Finite Group Databasebeta

← C2×#11734134 #13523870

Subgroups — C2×#11734134 #13523870

Order 1792.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6498C211yesmaximal, characteristic, complemented
2C22×#6442C211yesmaximal, characteristic, complemented
3C2×C7×#392C211yesmaximal, characteristic
4C2×#89994C211yesmaximal, characteristic, complemented
5C2×#89993C211yesmaximal, characteristic, complemented
6C2×#89993C211yesmaximal, characteristic, complemented
7C2×#89993C211yesmaximal, characteristic, complemented
8C2×#89992C211yesmaximal, characteristic, complemented
9C2×#89720C211yesmaximal, characteristic, complemented
10C2×#89717C211yesmaximal, characteristic, complemented
11C2×#89716C211yesmaximal, characteristic, complemented
12C2×#89723C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
14#11734134C2116yesmaximal, direct product factor
15C2×#89433C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C2×#6498—28no—
36C2×#6498C2218yescomplemented
37C22×C4⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C2×#6442—28no—
49C2×#6442C2218yescomplemented
50C7×#392C2218yes—
51C2×C7×#95C2211yescharacteristic
52#89994C2218yescomplemented
53#89993C2218yescomplemented
54#89993C2218yescomplemented
55#89993C2218yescomplemented
56#89992C2218yescomplemented
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62#89723C2218yescomplemented
63#89720C2218yescomplemented
64#89717C2218yescomplemented
65#89716C2218yescomplemented
66C22⋊C4×Dic7C2218yescomplemented
67#89433C2218yescomplemented
68#89421C2218yescomplemented
69C2×#2554—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C25×C7C2311yescharacteristic
72C25×C7C2311yescharacteristic
73C22×C7×D4—24no—
74C22×C7×D4—24no—
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—24no—
78C22×C7×D4—42no—
79C22×C7×D4—42no—
80C22×C7×D4—42no—
81C22×C7×D4—42no—
82C22×C7×D4C2314yes—
83C22×C7×D4C2314yes—
84C22×C7×D4C2314yes—
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×Dic7—24no—
90C23×Dic7—24no—
91C23×Dic7—42no—
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2314yes—
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4C2314yes—
105C2×C7×C22⋊C4C2314yes—
106C2×C7×C22⋊C4C2314yes—
107C2×C22⋊Dic7—24no—
108C2×C22⋊Dic7—24no—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7—24no—
111C2×C22⋊Dic7—24no—
112C2×C22⋊Dic7—24no—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7—42no—
116C2×C22⋊Dic7—42no—
117C2×C22⋊Dic7—42no—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129#6498—232no—
130C2×C4⋊Dic7—24no—
131C2×C4⋊Dic7—42no—
132C2×C4⋊Dic7—42no—
133C2×C4⋊Dic7C2314yes—
134C2×C4⋊Dic7C2314yes—
135C2×C4⋊Dic7C2314yes—
136C2×Dic7⋊C4—24no—
137C2×Dic7⋊C4—24no—
138C2×Dic7⋊C4—24no—
139C2×Dic7⋊C4D418yescomplemented
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×Dic7⋊C4C2314yes—
144C2×C4×Dic7—24no—
145C2×C4×Dic7—24no—
146C2×C4×Dic7—42no—
147C2×C4×Dic7—42no—
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2314yes—
150C2×C4×Dic7C2314yes—
151C2×C4×Dic7C2314yes—
152#6442—232no—
153C7×#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157C7⋊#95C2314yes—
158C7⋊#95C2314yes—
159C22×#126—71no—
160C22×#123—71no—
161#2554—716no—
162C2×#398—71no—
163C2×#396—71no—
164C2×#394—71no—
165C2×#392D711yescharacteristic
166C2×#390—71no—
167C2×#390—71no—
168C2×#390—71no—
169C2×#388—71no—
170C2×#388—71no—
171C2×#388—71no—
172C2×#386—71no—
