Finite Group Databasebeta

← C2×#11732202 #13523907

Subgroups — C2×#11732202 #13523907

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×#6492C211yesmaximal, characteristic, complemented
2C22×#6448C211yesmaximal, characteristic, complemented
3C2×C7×#386C211yesmaximal, characteristic, complemented
4C2×#89995C211yesmaximal, characteristic
5C2×#89993C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
7C2×#89728C211yesmaximal, characteristic, complemented
8C2×#89728C211yesmaximal, characteristic, complemented
9C2×#89724C211yesmaximal, characteristic, complemented
10C2×#89719C211yesmaximal, characteristic, complemented
11C2×#89717C211yesmaximal, characteristic, complemented
12#11732202C2116yesmaximal, direct product factor
13C2×#89446C211yesmaximal, characteristic, complemented
14C2×#89418C211yesmaximal, characteristic, complemented
15C2×#89425C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C23×Dic14C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C2×#6492—28no—
33C2×#6492C2218yescomplemented
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6448—28no—
45C2×#6448C2218yescomplemented
46C7×#386C2218yescomplemented
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49#89995C2218yes—
50#89993C2218yescomplemented
51C4×C22⋊Dic7C2218yescomplemented
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#89728C2218yescomplemented
61#89728C2218yescomplemented
62#89724C2218yescomplemented
63#89719C2218yescomplemented
64#89717C2218yescomplemented
65#89446C2218yescomplemented
66#89438C2218yescomplemented
67#89425C2218yescomplemented
68#89418C2218yescomplemented
69C2×#2557—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C24×D7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—42no—
76C22×C7×D4C2314yes—
77C23×C4×C7—24no—
78C23×C4×C7—24no—
79C23×C4×C7—42no—
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2314yes—
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×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C22×C4×D7—24no—
102C22×C4×D7—42no—
103C22×C4×D7—42no—
104C22×C4×D7C2314yes—
105C22×Dic14—24no—
106C22×Dic14—24no—
107C22×Dic14—42no—
108C22×Dic14C2314yes—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—42no—
111C2×C7×C22⋊C4—42no—
112C2×C7×C22⋊C4C2314yes—
113C2×C7×C22⋊C4C2314yes—
114C2×C7×C22⋊C4C2314yes—
115C2×C22⋊Dic7—24no—
116C2×C22⋊Dic7—24no—
117C2×C22⋊Dic7—24no—
118C2×C22⋊Dic7—24no—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—42no—
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127#6492—232no—
128C2×(C2×D7)⋊C4—24no—
129C2×(C2×D7)⋊C4—24no—
130C2×(C2×D7)⋊C4—24no—
131C2×(C2×D7)⋊C4D418yescomplemented
132C2×(C2×D7)⋊C4C2314yes—
133C2×(C2×D7)⋊C4C2314yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×C4⋊Dic7—24no—
137C2×C4⋊Dic7C2314yes—
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4—24no—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×C4×Dic7—24no—
143C2×C4×Dic7—42no—
144C2×C4×Dic7—42no—
145C2×C4×Dic7C2314yes—
146C2×C4×Dic7C2314yes—
147C2×C4×Dic7C2314yes—
148#6448—232no—
149C7×#95C2314yes—
150C7×#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#124—71no—
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×#386D711yescharacteristic, complemented
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×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×D7C2×D414yes—
199C23×D7C2412yes—
200C2×C7×D4—28no—
201C2×C7×D4—28no—
202C2×C7×D4—44no—
203C2×C7×D4—416no—
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—28no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—28no—
219C22×C4×C7—44no—
220C22×C4×C7—416no—
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×Dic7C2×D414yes—
