Finite Group Databasebeta

← C2×#11732200 #13523875

Subgroups — C2×#11732200 #13523875

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×#6492C211yesmaximal, characteristic, complemented
2C22×#6442C211yesmaximal, characteristic, complemented
3C2×C7×#386C211yesmaximal, characteristic, complemented
4C2×#89995C211yesmaximal, characteristic
5C2×#89993C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
7C2×#89731C211yesmaximal, characteristic, complemented
8C2×#89720C211yesmaximal, characteristic, complemented
9C2×#89729C211yesmaximal, characteristic, complemented
10C2×#89729C211yesmaximal, characteristic, complemented
11C2×#89716C211yesmaximal, characteristic, complemented
12#11732200C2116yesmaximal, direct product factor
13C2×#89429C211yesmaximal, characteristic, complemented
14C2×#89442C211yesmaximal, characteristic, complemented
15C2×#89442C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
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
30C2×#6492—28no—
31C2×#6492C2218yescomplemented
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
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×#386C2218yescomplemented
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53#89995C2218yes—
54#89993C2218yescomplemented
55C4×C22⋊Dic7C2218yescomplemented
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60#89731C2218yescomplemented
61#89729C2218yescomplemented
62#89729C2218yescomplemented
63#89720C2218yescomplemented
64#89716C2218yescomplemented
65#89442C2218yescomplemented
66#89442C2218yescomplemented
67#89429C2218yescomplemented
68#89421C2218yescomplemented
69C2×#2554—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—42no—
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
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—42no—
103C2×C7×C22⋊C4—42no—
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⋊Dic7C2314yes—
114C2×C22⋊Dic7C2314yes—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119#6492—232no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—24no—
123C2×(C2×D7)⋊C4—24no—
124C2×(C2×D7)⋊C4—42no—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×C4⋊Dic7—24no—
131C2×C4⋊Dic7—42no—
132C2×C4⋊Dic7C2314yes—
133C2×C4⋊Dic7C2314yes—
134C2×Dic7⋊C4—24no—
135C2×Dic7⋊C4—24no—
136C2×Dic7⋊C4—24no—
137C2×Dic7⋊C4—42no—
138C2×Dic7⋊C4D418yescomplemented
139C2×Dic7⋊C4C2314yes—
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×#392—71no—
166C2×#390—71no—
167C2×#390—71no—
168C2×#390—71no—
169C2×#388—71no—
170C2×#388—71no—
171C2×#388—71no—
172C2×#386D711yescharacteristic, complemented
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#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—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—44no—
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×Dic7C2×D414yes—
254C22×Dic7C2×D414yes—
255C22×Dic7#4114yes—
256C22×Dic7#4114yes—
257C22×Dic7C2412yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C7×C22⋊C4—28no—
265C7×C22⋊C4—44no—
266C7×C22⋊C4—44no—
267C22⋊Dic7—28no—
268C22⋊Dic7—28no—
269C22⋊Dic7—28no—
270C22⋊Dic7—28no—
271C22⋊Dic7—28no—
272C22⋊Dic7—28no—
273(C2×D7)⋊C4—28no—
274(C2×D7)⋊C4—28no—
275(C2×D7)⋊C4—28no—
276(C2×D7)⋊C4—28no—
277(C2×D7)⋊C4—44no—
278C4⋊Dic7—28no—
279C4⋊Dic7—44no—
280Dic7⋊C4—28no—
281Dic7⋊C4—28no—
282Dic7⋊C4—28no—
283Dic7⋊C4—44no—
284Dic7⋊C4C2×D4116yescomplemented
285C4×Dic7—28no—
286C4×Dic7—28no—
287C4×Dic7—44no—
288C4×Dic7—44no—
289C23×D4—71no—
290C23×D4—71no—
291C23×D4C2×D711yescharacteristic
292C24×C4C2×D711yescharacteristic
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#392—78no—
326#390—78no—
327#390—78no—
328#390—78no—
329#388—78no—
330#388—78no—