173C2×C4×C4⋊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—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7—22no—
195C24×C7#4114yes—
196C24×C7C2412yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C2×C7×D4—28no—
201C2×C7×D4—28no—
202C2×C7×D4—28no—
203C2×C7×D4—28no—
204C2×C7×D4—28no—
205C2×C7×D4—44no—
206C2×C7×D4—44no—
207C2×C7×D4—44no—
208C2×C7×D4—44no—
209C2×C7×D4—416no—
210C2×C7×D4—416no—
211C2×C7×D4—416no—
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×C7C2×D414yes—
222C22×C4×C7#4114yes—
223C22×C4×C7#4114yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2412yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—28no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—28no—
251C22×Dic7—44no—
252C22×Dic7—416no—
253C22×Dic7C2×D414yes—
254C22×Dic7C2×D414yes—
255C22×Dic7#4114yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C7×C22⋊C4—28no—
265C7×C22⋊C4—28no—
266C7×C22⋊C4—28no—
267C22⋊Dic7—28no—
268C22⋊Dic7—28no—
269C22⋊Dic7—28no—
270C22⋊Dic7—28no—
271C22⋊Dic7—28no—
272C22⋊Dic7—28no—
273C22⋊Dic7—28no—
274C22⋊Dic7—28no—
275C22⋊Dic7—44no—
276C22⋊Dic7—44no—
277C22⋊Dic7—44no—
278C4⋊Dic7—28no—
279C4⋊Dic7—44no—
280C4⋊Dic7—44no—
281Dic7⋊C4—28no—
282Dic7⋊C4—28no—
283Dic7⋊C4—28no—
284Dic7⋊C4C2×D4116yescomplemented
285C4×Dic7—28no—
286C4×Dic7—28no—
287C4×Dic7—44no—
288C4×Dic7—44no—
289C23×D4C2×D711yescharacteristic
290C23×D4C2×D711yescharacteristic
291C23×D4C2×D711yescharacteristic
292C24×C4—71no—
293C2×#126—78no—
294C2×#126—148no—
295C2×#123—78no—
296C2×#123—148no—
297C22×C4⋊C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
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⋊C4—71no—
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C22⋊C4C2×D711yescharacteristic
317C22×C22⋊C4C2×D711yescharacteristic
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321C22×C42—71no—
322#398—78no—
323#396—78no—
324#394—78no—
325#392C2×D718yes—
326#390—78no—
327#390—78no—
328#390—78no—
329#388—78no—
330#388—78no—
331#388—78no—
332#386—78no—
333C4×C4⋊C4—78no—
334C4×C22⋊C4—78no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95C2×D711yescharacteristic
341C23×C7—28no—
342C23×C7—28no—
343C23×C7—28no—
344C23×C7—22no—
345C23×C7—22no—
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—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—44no—
365C23×C7—44no—
366C23×C7—44no—
367C23×C7—44no—
368C23×C7—44no—
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×C7C22×D412yes—
383C23×C7C2×#4114yes—
384C23×C7C2×#4112yes—
385C23×C7C2×#4112yes—
386C23×C7C2×#4112yes—
387C23×C7C2×#4112yes—
388C23×C7H(5,𝔽2)12yes—
389C23×C7H(5,𝔽2)12yes—
390C23×C7C2511yescharacteristic
391C7×D4—416no—
392C7×D4—416no—
393C7×D4—416no—
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—44no—
407C2×C4×C7C22×D414yes—
408C2×C4×C7C2×#4114yes—
409C2×C4×C7C2×#4114yes—
410C2×Dic7—28no—
411C2×Dic7—28no—
412C2×Dic7—28no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
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—416no—
435C2×Dic7—44no—
436C2×Dic7—44no—
437C2×Dic7—44no—
438C2×Dic7—44no—
439C2×Dic7—44no—
440C2×Dic7C22×D414yes—
441C2×Dic7C22×D414yes—
442C2×Dic7C2×#4114yes—
443C25C22×D711yescharacteristic
444C25C22×D711yescharacteristic
445C25C22×D711yescharacteristic
446C22×D4—24no—
447C22×D4—24no—
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—42no—
452C22×D4—42no—
453C22×D4—42no—
454C22×D4—42no—
455C22×D4C22×D714yes—