255C22×Dic7#4114yes—
256C22×Dic7#4114yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C2×C4×D7—28no—
265C2×C4×D7—44no—
266C2×C4×D7—44no—
267C2×C4×D7—416no—
268C2×Dic14—28no—
269C2×Dic14—28no—
270C2×Dic14—44no—
271C2×Dic14—416no—
272C7×C22⋊C4—28no—
273C7×C22⋊C4—44no—
274C7×C22⋊C4—44no—
275C22⋊Dic7—28no—
276C22⋊Dic7—28no—
277C22⋊Dic7—28no—
278C22⋊Dic7—28no—
279C22⋊Dic7—28no—
280C22⋊Dic7—44no—
281(C2×D7)⋊C4—28no—
282(C2×D7)⋊C4—28no—
283(C2×D7)⋊C4—28no—
284(C2×D7)⋊C4C2×D4116yescomplemented
285C4⋊Dic7—28no—
286Dic7⋊C4—28no—
287Dic7⋊C4—28no—
288C4×Dic7—28no—
289C4×Dic7—44no—
290C4×Dic7—44no—
291C23×Q8—71no—
292C23×D4—71no—
293C23×D4—71no—
294C23×D4C2×D711yescharacteristic
295C24×C4—71no—
296C24×C4C2×D711yescharacteristic
297C2×#124—78no—
298C2×#124—148no—
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⋊C4—71no—
314C22×C22⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C42—71no—
318C22×C42—71no—
319C22×C42—71no—
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#386C2×D718yescomplemented
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×#95C2×D711yescharacteristic
342C2×#95C2×D711yescharacteristic
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×D412yes—
371C23×C7C2×#4112yes—
372C23×C7C2×#4114yes—
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×D7C22×D414yes—
393C7×D4—416no—
394C2×C4×C7—28no—
395C2×C4×C7—28no—
396C2×C4×C7—22no—
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—22no—
409C2×C4×C7—416no—
410C2×C4×C7—44no—
411C2×C4×C7—44no—
412C2×C4×C7—44no—
413C2×C4×C7C22×D414yes—
414C2×C4×C7C2×#4114yes—
415C22⋊D7—416no—
416C22⋊D7—416no—
417C2×Dic7—28no—
418C2×Dic7—28no—
419C2×Dic7—28no—
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×Dic7C22×D414yes—
443C2×Dic7C2×#4114yes—
444C2×Dic7C2×#4114yes—
445C4×D7—416no—
446Dic14—416no—
447C25—71no—
448C25C22×D711yescharacteristic
449C25C22×D711yescharacteristic
450C22×Q8—74no—
451C22×Q8—144no—
452C22×Q8—144no—
453C22×Q8—282no—
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—24no—
467C23×C4—24no—
468C23×C4—42no—
469C23×C4—71no—
470C23×C4—71no—
471C23×C4—71no—
472C23×C4—71no—
473C23×C4—71no—
474C23×C4—71no—
475C23×C4—71no—
476C23×C4—74no—
477C23×C4—144no—
478C23×C4—282no—
479C23×C4—282no—
480C23×C4C22×D711yescharacteristic
481C23×C4C22×D711yescharacteristic
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D714yes—
484C23×C4C22×D711yescharacteristic
485C23×C4C22×D711yescharacteristic
486#124—1432no—
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—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—78no—
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—74no—
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—144no—
515C2×C22⋊C4—144no—
516C2×C22⋊C4—282no—
517C2×C22⋊C4C22×D714yes—
518C2×C22⋊C4C22×D714yes—
519C2×C22⋊C4C22×D714yes—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—74no—
523C2×C42—144no—
524C2×C42—282no—
525C2×C42—282no—
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#95C22×D714yes—
535#95C22×D714yes—
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—42no—
577C4×C7—42no—
578C4×C7—42no—
579Dic7—24no—
580Dic7—24no—
581Dic7—24no—
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—
607C24#115914yes—
608C24C23×D712yes—
609C24C23×D712yes—
610C24C23×D711yescharacteristic
611C2×Q8—148no—
612C2×Q8—148no—
613C2×Q8—284no—
614C2×Q8—2816no—
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—28no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—28no—
642C22×C4—44no—
643C22×C4—416no—
644C22×C4—74no—
645C22×C4—74no—
646C22×C4—74no—
647C22×C4—72no—
648C22×C4—72no—
649C22×C4—72no—