331#388—78no—
332#386C2×D718yescomplemented
333C4×C4⋊C4—78no—
334C4×C22⋊C4—78no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95C2×D711yescharacteristic
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—44no—
358C23×C7—44no—
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×C7C22×D412yes—
369C23×C7C2×#4112yes—
370C23×C7C2×#4114yes—
371C23×C7C2×#4112yes—
372C23×C7C2×#4112yes—
373C23×C7C2×#4112yes—
374C23×C7H(5,𝔽2)12yes—
375C23×C7H(5,𝔽2)12yes—
376C23×C7C2511yescharacteristic
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—44no—
385C22×D7—44no—
386C22×D7—44no—
387C22×D7—44no—
388C22×D7—44no—
389C22×D7—44no—
390C22×D7—44no—
391C7×D4—416no—
392C2×C4×C7—28no—
393C2×C4×C7—28no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
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—416no—
408C2×C4×C7—44no—
409C2×C4×C7—44no—
410C2×C4×C7—44no—
411C2×C4×C7C22×D414yes—
412C2×C4×C7C2×#4114yes—
413C22⋊D7—416no—
414C22⋊D7—416no—
415C2×Dic7—28no—
416C2×Dic7—28no—
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—44no—
437C2×Dic7—44no—
438C2×Dic7—44no—
439C2×Dic7C22×D414yes—
440C2×Dic7C22×D414yes—
441C2×Dic7C2×#4114yes—
442C2×Dic7C2×#4114yes—
443C25—71no—
444C25C22×D711yescharacteristic
445C25C22×D711yescharacteristic
446C22×D4—24no—
447C22×D4—24no—
448C22×D4—42no—
449C22×D4—74no—
450C22×D4—74no—
451C22×D4—144no—
452C22×D4—144no—
453C22×D4—144no—
454C22×D4—282no—
455C22×D4—282no—
456C22×D4—282no—
457C22×D4C22×D714yes—
458C23×C4—24no—
459C23×C4—24no—
460C23×C4—42no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—71no—
468C23×C4C22×D711yescharacteristic
469C23×C4C22×D711yescharacteristic
470C23×C4C22×D711yescharacteristic
471C23×C4C22×D714yes—
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—42no—
492C2×C22⋊C4—42no—
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—144no—
513C2×C22⋊C4—144no—
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#95C22×D714yes—
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—88no—
548C22×C7#52914yes—
549C22×C7#53214yes—
550C22×C7#53814yes—
551C22×C7#54614yes—
552C22×C7#55014yes—
553C22×C7#55114yes—
554C22×C7#55314yes—
555C22×C7C23×D411yescharacteristic
556C22×C7C22×#4111yescharacteristic
557C22×C7C22×#4111yescharacteristic
558C22×C7C22×#4111yescharacteristic
559C22×C7C22×#4111yescharacteristic
560C22×C7C2×H(5,𝔽2)11yescharacteristic
561C22×C7C2×H(5,𝔽2)11yescharacteristic
562C2×D7—42no—
563C2×D7—42no—
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—42no—
569C2×D7—88no—
570C4×C7—24no—
571C4×C7—24no—
572C4×C7—42no—
573C4×C7—42no—
574C4×C7—42no—
575Dic7—24no—
576Dic7—24no—
577Dic7—24no—
578Dic7—24no—
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—72no—
596C24—142no—
597C24—142no—
598C24—142no—
599C24—142no—
600C24—142no—
601C24—142no—
602C24—142no—
603C24#115914yes—
604C24C23×D712yes—
605C24C23×D712yes—
606C24C23×D711yescharacteristic
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—44no—
610C2×D4—416no—
611C2×D4—148no—
612C2×D4—148no—
613C2×D4—148no—
614C2×D4—284no—
615C2×D4—284no—
616C2×D4—284no—
617C2×D4—2816no—
618C2×D4—2816no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—28no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—28no—
634C22×C4—44no—
635C22×C4—416no—
636C22×C4—74no—
637C22×C4—74no—
638C22×C4—74no—
639C22×C4—74no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—72no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—142no—
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#115714yes—
665C22×C4D4×D714yes—
666C22×C4C23×D712yes—
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—44no—
680C22⋊C4—44no—
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—148no—