456C22×D4C22×D714yes—
457C22×D4C22×D714yes—
458C23×C4—71no—
459C23×C4—71no—
460C23×C4—71no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—74no—
467C23×C4—144no—
468C23×C4—144no—
469C23×C4—282no—
470C23×C4C22×D711yescharacteristic
471C23×C4C22×D711yescharacteristic
472C23×C4C22×D711yescharacteristic
473C23×C4C22×D711yescharacteristic
474#126—1432no—
475#123—1432no—
476C2×C4⋊C4—78no—
477C2×C4⋊C4—74no—
478C2×C4⋊C4—74no—
479C2×C4⋊C4—74no—
480C2×C4⋊C4—74no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—144no—
485C2×C4⋊C4—144no—
486C2×C4⋊C4—144no—
487C2×C4⋊C4—144no—
488C2×C4⋊C4—282no—
489C2×C4⋊C4—282no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—74no—
494C2×C22⋊C4—74no—
495C2×C22⋊C4—74no—
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—144no—
505C2×C22⋊C4—144no—
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×D714yes—
516C2×C22⋊C4C22×D714yes—
517C2×C22⋊C4C22×D714yes—
518C2×C42—74no—
519C2×C42—74no—
520C2×C42—74no—
521C2×C42—74no—
522C2×C42—144no—
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#95C22×D714yes—
532C22×C7—24no—
533C22×C7—24no—
534C22×C7—24no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—416no—
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—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—42no—
553C22×C7—42no—
554C22×C7—88no—
555C22×C7—88no—
556C22×C7#52914yes—
557C22×C7#53214yes—
558C22×C7#53814yes—
559C22×C7#54614yes—
560C22×C7#55014yes—
561C22×C7#55114yes—
562C22×C7#55314yes—
563C22×C7C23×D411yescharacteristic
564C22×C7C22×#4111yescharacteristic
565C22×C7C22×#4111yescharacteristic
566C22×C7C22×#4111yescharacteristic
567C22×C7C22×#4111yescharacteristic
568C22×C7C2×H(5,𝔽2)11yescharacteristic
569C22×C7C2×H(5,𝔽2)11yescharacteristic
570C4×C7—24no—
571C4×C7—24no—
572C4×C7—24no—
573C4×C7—42no—
574Dic7—24no—
575Dic7—24no—
576Dic7—24no—
577Dic7—42no—
578Dic7—42no—
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582C24—22no—
583C24—22no—
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—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24#115914yes—
603C24C23×D712yes—
604C24C23×D712yes—
605C24C23×D712yes—
606C24C23×D711yescharacteristic
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—416no—
617C2×D4—416no—
618C2×D4—416no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—74no—
629C22×C4—74no—
630C22×C4—74no—
631C22×C4—72no—
632C22×C4—72no—
633C22×C4—72no—
634C22×C4—72no—
635C22×C4—72no—
636C22×C4—72no—
637C22×C4—72no—
638C22×C4—72no—
639C22×C4—148no—
640C22×C4—142no—
641C22×C4—142no—
642C22×C4—142no—
643C22×C4—142no—
644C22×C4—142no—
645C22×C4—142no—
646C22×C4—142no—
647C22×C4—142no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—148no—
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—284no—
663C22×C4—2816no—
664C22×C4D4×D714yes—
665C22×C4#115914yes—
666C22×C4#115914yes—
667C22×C4C23×D712yes—
668C22×C4C23×D712yes—
669C22×C4C23×D712yes—
670C22×C4C23×D712yes—
671C4⋊C4—716no—
672C4⋊C4—148no—
673C4⋊C4—148no—
674C4⋊C4—148no—
675C4⋊C4—148no—
676C4⋊C4—284no—
677C4⋊C4—284no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—148no—
682C22⋊C4—148no—
683C22⋊C4—148no—
684C22⋊C4—148no—
685C22⋊C4—148no—
686C22⋊C4—148no—
687C22⋊C4—148no—
688C22⋊C4—148no—
689C22⋊C4—284no—
690C22⋊C4—284no—
691C22⋊C4—284no—
692C42—148no—
693C42—148no—
694C42—284no—
695C42—284no—
696C2×C7—44no—
697C2×C7—82no—
698C2×C7—82no—
699C2×C7#255418yescomplemented