650C22×C4—72no—
651C22×C4—72no—
652C22×C4—72no—
653C22×C4—72no—
654C22×C4—148no—
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—142no—
670C22×C4—142no—
671C22×C4—142no—
672C22×C4—142no—
673C22×C4—284no—
674C22×C4—284no—
675C22×C4—2816no—
676C22×C4#115714yes—
677C22×C4D4×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—44no—
688C22⋊C4—44no—
689C22⋊C4—716no—
690C22⋊C4—148no—
691C22⋊C4—148no—
692C22⋊C4—148no—
693C22⋊C4—148no—
694C22⋊C4—148no—
695C22⋊C4—148no—
696C22⋊C4—148no—
697C22⋊C4—148no—
698C22⋊C4—284no—
699C42—148no—
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×#115712yes—
755C23C2×D4×D712yes—
756C23C2×#115914yes—
757C23C2×#115912yes—
758C23#654812yes—
759C23#654812yes—
760C23D7×#4112yes—
761C23D7×#4112yes—
762C23C24×D711yescharacteristic
763Q8—2816no—
764D4—416no—
765D4—2816no—
766D4—2816no—
767C2×C4—28no—
768C2×C4—28no—
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—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—74no—
787C2×C4—74no—
788C2×C4—74no—
789C2×C4—148no—
790C2×C4—148no—
791C2×C4—148no—
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—142no—
808C2×C4—142no—
809C2×C4—142no—
810C2×C4—2816no—
811C2×C4—284no—
812C2×C4—284no—
813C2×C4—284no—
814C2×C4—284no—
815C2×C4C2×#115714yes—
816C2×C4C2×D4×D714yes—
817C7C2×#255711yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—416no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—88no—
834C22—144no—
835C22—144no—
836C22—144no—
837C22—282no—
838C22—282no—
839C22—282no—
840C22—282no—
841C22—2816no—
842C22#9018614yes—
843C22#9023914yes—
844C22#9025014yes—
845C22#9028214yes—
846C22#9030314yes—
847C22#9030414yes—
848C22#9034014yes—
849C22C22×#115711yescharacteristic
850C22C22×D4×D711yescharacteristic
851C22C22×#115911yescharacteristic
852C22C2×#654811yescharacteristic
853C22C2×#654811yescharacteristic
854C22C2×D7×#4111yescharacteristic
855C22C2×D7×#4111yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—144no—
862C4—144no—
863C4—144no—
864C4—282no—
865C4—282no—
866C4—282no—
867C4—282no—
868C2—44no—
869C2—82no—
870C2—284no—
871C2#1173220218yesdirect product factor
872C2C2×#9018611yescharacteristic
873C2C2×#9025011yescharacteristic
874C2C2×#9023911yescharacteristic
875C2C2×#9028211yescharacteristic
876C2C2×#9030411yescharacteristic
877C2C2×#9030311yescharacteristic
878C2C2×#9034011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#386D7
hypocenterC7C2×#2557
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#6492C2semidirect
2. C22×#6448C2semidirect
3. C2×C7×#386C2semidirect
5. C2×#89993C2semidirect
6. C2×C4×C22⋊Dic7C2semidirect
7. C2×#89728C2semidirect
8. C2×#89728C2semidirect
9. C2×#89724C2semidirect
10. C2×#89719C2semidirect
11. C2×#89717C2semidirect
12. #11732202C2direct (N × H)
13. C2×#89446C2semidirect
14. C2×#89418C2semidirect
15. C2×#89425C2semidirect
16. C2×#89438C2semidirect
33. C2×#6492C22semidirect
45. C2×#6448C22semidirect
46. C7×#386C22semidirect
50. #89993C22semidirect
51. C4×C22⋊Dic7C22semidirect
60. #89728C22semidirect
61. #89728C22semidirect
62. #89724C22semidirect
63. #89719C22semidirect
64. #89717C22semidirect
65. #89446C22semidirect
66. #89438C22semidirect
67. #89425C22semidirect
68. #89418C22semidirect
131. C2×(C2×D7)⋊C4D4semidirect
172. C2×#386D7semidirect
284. (C2×D7)⋊C4C2×D4semidirect
330. #386C2×D7semidirect
704. C2×C7#2557semidirect
817. C7C2×#2557semidirect
871. C2#11732202direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64922
C22×#64482
C2×C7×#3862
C2×#899952
C2×#899932
C2×C4×C22⋊Dic72
C2×#897282
C2×#897242
C2×#897192
C2×#897172
#117322022
C2×#894462
C2×#894182
C2×#894252
C2×#894382
C2×#25577