690C22⋊C4—148no—
691C22⋊C4—284no—
692C42—148no—
693C42—148no—
694C42—284no—
695C42—284no—
696C2×C7—44no—
697C2×C7—82no—
698C2×C7#255418yescomplemented
699C2×C7C2×#52911yescharacteristic
700C2×C7C2×#53211yescharacteristic
701C2×C7C2×#53811yescharacteristic
702C2×C7C2×#54611yescharacteristic
703C2×C7C2×#55011yescharacteristic
704C2×C7C2×#55111yescharacteristic
705C2×C7C2×#55311yescharacteristic
706D7—82no—
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—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—142no—
735C23—142no—
736C23—142no—
737C23—142no—
738C23—142no—
739C23—142no—
740C23—142no—
741C23—284no—
742C23—284no—
743C23—284no—
744C23—284no—
745C23—284no—
746C23—284no—
747C23—284no—
748C23C2×#115712yes—
749C23C2×D4×D712yes—
750C23C2×#115914yes—
751C23C2×#115912yes—
752C23#654812yes—
753C23#654812yes—
754C23D7×#4112yes—
755C23D7×#4112yes—
756C23C24×D711yescharacteristic
757D4—416no—
758D4—2816no—
759D4—2816no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—22no—
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—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—416no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—74no—
780C2×C4—74no—
781C2×C4—74no—
782C2×C4—74no—
783C2×C4—148no—
784C2×C4—148no—
785C2×C4—148no—
786C2×C4—148no—
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—142no—
804C2×C4—284no—
805C2×C4—284no—
806C2×C4—284no—
807C2×C4C2×#115714yes—
808C2×C4C2×D4×D714yes—
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—88no—
826C22—282no—
827C22—282no—
828C22—282no—
829C22—282no—
830C22—282no—
831C22—282no—
832C22—282no—
833C22—568no—
834C22#9018614yes—
835C22#9023914yes—
836C22#9024914yes—
837C22#9028214yes—
838C22#9029014yes—
839C22#9030414yes—
840C22#9034014yes—
841C22C22×#115711yescharacteristic
842C22C22×D4×D711yescharacteristic
843C22C22×#115911yescharacteristic
844C22C2×#654811yescharacteristic
845C22C2×#654811yescharacteristic
846C22C2×D7×#4111yescharacteristic
847C22C2×D7×#4111yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—144no—
854C4—144no—
855C4—144no—
856C4—144no—
857C4—282no—
858C4—282no—
859C4—282no—
860C2—44no—
861C2—82no—
862C2—562no—
863C2#1173220018yesdirect product factor
864C2C2×#9018611yescharacteristic
865C2C2×#9023911yescharacteristic
866C2C2×#9024911yescharacteristic
867C2C2×#9028211yescharacteristic
868C2C2×#9029011yescharacteristic
869C2C2×#9030411yescharacteristic
870C2C2×#9034011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#386D7
hypocenterC7C2×#2554
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×#6442C2semidirect
3. C2×C7×#386C2semidirect
5. C2×#89993C2semidirect
6. C2×C4×C22⋊Dic7C2semidirect
7. C2×#89731C2semidirect
8. C2×#89720C2semidirect
9. C2×#89729C2semidirect
10. C2×#89729C2semidirect
11. C2×#89716C2semidirect
12. #11732200C2direct (N × H)
13. C2×#89429C2semidirect
14. C2×#89442C2semidirect
15. C2×#89442C2semidirect
16. C2×#89421C2semidirect
31. C2×#6492C22semidirect
49. C2×#6442C22semidirect
50. C7×#386C22semidirect
54. #89993C22semidirect
55. C4×C22⋊Dic7C22semidirect
60. #89731C22semidirect
61. #89729C22semidirect
62. #89729C22semidirect
63. #89720C22semidirect
64. #89716C22semidirect
65. #89442C22semidirect
66. #89442C22semidirect
67. #89429C22semidirect
68. #89421C22semidirect
138. C2×Dic7⋊C4D4semidirect
172. C2×#386D7semidirect
284. Dic7⋊C4C2×D4semidirect
332. #386C2×D7semidirect
698. C2×C7#2554semidirect
809. C7C2×#2554semidirect
863. C2#11732200direct (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×#64422
C2×C7×#3862
C2×#899952
C2×#899932
C2×C4×C22⋊Dic72
C2×#897312
C2×#897202
C2×#897292
C2×#897162
#117322002
C2×#894292
C2×#894422
C2×#894212
C2×#25547