700C2×C7C2×#52911yescharacteristic
701C2×C7C2×#53211yescharacteristic
702C2×C7C2×#53811yescharacteristic
703C2×C7C2×#54611yescharacteristic
704C2×C7C2×#55011yescharacteristic
705C2×C7C2×#55111yescharacteristic
706C2×C7C2×#55311yescharacteristic
707C23—28no—
708C23—28no—
709C23—28no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
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—22no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23C2×D4×D712yes—
749C23C2×#115914yes—
750C23C2×#115912yes—
751C23C2×#115912yes—
752C23C2×#115912yes—
753C23#654812yes—
754C23#654812yes—
755C23D7×#4112yes—
756C23C24×D711yescharacteristic
757D4—416no—
758D4—416no—
759D4—416no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—44no—
773C2×C4—74no—
774C2×C4—74no—
775C2×C4—74no—
776C2×C4—148no—
777C2×C4—148no—
778C2×C4—148no—
779C2×C4—142no—
780C2×C4—142no—
781C2×C4—142no—
782C2×C4—142no—
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—2816no—
801C2×C4—284no—
802C2×C4—284no—
803C2×C4—284no—
804C2×C4—284no—
805C2×C4—284no—
806C2×C4C2×D4×D714yes—
807C2×C4C2×#115914yes—
808C2×C4C2×#115914yes—
809C7C2×#255411yescharacteristic, complemented, Sylow
810C22—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—416no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—88no—
833C22—88no—
834C22#9027814yes—
835C22#9028214yes—
836C22#9028414yes—
837C22#9029014yes—
838C22#9029114yes—
839C22#9030514yes—
840C22#9040714yes—
841C22C22×D4×D711yescharacteristic
842C22C22×#115911yescharacteristic
843C22C22×#115911yescharacteristic
844C22C22×#115911yescharacteristic
845C22C2×#654811yescharacteristic
846C22C2×#654811yescharacteristic
847C22C2×D7×#4111yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—144no—
853C4—144no—
854C4—144no—
855C4—282no—
856C4—282no—
857C4—282no—
858C4—282no—
859C4—282no—
860C2—44no—
861C2—82no—
862C2—82no—
863C2#1173413418yesdirect product factor
864C2C2×#9028411yescharacteristic
865C2C2×#9027811yescharacteristic
866C2C2×#9028211yescharacteristic
867C2C2×#9029111yescharacteristic
868C2C2×#9029011yescharacteristic
869C2C2×#9030511yescharacteristic
870C2C2×#9040711yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC2×C7×#392C2
socleC24×C7C24
hypercenterC2×#392D7
hypocenterC7C2×#2554
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#6498C2semidirect
2. C22×#6442C2semidirect
4. C2×#89994C2semidirect
5. C2×#89993C2semidirect
6. C2×#89993C2semidirect
7. C2×#89993C2semidirect
8. C2×#89992C2semidirect
9. C2×#89720C2semidirect
10. C2×#89717C2semidirect
11. C2×#89716C2semidirect
12. C2×#89723C2semidirect
13. C2×C22⋊C4×Dic7C2semidirect
14. #11734134C2direct (N × H)
15. C2×#89433C2semidirect
16. C2×#89421C2semidirect
36. C2×#6498C22semidirect
49. C2×#6442C22semidirect
52. #89994C22semidirect
53. #89993C22semidirect
54. #89993C22semidirect
55. #89993C22semidirect
56. #89992C22semidirect
62. #89723C22semidirect
63. #89720C22semidirect
64. #89717C22semidirect
65. #89716C22semidirect
66. C22⋊C4×Dic7C22semidirect
67. #89433C22semidirect
68. #89421C22semidirect
139. C2×Dic7⋊C4D4semidirect
284. Dic7⋊C4C2×D4semidirect
699. C2×C7#2554semidirect
809. C7C2×#2554semidirect
863. C2#11734134direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64982
C22×#64422
C2×C7×#3922
C2×#899942
C2×#899932
C2×#899922
C2×#897202
C2×#897172
C2×#897162
C2×#897232
C2×C22⋊C4×Dic72
#117341342
C2×#894332
C2×#894212
C2×#25547