
761C23C22×C22⋊D712yes—
762C23C24×D711yescharacteristic
763Q8—416no—
764D4—416no—
765D4—2816no—
766D4—2816no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
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—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—74no—
785C2×C4—74no—
786C2×C4—148no—
787C2×C4—148no—
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—142no—
804C2×C4—142no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—2816no—
808C2×C4—2816no—
809C2×C4—284no—
810C2×C4—284no—
811C2×C4—284no—
812C2×C4—284no—
813C2×C4—284no—
814C2×C4C2×#115914yes—
815C2×C4C22×C22⋊D714yes—
816C2×C4C22×C22⋊D714yes—
817C7C2×#255711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—416no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—88no—
834C22—144no—
835C22—144no—
836C22—144no—
837C22—2816no—
838C22—282no—
839C22—282no—
840C22—282no—
841C22—282no—
842C22#9036914yes—
843C22#9037014yes—
844C22#9037114yes—
845C22#9037214yes—
846C22#9049714yes—
847C22#9052014yes—
848C22#9052314yes—
849C22C22×#115911yescharacteristic
850C22C2×#654811yescharacteristic
851C22C2×D7×#4111yescharacteristic
852C22C2×D7×#4111yescharacteristic
853C22C2×D7×#4111yescharacteristic
854C22C2×#655311yescharacteristic
855C22C23×C22⋊D711yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—42no—
860C4—42no—
861C4—144no—
862C4—144no—
863C4—282no—
864C4—282no—
865C4—282no—
866C4—282no—
867C4—282no—
868C2—44no—
869C2—82no—
870C2—284no—
871C2#1174044418yesdirect product factor
872C2C2×#9037111yescharacteristic
873C2C2×#9037211yescharacteristic
874C2C2×#9036911yescharacteristic
875C2C2×#9037011yescharacteristic
876C2C2×#9049711yescharacteristic
877C2C2×#9052311yescharacteristic
878C2C2×#9052011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#124C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC22×#124D7
hypocenterC7C2×#2557
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×C7×#124C2semidirect
2. C22×#6446C2semidirect
3. C2×#90003C2semidirect
4. C2×#90002C2semidirect
6. C2×#89992C2semidirect
7. #11740444C2direct (N × H)
8. C2×#89728C2semidirect
9. C2×#89725C2semidirect
10. C2×#89724C2semidirect
11. C2×#89729C2semidirect
12. C2×#89717C2semidirect
13. C2×#89730C2semidirect
14. C2×C22⋊C4×Dic7C2semidirect
15. C2×#89705C2semidirect
16. C2×C4×(C2×D7)⋊C4C2semidirect
24. C2×C7×#124C22semidirect
45. C2×#6446C22semidirect
46. #90003C22semidirect
47. #90002C22semidirect
49. #89992C22semidirect
60. #89730C22semidirect
61. #89729C22semidirect
62. #89728C22semidirect
63. #89725C22semidirect
64. #89724C22semidirect
65. #89717C22semidirect
66. C22⋊C4×Dic7C22semidirect
67. C4×(C2×D7)⋊C4C22semidirect
68. #89705C22semidirect
113. C2×C7×C22⋊C4D4semidirect
159. C22×#124D7semidirect
275. C7×C22⋊C4C2×D4semidirect
298. C2×#124C2×D7semidirect
515. C2×C22⋊C4C22⋊D7semidirect
698. C22⋊C4C2×C22⋊D7semidirect
704. C2×C7#2557semidirect
817. C7C2×#2557semidirect
871. C2#11740444direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1242
C22×#64462
C2×#900032
C2×#900022
C2×#899952
C2×#899922
#117404442
C2×#897282
C2×#897252
C2×#897242
C2×#897292
C2×#897172
C2×#897302
C2×C22⋊C4×Dic72
C2×#897052
C2×C4×(C2×D7)⋊C42
C2×#25577